%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU817^1 : 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.snVJUShJb4 true
% Computer : n023.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 04:56:36 PM UTC 2025
% Result : Theorem 101.43s 16.98s
% Output : Refutation 103.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU817^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.snVJUShJb4 true
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Oct 1 16:13:08 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % Running portfolio for 300 s
% 0.13/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in HO mode
% 0.54/0.68 % Total configuration time : 828
% 0.54/0.68 % Estimated wc time : 1656
% 0.54/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.56/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.78 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.56/0.82 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.56/0.87 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.57/1.10 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 101.43/16.98 % Solved by lams/30_b.l.sh.
% 101.43/16.98 % done 326 iterations in 15.239s
% 101.43/16.98 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 101.43/16.98 % SZS output start Refutation
% 101.43/16.98 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 101.43/16.98 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 101.43/16.98 thf(notdexE_type, type, notdexE: $o).
% 101.43/16.98 thf(setunionAx_type, type, setunionAx: $o).
% 101.43/16.98 thf(setminusELneg_type, type, setminusELneg: $o).
% 101.43/16.98 thf(breln1unionEcases_type, type, breln1unionEcases: $o).
% 101.43/16.98 thf('#sk16_type', type, '#sk16': $i > $i).
% 101.43/16.98 thf(omegaSp_type, type, omegaSp: $o).
% 101.43/16.98 thf(powersetE_type, type, powersetE: $o).
% 101.43/16.98 thf(woz1_1_type, type, woz1_1: $o).
% 101.43/16.98 thf(omegaSAx_type, type, omegaSAx: $o).
% 101.43/16.98 thf(breln1unionI_type, type, breln1unionI: $o).
% 101.43/16.98 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 101.43/16.98 $o).
% 101.43/16.98 thf(surjCantorThm_type, type, surjCantorThm: $o).
% 101.43/16.98 thf(exuI1_type, type, exuI1: $o).
% 101.43/16.98 thf(exuI2_type, type, exuI2: $o).
% 101.43/16.98 thf(notequalI2_type, type, notequalI2: $o).
% 101.43/16.98 thf('#form172_type', type, '#form172': $i > $i > $o).
% 101.76/16.98 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 101.76/16.98 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 101.76/16.98 thf(upairsubunion_type, type, upairsubunion: $o).
% 101.76/16.98 thf(binunionTE_type, type, binunionTE: $o).
% 101.76/16.98 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 101.76/16.98 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 101.76/16.98 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 101.76/16.98 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 101.76/16.98 thf(setminusILneg_type, type, setminusILneg: $o).
% 101.76/16.98 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 101.76/16.98 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 101.76/16.98 thf(funcextLem_type, type, funcextLem: $o).
% 101.76/16.98 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 101.76/16.98 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 101.76/16.98 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 101.76/16.98 thf('#sk111_type', type, '#sk111': $i > $i > $i).
% 101.76/16.98 thf(eta1_type, type, eta1: $o).
% 101.76/16.98 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 101.76/16.98 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 101.76/16.98 thf(notinself_type, type, notinself: $o).
% 101.76/16.98 thf(apProp_type, type, apProp: $o).
% 101.76/16.98 thf(setextT_type, type, setextT: $o).
% 101.76/16.98 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 101.76/16.98 $o).
% 101.76/16.98 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 101.76/16.98 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 101.76/16.98 thf(breln1invprop_type, type, breln1invprop: $o).
% 101.76/16.98 thf(lamProp_type, type, lamProp: $o).
% 101.76/16.98 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 101.76/16.98 thf(setunionTransitive_type, type, setunionTransitive: $o).
% 101.76/16.98 thf(ex1E1_type, type, ex1E1: $o).
% 101.76/16.98 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 101.76/16.98 thf(setukpairIR_type, type, setukpairIR: $o).
% 101.76/16.98 thf(brelnall1_type, type, brelnall1: $o).
% 101.76/16.98 thf(binunionE_type, type, binunionE: $o).
% 101.76/16.98 thf(setext_type, type, setext: $o).
% 101.76/16.98 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 101.76/16.98 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 101.76/16.98 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 101.76/16.98 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 101.76/16.98 thf(iftrue_type, type, iftrue: $o).
% 101.76/16.98 thf(woz13rule4_type, type, woz13rule4: $o).
% 101.76/16.98 thf(descr__Cong_type, type, descr__Cong: $o).
% 101.76/16.98 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 101.76/16.98 thf(theprop_type, type, theprop: $o).
% 101.76/16.98 thf(image1I_type, type, image1I: $o).
% 101.76/16.98 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 101.76/16.98 thf(in_type, type, in: $i > $i > $o).
% 101.76/16.98 thf('#sk1597_type', type, '#sk1597': $i).
% 101.76/16.98 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 101.76/16.98 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 101.76/16.98 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 101.76/16.98 thf(demorgan1_type, type, demorgan1: $o).
% 101.76/16.98 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 101.76/16.98 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 101.76/16.98 $o).
% 101.76/16.98 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 101.76/16.98 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o).
% 101.76/16.98 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 101.76/16.98 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 101.76/16.98 thf(ex1I2_type, type, ex1I2: $o).
% 101.76/16.98 thf(foundation2_type, type, foundation2: $o).
% 101.76/16.98 thf(symdiffI2_type, type, symdiffI2: $o).
% 101.76/16.98 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 101.76/16.98 thf(ifSingleton_type, type, ifSingleton: $o).
% 101.76/16.98 thf(upairset2IR_type, type, upairset2IR: $o).
% 101.76/16.98 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 101.76/16.98 thf(complementTI1_type, type, complementTI1: $o).
% 101.76/16.98 thf(subsetE_type, type, subsetE: $o).
% 101.76/16.98 thf(wellorderedByIn_type, type, wellorderedByIn: $i > $o).
% 101.76/16.98 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 101.76/16.98 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 101.76/16.98 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 101.76/16.98 $o).
% 101.76/16.98 thf(iffalse_type, type, iffalse: $o).
% 101.76/16.98 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 101.76/16.98 thf(setbeta_type, type, setbeta: $o).
% 101.76/16.98 thf(eqinunit_type, type, eqinunit: $o).
% 101.76/16.98 thf(upairsetIL_type, type, upairsetIL: $o).
% 101.76/16.98 thf(powersetI1_type, type, powersetI1: $o).
% 101.76/16.98 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 101.76/16.98 thf(lamp_type, type, lamp: $o).
% 101.76/16.98 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 101.76/16.98 thf(breln1invI_type, type, breln1invI: $o).
% 101.76/16.98 thf('#sk337_type', type, '#sk337': $i > ($i > $o) > $i).
% 101.76/16.98 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 101.76/16.98 thf(breln1unionE_type, type, breln1unionE: $o).
% 101.76/16.98 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 101.76/16.98 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 101.76/16.98 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 101.76/16.98 thf(powersetAx_type, type, powersetAx: $o).
% 101.76/16.98 thf(woz2Ex_type, type, woz2Ex: $o).
% 101.76/16.98 thf(eta2_type, type, eta2: $o).
% 101.76/16.98 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 101.76/16.98 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 101.76/16.98 thf(image1Ex_type, type, image1Ex: $o).
% 101.76/16.98 thf(powersetI_type, type, powersetI: $o).
% 101.76/16.98 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 101.76/16.98 thf(powersetTE1_type, type, powersetTE1: $o).
% 101.76/16.98 thf(upairsetIR_type, type, upairsetIR: $o).
% 101.76/16.98 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 101.76/16.98 thf(lam2p_type, type, lam2p: $o).
% 101.76/16.98 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 101.76/16.98 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 101.76/16.98 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 101.76/16.98 thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o).
% 101.76/16.98 thf(inCongP_type, type, inCongP: $o).
% 101.76/16.98 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 101.76/16.98 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 101.76/16.98 thf(exuE3e_type, type, exuE3e: $o).
% 101.76/16.98 thf(emptysetE_type, type, emptysetE: $o).
% 101.76/16.98 thf(woz13rule2_type, type, woz13rule2: $o).
% 101.76/16.98 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 101.76/16.98 thf(peano0notS_type, type, peano0notS: $o).
% 101.76/16.98 thf(image1E_type, type, image1E: $o).
% 101.76/16.98 thf(setunionI_type, type, setunionI: $o).
% 101.76/16.98 thf(breln1unionIR_type, type, breln1unionIR: $o).
% 101.76/16.98 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 101.76/16.98 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 101.76/16.98 thf(injFuncSetFuncInj_type, type, injFuncSetFuncInj: $o).
% 101.76/16.98 thf(prop2setI_type, type, prop2setI: $o).
% 101.76/16.98 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 101.76/16.98 thf(setminusER_type, type, setminusER: $o).
% 101.76/16.98 thf(peanoSinj_type, type, peanoSinj: $o).
% 101.76/16.98 thf(exuE2_type, type, exuE2: $o).
% 101.76/16.98 thf(woz1_2_type, type, woz1_2: $o).
% 101.76/16.98 thf(emptyset_type, type, emptyset: $i).
% 101.76/16.98 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 101.76/16.98 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 101.76/16.98 thf(setminus_type, type, setminus: $i > $i > $i).
% 101.76/16.98 thf(powersetsubset_type, type, powersetsubset: $o).
% 101.76/16.98 thf(upairequniteq_type, type, upairequniteq: $o).
% 101.76/16.98 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 101.76/16.98 thf(ordinal_type, type, ordinal: $i > $o).
% 101.76/16.98 thf(injFuncInInjFuncSet_type, type, injFuncInInjFuncSet: $o).
% 101.76/16.98 thf(subPowSU_type, type, subPowSU: $o).
% 101.76/16.98 thf('#form1598_type', type, '#form1598': $i > $o).
% 101.76/16.98 thf(breln1compprop_type, type, breln1compprop: $o).
% 101.76/16.98 thf(woz2B_type, type, woz2B: $o).
% 101.76/16.98 thf(notequalI1_type, type, notequalI1: $o).
% 101.76/16.98 thf(demorgan2b_type, type, demorgan2b: $o).
% 101.76/16.98 thf(notinemptyset_type, type, notinemptyset: $o).
% 101.76/16.98 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 101.76/16.98 thf(breln1unionIL_type, type, breln1unionIL: $o).
% 101.76/16.98 thf(subsetTrans_type, type, subsetTrans: $o).
% 101.76/16.98 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 101.76/16.98 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 101.76/16.98 thf(kpairp_type, type, kpairp: $o).
% 101.76/16.98 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 101.76/16.98 thf(setminusI_type, type, setminusI: $o).
% 101.76/16.98 thf(notinself2_type, type, notinself2: $o).
% 101.76/16.98 thf(binunionIL_type, type, binunionIL: $o).
% 101.76/16.98 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 101.76/16.98 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 101.76/16.98 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 101.76/16.98 thf(powersetTI1_type, type, powersetTI1: $o).
% 101.76/16.98 thf(subsetE2_type, type, subsetE2: $o).
% 101.76/16.98 thf(image1Ex1_type, type, image1Ex1: $o).
% 101.76/16.98 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 101.76/16.98 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 101.76/16.98 thf(setextsub_type, type, setextsub: $o).
% 101.76/16.98 thf(binunionLsub_type, type, binunionLsub: $o).
% 101.76/16.98 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 101.76/16.98 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 101.76/16.98 thf(breln1compE_type, type, breln1compE: $o).
% 101.76/16.98 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 101.76/16.98 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 101.76/16.98 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 101.76/16.98 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 101.76/16.98 thf(setunionE_type, type, setunionE: $o).
% 101.76/16.98 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 101.76/16.98 thf(complementT_lem_type, type, complementT_lem: $o).
% 101.76/16.98 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 101.76/16.98 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 101.76/16.98 thf(binunionIR_type, type, binunionIR: $o).
% 101.76/16.98 thf(injFuncSetFuncIn_type, type, injFuncSetFuncIn: $o).
% 101.76/16.98 thf(setadjoinE_type, type, setadjoinE: $o).
% 101.76/16.98 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 101.76/16.98 thf(eqbreln1_type, type, eqbreln1: $o).
% 101.76/16.98 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 101.76/16.98 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 101.76/16.98 thf(leftInvIsSurj_type, type, leftInvIsSurj: $o).
% 101.76/16.98 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 101.76/16.98 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 101.76/16.98 thf(exuE1_type, type, exuE1: $o).
% 101.76/16.98 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 101.76/16.98 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 101.76/16.98 thf(setminusLsub_type, type, setminusLsub: $o).
% 101.76/16.98 thf(notinsingleton_type, type, notinsingleton: $o).
% 101.76/16.98 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 101.76/16.98 $o).
% 101.76/16.98 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 101.76/16.98 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 101.76/16.98 thf(exuEu_type, type, exuEu: $o).
% 101.76/16.98 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 101.76/16.98 thf(upairsetE_type, type, upairsetE: $o).
% 101.76/16.98 thf(omega0Ax_type, type, omega0Ax: $o).
% 101.76/16.98 thf(breln1invE_type, type, breln1invE: $o).
% 101.76/16.98 thf(breln1unionCommutes_type, type, breln1unionCommutes: $o).
% 101.76/16.98 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 101.76/16.98 thf(app_type, type, app: $o).
% 101.76/16.98 thf(transitiveset_type, type, transitiveset: $i > $o).
% 101.76/16.98 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 101.76/16.98 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 101.76/16.98 thf(notsubsetI_type, type, notsubsetI: $o).
% 101.76/16.98 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 101.76/16.98 thf(binintTransitive_type, type, binintTransitive: $o).
% 101.76/16.98 thf(woz2W_type, type, woz2W: $o).
% 101.76/16.98 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 101.76/16.98 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 101.76/16.98 thf(setextAx_type, type, setextAx: $o).
% 101.76/16.98 thf(breln1all1_type, type, breln1all1: $o).
% 101.76/16.98 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o).
% 101.76/16.98 thf(breln1compI_type, type, breln1compI: $o).
% 101.76/16.98 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 101.76/16.98 thf(powersetE1_type, type, powersetE1: $o).
% 101.76/16.98 thf(bs114d_type, type, bs114d: $o).
% 101.76/16.98 thf(complementTE1_type, type, complementTE1: $o).
% 101.76/16.98 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 101.76/16.98 thf(breln1all2_type, type, breln1all2: $o).
% 101.76/16.98 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 101.76/16.98 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 101.76/16.98 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 101.76/16.98 thf('#sk134_type', type, '#sk134': $i > $i > $i).
% 101.76/16.98 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 101.76/16.98 thf(subsetI1_type, type, subsetI1: $o).
% 101.76/16.98 thf(symdiffE_type, type, symdiffE: $o).
% 101.76/16.98 thf(woz13rule1_type, type, woz13rule1: $o).
% 101.76/16.98 thf(breln1unionprop_type, type, breln1unionprop: $o).
% 101.76/16.98 thf(descrp_type, type, descrp: $o).
% 101.76/16.98 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 101.76/16.98 thf(foundationAx_type, type, foundationAx: $o).
% 101.76/16.98 thf(brelnall2_type, type, brelnall2: $o).
% 101.76/16.98 thf(emptysetAx_type, type, emptysetAx: $o).
% 101.76/16.98 thf(emptyI_type, type, emptyI: $o).
% 101.76/16.98 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 101.76/16.98 thf(binintersectEL_type, type, binintersectEL: $o).
% 101.76/16.98 thf(emptyE1_type, type, emptyE1: $o).
% 101.76/16.98 thf(demorgan2a_type, type, demorgan2a: $o).
% 101.76/16.98 thf(woz1_3_type, type, woz1_3: $o).
% 101.76/16.98 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 101.76/16.98 thf(vacuousDall_type, type, vacuousDall: $o).
% 101.76/16.98 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 101.76/16.98 thf(demorgan1a_type, type, demorgan1a: $o).
% 101.76/16.98 thf(ifp_type, type, ifp: $o).
% 101.76/16.98 thf(binintersectI_type, type, binintersectI: $o).
% 101.76/16.98 thf(beta1_type, type, beta1: $o).
% 101.76/16.98 thf(funcext2_type, type, funcext2: $o).
% 101.76/16.98 thf(subbreln_type, type, subbreln: $o).
% 101.76/16.98 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 101.76/16.98 thf(ordinalMinLem1_type, type, ordinalMinLem1: $o).
% 101.76/16.98 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 101.76/16.98 thf(subbreln1_type, type, subbreln1: $o).
% 101.76/16.98 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 101.76/16.98 thf(image1Equiv_type, type, image1Equiv: $o).
% 101.76/16.98 thf(subsetTI_type, type, subsetTI: $o).
% 101.76/16.98 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 101.76/16.98 thf(ap2p_type, type, ap2p: $o).
% 101.76/16.98 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 101.76/16.98 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 101.76/16.98 thf(symdiffI1_type, type, symdiffI1: $o).
% 101.76/16.98 thf(woz1_4_type, type, woz1_4: $o).
% 101.76/16.98 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 101.76/16.98 thf(subsetI2_type, type, subsetI2: $o).
% 101.76/16.98 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 101.76/16.98 thf('#sk1599_type', type, '#sk1599': $i).
% 101.76/16.98 thf(theeq_type, type, theeq: $o).
% 101.76/16.98 thf(setminusERneg_type, type, setminusERneg: $o).
% 101.76/16.98 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 101.76/16.98 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 101.76/16.98 thf(omega__Cong_type, type, omega__Cong: $o).
% 101.76/16.98 thf(demorgan1b_type, type, demorgan1b: $o).
% 101.76/16.98 thf(subsetRefl_type, type, subsetRefl: $o).
% 101.76/16.98 thf(uniqinunit_type, type, uniqinunit: $o).
% 101.76/16.98 thf(eqbreln_type, type, eqbreln: $o).
% 101.76/16.98 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 101.76/16.98 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 101.76/16.98 thf(breln1compEex_type, type, breln1compEex: $o).
% 101.76/16.98 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 101.76/16.98 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 101.76/16.98 thf(prop2setE_type, type, prop2setE: $o).
% 101.76/16.98 thf(omegaSclos_type, type, omegaSclos: $o).
% 101.76/16.98 thf(binunionEcases_type, type, binunionEcases: $o).
% 101.76/16.98 thf(omega_type, type, omega: $i).
% 101.76/16.98 thf('#sk1600_type', type, '#sk1600': $i).
% 101.76/16.98 thf(nonemptyI_type, type, nonemptyI: $o).
% 101.76/16.98 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 101.76/16.98 thf(woz2A_type, type, woz2A: $o).
% 101.76/16.98 thf(transitivesetOp1_type, type, transitivesetOp1: $o).
% 101.76/16.98 thf(exuE3u_type, type, exuE3u: $o).
% 101.76/16.98 thf(setminusEL_type, type, setminusEL: $o).
% 101.76/16.98 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 101.76/16.98 thf(woz1_5_type, type, woz1_5: $o).
% 101.76/16.98 thf(demorgan2_type, type, demorgan2: $o).
% 101.76/16.98 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 101.76/16.98 thf(sepSubset_type, type, sepSubset: $o).
% 101.76/16.98 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 101.76/16.98 $o).
% 101.76/16.98 thf(transitivesetOp2_type, type, transitivesetOp2: $o).
% 101.76/16.98 thf(funcext_type, type, funcext: $o).
% 101.76/16.98 thf(surjFuncSetFuncSurj_type, type, surjFuncSetFuncSurj: $o).
% 101.76/16.98 thf(upairset2E_type, type, upairset2E: $o).
% 101.76/16.98 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 101.76/16.98 thf(exuI3_type, type, exuI3: $o).
% 101.76/16.98 thf(notdallE_type, type, notdallE: $o).
% 101.76/16.98 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 101.76/16.98 thf(binintersectER_type, type, binintersectER: $o).
% 101.76/16.98 thf(powerset_type, type, powerset: $i > $i).
% 101.76/16.98 thf(woz13rule0_type, type, woz13rule0: $o).
% 101.76/16.98 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 101.76/16.98 thf(beta2_type, type, beta2: $o).
% 101.76/16.98 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 101.76/16.98 thf(exu__Cong_type, type, exu__Cong: $o).
% 101.76/16.98 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 101.76/16.98 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 101.76/16.98 thf(surjFuncSetFuncIn_type, type, surjFuncSetFuncIn: $o).
% 101.76/16.98 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 101.76/16.98 thf(ex1I_type, type, ex1I: $o).
% 101.76/16.98 thf(secondinupair_type, type, secondinupair: $o).
% 101.76/16.98 thf(singletonprop_type, type, singletonprop: $o).
% 101.76/16.98 thf(singletonsubset_type, type, singletonsubset: $o).
% 101.76/16.98 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 101.76/16.98 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 101.76/16.98 thf(ex1E2_type, type, ex1E2: $o).
% 101.76/16.98 thf(replAx_type, type, replAx: $o).
% 101.76/16.98 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 101.76/16.98 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 101.76/16.98 thf(setukpairIL_type, type, setukpairIL: $o).
% 101.76/16.98 thf(setunionE2_type, type, setunionE2: $o).
% 101.76/16.98 thf(inPowerset_type, type, inPowerset: $o).
% 101.76/16.98 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 101.76/16.98 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 101.76/16.98 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 101.76/16.98 thf(subset_type, type, subset: $i > $i > $o).
% 101.76/16.98 thf(woz13rule3_type, type, woz13rule3: $o).
% 101.76/16.98 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 101.76/16.98 $o).
% 101.76/16.98 thf(in__Cong_type, type, in__Cong: $o).
% 101.76/16.98 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 101.76/16.98 thf(binunionRsub_type, type, binunionRsub: $o).
% 101.76/16.98 thf(subset2powerset_type, type, subset2powerset: $o).
% 101.76/16.98 thf(ordinalTransSet, conjecture,
% 101.76/16.98 (( setextAx ) =>
% 101.76/16.98 ( ( emptysetAx ) =>
% 101.76/16.98 ( ( setadjoinAx ) =>
% 101.76/16.98 ( ( powersetAx ) =>
% 101.76/16.98 ( ( setunionAx ) =>
% 101.76/16.98 ( ( omega0Ax ) =>
% 101.76/16.98 ( ( omegaSAx ) =>
% 101.76/16.98 ( ( omegaIndAx ) =>
% 101.76/16.98 ( ( replAx ) =>
% 101.76/16.98 ( ( foundationAx ) =>
% 101.76/16.98 ( ( wellorderingAx ) =>
% 101.76/16.98 ( ( descrp ) =>
% 101.76/16.98 ( ( dsetconstrI ) =>
% 101.76/16.98 ( ( dsetconstrEL ) =>
% 101.76/16.98 ( ( dsetconstrER ) =>
% 101.76/16.98 ( ( exuE1 ) =>
% 101.76/16.98 ( ( prop2setE ) =>
% 101.76/16.98 ( ( emptysetE ) =>
% 101.76/16.98 ( ( emptysetimpfalse ) =>
% 101.76/16.98 ( ( notinemptyset ) =>
% 101.76/16.98 ( ( exuE3e ) =>
% 101.76/16.98 ( ( setext ) =>
% 101.76/16.98 ( ( emptyI ) =>
% 101.76/16.98 ( ( noeltsimpempty ) =>
% 101.76/16.98 ( ( setbeta ) =>
% 101.76/16.98 ( ( nonemptyE1 ) =>
% 101.76/16.98 ( ( nonemptyI ) =>
% 101.76/16.98 ( ( nonemptyI1 ) =>
% 101.76/16.98 ( ( setadjoinIL ) =>
% 101.76/16.98 ( ( emptyinunitempty ) =>
% 101.76/16.98 ( ( setadjoinIR ) =>
% 101.76/16.98 ( ( setadjoinE ) =>
% 101.76/16.98 ( (
% 101.76/16.98 setadjoinOr ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setoftrueEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powersetI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 emptyinPowerset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 emptyInPowerset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powersetE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunionI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunionE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subPowSU ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exuE2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 nonemptyImpWitness ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 uniqinunit ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notinsingleton ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 eqinunit ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 singletonsswitch ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairsetE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairsetIL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairsetIR ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 emptyE1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 vacuousDall ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 quantDeMorgan1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 quantDeMorgan2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 quantDeMorgan3 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 quantDeMorgan4 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 prop2setI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 prop2set2propI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notdexE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notdallE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exuI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exuI3 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exuI2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 inCongP ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 in__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exuE3u ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exu__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 emptyset__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setadjoin__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powerset__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunion__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 omega__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exuEu ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 descr__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dsetconstr__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 eqimpsubset2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 eqimpsubset1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetI2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 emptysetsubset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetE2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notsubsetI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notequalI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notequalI2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetRefl ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetTrans ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setadjoinSub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setadjoinSub2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subset2powerset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setextsub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetemptysetimpeq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powersetI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powersetE1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 inPowerset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powersetsubset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 sepInPowerset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 sepSubset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionIL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairset2IR ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionIR ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionEcases ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionLsub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionRsub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectSubset5 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectEL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectLsub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectSubset2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectSubset3 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectER ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 disjointsetsI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectRsub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectSubset4 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectSubset1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 bs114d ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusEL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusER ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusSubset2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusERneg ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusELneg ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusILneg ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusIRneg ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusLsub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusSubset1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 symdiffE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 symdiffI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 symdiffI2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 symdiffIneg1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 symdiffIneg2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 secondinupair ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairIL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairIR ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 kpairiskpair ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 kpairp ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 singletonsubset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 singletoninpowerset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 singletoninpowunion ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairset2E ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairsubunion ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairinpowunion ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ubforcartprodlem1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ubforcartprodlem2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ubforcartprodlem3 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodpairin ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodmempair1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodmempair ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunionE2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunionsingleton1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunionsingleton2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunionsingleton ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 singletonprop ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ex1E1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ex1I ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ex1I2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 singletonsuniq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjL1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 kfstsingleton ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 theprop ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 kfstpairEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodfstin ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjL2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjR11 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjR12 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjR1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairequniteq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjR2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjR ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ksndsingleton ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ksndpairEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 kpairsurjEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodsndin ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodpairmemEL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodpairmemER ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodmempaircEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodfstpairEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodsndpairEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodpairsurjEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dpsetconstrI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dpsetconstrSub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setOfPairsIsBReln ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dpsetconstrERa ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dpsetconstrEL1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dpsetconstrEL2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dpsetconstrER ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 funcImageSingleton ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 apProp ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 app ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 infuncsetfunc ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ap2p ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 funcinfuncset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 lamProp ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 lamp ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 lam2p ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 brelnall1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 brelnall2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ex1E2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 funcGraphProp1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 funcGraphProp3 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 funcGraphProp2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 funcextLem ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 funcGraphProp4 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subbreln ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 eqbreln ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 funcext ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 funcext2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ap2apEq1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ap2apEq2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 beta1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 eta1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 lam2lamEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 beta2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 eta2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 iffalseProp1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 iffalseProp2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 iftrueProp1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 iftrueProp2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ifSingleton ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ifp ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 theeq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 iftrue ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 iffalse ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 iftrueorfalse ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectT_lem ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionT_lem ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powersetT_lem ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusT_lem ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 complementT_lem ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setextT ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetTI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powersetTI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powersetTE1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 complementTI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 complementTE1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectTELcontra ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectTERcontra ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 contrasubsetT ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 contrasubsetT1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 contrasubsetT2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 contrasubsetT3 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 doubleComplementI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 doubleComplementE1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 doubleComplementSub1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 doubleComplementSub2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 doubleComplementEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 complementTnotintersectT ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 complementImpComplementIntersect ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 complementSubsetComplementIntersect ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 complementInPowersetComplementIntersect ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 contraSubsetComplement ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 complementTcontraSubset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionTILcontra ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionTIRcontra ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 inIntersectImpInUnion ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 inIntersectImpInUnion2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 inIntersectImpInIntersectUnions ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 intersectInPowersetIntersectUnions ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 inComplementUnionImpNotIn1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 inComplementUnionImpInComplement1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionTE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionTEcontra ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 demorgan2a1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 complementUnionInPowersetComplement ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 demorgan2a2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 demorgan1a ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 demorgan1b ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 demorgan1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 demorgan2a ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 demorgan2b2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 demorgan2b ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 demorgan2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz13rule0 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz13rule1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz13rule2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz13rule3 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz13rule4 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz1_1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz1_2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz1_3 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz1_4 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz1_5 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1all2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1SetBreln1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 choice2fnsingleton ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setOfPairsIsBReln1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1all1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subbreln1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 eqbreln1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1invprop ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1invI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1invE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1compprop ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1compI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1compE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1compEex ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1unionprop ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1unionIL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1unionIR ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1unionI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1unionE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1unionEcases ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 breln1unionCommutes ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz2Ex ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz2W ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz2A ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 woz2B ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 image1Ex ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 image1Ex1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 image1Equiv ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 image1E ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 image1I ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 injFuncInInjFuncSet ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 injFuncSetFuncIn ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 injFuncSetFuncInj ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 surjFuncSetFuncIn ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 surjFuncSetFuncSurj ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 leftInvIsSurj ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 surjCantorThm ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 foundation2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notinself ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notinself2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 omegaSp ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 omegaSclos ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 peano0notS ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 peanoSinj ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 transitivesetOp1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintTransitive ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 transitivesetOp2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunionTransitive ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ordinalMinLem1 ) =>
% 101.76/16.98 (
% 101.76/16.98 ![
% 101.76/16.98 X:$i]:
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ordinal @
% 101.76/16.98 X ) =>
% 101.76/16.98 (
% 101.76/16.98 ![
% 101.76/16.98 Xx:$i,A:$i]:
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 in @ A @ X ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 in @
% 101.76/16.98 Xx @ A ) =>
% 101.76/16.98 (
% 101.76/16.98 in @
% 101.76/16.98 Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 101.76/16.98 thf(zf_stmt_0, negated_conjecture,
% 101.76/16.98 (~( ( setextAx ) =>
% 101.76/16.98 ( ( emptysetAx ) =>
% 101.76/16.98 ( ( setadjoinAx ) =>
% 101.76/16.98 ( ( powersetAx ) =>
% 101.76/16.98 ( ( setunionAx ) =>
% 101.76/16.98 ( ( omega0Ax ) =>
% 101.76/16.98 ( ( omegaSAx ) =>
% 101.76/16.98 ( ( omegaIndAx ) =>
% 101.76/16.98 ( ( replAx ) =>
% 101.76/16.98 ( ( foundationAx ) =>
% 101.76/16.98 ( ( wellorderingAx ) =>
% 101.76/16.98 ( ( descrp ) =>
% 101.76/16.98 ( ( dsetconstrI ) =>
% 101.76/16.98 ( ( dsetconstrEL ) =>
% 101.76/16.98 ( ( dsetconstrER ) =>
% 101.76/16.98 ( ( exuE1 ) =>
% 101.76/16.98 ( ( prop2setE ) =>
% 101.76/16.98 ( ( emptysetE ) =>
% 101.76/16.98 ( ( emptysetimpfalse ) =>
% 101.76/16.98 ( ( notinemptyset ) =>
% 101.76/16.98 ( ( exuE3e ) =>
% 101.76/16.98 ( ( setext ) =>
% 101.76/16.98 ( ( emptyI ) =>
% 101.76/16.98 ( ( noeltsimpempty ) =>
% 101.76/16.98 ( ( setbeta ) =>
% 101.76/16.98 ( ( nonemptyE1 ) =>
% 101.76/16.98 ( ( nonemptyI ) =>
% 101.76/16.98 ( ( nonemptyI1 ) =>
% 101.76/16.98 ( ( setadjoinIL ) =>
% 101.76/16.98 ( ( emptyinunitempty ) =>
% 101.76/16.98 ( ( setadjoinIR ) =>
% 101.76/16.98 ( (
% 101.76/16.98 setadjoinE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setadjoinOr ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setoftrueEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powersetI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 emptyinPowerset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 emptyInPowerset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powersetE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunionI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunionE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subPowSU ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exuE2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 nonemptyImpWitness ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 uniqinunit ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notinsingleton ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 eqinunit ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 singletonsswitch ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairsetE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairsetIL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairsetIR ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 emptyE1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 vacuousDall ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 quantDeMorgan1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 quantDeMorgan2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 quantDeMorgan3 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 quantDeMorgan4 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 prop2setI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 prop2set2propI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notdexE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notdallE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exuI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exuI3 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exuI2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 inCongP ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 in__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exuE3u ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exu__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 emptyset__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setadjoin__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powerset__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunion__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 omega__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 exuEu ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 descr__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dsetconstr__Cong ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 eqimpsubset2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 eqimpsubset1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetI2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 emptysetsubset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetE2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notsubsetI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notequalI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 notequalI2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetRefl ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetTrans ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setadjoinSub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setadjoinSub2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subset2powerset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setextsub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 subsetemptysetimpeq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powersetI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powersetE1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 inPowerset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 powersetsubset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 sepInPowerset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 sepSubset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionIL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairset2IR ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionIR ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionEcases ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionLsub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binunionRsub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectSubset5 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectEL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectLsub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectSubset2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectSubset3 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectER ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 disjointsetsI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectRsub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectSubset4 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 binintersectSubset1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 bs114d ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusEL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusER ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusSubset2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusERneg ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusELneg ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusILneg ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusIRneg ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusLsub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setminusSubset1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 symdiffE ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 symdiffI1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 symdiffI2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 symdiffIneg1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 symdiffIneg2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 secondinupair ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairIL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairIR ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 kpairiskpair ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 kpairp ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 singletonsubset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 singletoninpowerset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 singletoninpowunion ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairset2E ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairsubunion ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairinpowunion ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ubforcartprodlem1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ubforcartprodlem2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ubforcartprodlem3 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodpairin ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodmempair1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodmempair ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunionE2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunionsingleton1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunionsingleton2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setunionsingleton ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 singletonprop ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ex1E1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ex1I ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ex1I2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 singletonsuniq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjL1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 kfstsingleton ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 theprop ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 kfstpairEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodfstin ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjL2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjR11 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjR12 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjR1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 upairequniteq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjR2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setukpairinjR ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ksndsingleton ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ksndpairEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 kpairsurjEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodsndin ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodpairmemEL ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodpairmemER ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodmempaircEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodfstpairEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodsndpairEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 cartprodpairsurjEq ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dpsetconstrI ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dpsetconstrSub ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 setOfPairsIsBReln ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dpsetconstrERa ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dpsetconstrEL1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dpsetconstrEL2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 dpsetconstrER ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 funcImageSingleton ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 apProp ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 app ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 infuncsetfunc ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ap2p ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 funcinfuncset ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 lamProp ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 lamp ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 lam2p ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 brelnall1 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 brelnall2 ) =>
% 101.76/16.98 (
% 101.76/16.98 (
% 101.76/16.98 ex1E2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 funcGraphProp1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 funcGraphProp3 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 funcGraphProp2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 funcextLem ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 funcGraphProp4 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 subbreln ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 eqbreln ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 funcext ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 funcext2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 ap2apEq1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 ap2apEq2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 beta1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 eta1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 lam2lamEq ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 beta2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 eta2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 iffalseProp1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 iffalseProp2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 iftrueProp1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 iftrueProp2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 ifSingleton ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 ifp ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 theeq ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 iftrue ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 iffalse ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 iftrueorfalse ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 binintersectT_lem ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 binunionT_lem ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 powersetT_lem ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 setminusT_lem ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 complementT_lem ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 setextT ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 subsetTI ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 powersetTI1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 powersetTE1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 complementTI1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 complementTE1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 binintersectTELcontra ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 binintersectTERcontra ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 contrasubsetT ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 contrasubsetT1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 contrasubsetT2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 contrasubsetT3 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 doubleComplementI1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 doubleComplementE1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 doubleComplementSub1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 doubleComplementSub2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 doubleComplementEq ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 complementTnotintersectT ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 complementImpComplementIntersect ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 complementSubsetComplementIntersect ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 complementInPowersetComplementIntersect ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 contraSubsetComplement ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 complementTcontraSubset ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 binunionTILcontra ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 binunionTIRcontra ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 inIntersectImpInUnion ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 inIntersectImpInUnion2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 inIntersectImpInIntersectUnions ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 intersectInPowersetIntersectUnions ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 inComplementUnionImpNotIn1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 inComplementUnionImpInComplement1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 binunionTE ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 binunionTEcontra ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 demorgan2a1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 complementUnionInPowersetComplement ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 demorgan2a2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 demorgan1a ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 demorgan1b ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 demorgan1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 demorgan2a ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 demorgan2b2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 demorgan2b ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 demorgan2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz13rule0 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz13rule1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz13rule2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz13rule3 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz13rule4 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz1_1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz1_2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz1_3 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz1_4 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz1_5 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1all2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1SetBreln1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 choice2fnsingleton ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 setOfPairsIsBReln1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1all1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 subbreln1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 eqbreln1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1invprop ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1invI ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1invE ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1compprop ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1compI ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1compE ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1compEex ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1unionprop ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1unionIL ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1unionIR ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1unionI ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1unionE ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1unionEcases ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 breln1unionCommutes ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz2Ex ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz2W ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz2A ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 woz2B ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 image1Ex ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 image1Ex1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 image1Equiv ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 image1E ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 image1I ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 injFuncInInjFuncSet ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 injFuncSetFuncIn ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 injFuncSetFuncInj ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 surjFuncSetFuncIn ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 surjFuncSetFuncSurj ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 leftInvIsSurj ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 surjCantorThm ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 foundation2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 notinself ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 notinself2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 omegaSp ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 omegaSclos ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 peano0notS ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 peanoSinj ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 transitivesetOp1 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 binintTransitive ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 transitivesetOp2 ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 setunionTransitive ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 ordinalMinLem1 ) =>
% 101.76/16.99 (
% 101.76/16.99 ![
% 101.76/16.99 X:$i]:
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 ordinal @
% 101.76/16.99 X ) =>
% 101.76/16.99 (
% 101.76/16.99 ![
% 101.76/16.99 Xx:$i,
% 101.76/16.99 A:$i]:
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 in @
% 101.76/16.99 A @ X ) =>
% 101.76/16.99 (
% 101.76/16.99 (
% 101.76/16.99 in @
% 101.76/16.99 Xx @ A ) =>
% 101.76/16.99 (
% 101.76/16.99 in @
% 101.76/16.99 Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 101.76/16.99 inference('cnf.neg', [status(esa)], [ordinalTransSet])).
% 101.76/16.99 thf(zip_derived_cl0, plain,
% 101.76/16.99 (~ (((setextAx) =>
% 101.76/16.99 (((emptysetAx) =>
% 101.76/16.99 (((setadjoinAx) =>
% 101.76/16.99 (((powersetAx) =>
% 101.76/16.99 (((setunionAx) =>
% 101.76/16.99 (((omega0Ax) =>
% 101.76/16.99 (((omegaSAx) =>
% 101.76/16.99 (((omegaIndAx) =>
% 101.76/16.99 (((replAx) =>
% 101.76/16.99 (((foundationAx) =>
% 101.76/16.99 (((wellorderingAx) =>
% 101.76/16.99 (((descrp) =>
% 101.76/16.99 (((dsetconstrI) =>
% 101.76/16.99 (((dsetconstrEL) =>
% 101.76/16.99 (((dsetconstrER) =>
% 101.76/16.99 (((exuE1) =>
% 101.76/16.99 (((prop2setE) =>
% 101.76/16.99 (((emptysetE) =>
% 101.76/16.99 (((emptysetimpfalse) =>
% 101.76/16.99 (((notinemptyset) =>
% 101.76/16.99 (((exuE3e) =>
% 101.76/16.99 (((setext) =>
% 101.76/16.99 (((emptyI) =>
% 101.76/16.99 (((noeltsimpempty) =>
% 101.76/16.99 (((setbeta) =>
% 101.76/16.99 (((nonemptyE1) =>
% 101.76/16.99 (((nonemptyI) =>
% 101.76/16.99 (((nonemptyI1) =>
% 101.76/16.99 (((setadjoinIL) =>
% 101.76/16.99 (((emptyinunitempty) =>
% 101.76/16.99 ((
% 101.76/16.99 (setadjoinIR) =>
% 101.76/16.99 ((
% 101.76/16.99 (setadjoinE) =>
% 101.76/16.99 ((
% 101.76/16.99 (setadjoinOr) =>
% 101.76/16.99 ((
% 101.76/16.99 (setoftrueEq) =>
% 101.76/16.99 ((
% 101.76/16.99 (powersetI) =>
% 101.76/16.99 ((
% 101.76/16.99 (emptyinPowerset) =>
% 101.76/16.99 ((
% 101.76/16.99 (emptyInPowerset) =>
% 101.76/16.99 ((
% 101.76/16.99 (powersetE) =>
% 101.76/16.99 ((
% 101.76/16.99 (setunionI) =>
% 101.76/16.99 ((
% 101.76/16.99 (setunionE) =>
% 101.76/16.99 ((
% 101.76/16.99 (subPowSU) =>
% 101.76/16.99 ((
% 101.76/16.99 (exuE2) =>
% 101.76/16.99 ((
% 101.76/16.99 (nonemptyImpWitness) =>
% 101.76/16.99 ((
% 101.76/16.99 (uniqinunit) =>
% 101.76/16.99 ((
% 101.76/16.99 (notinsingleton) =>
% 101.76/16.99 ((
% 101.76/16.99 (eqinunit) =>
% 101.76/16.99 ((
% 101.76/16.99 (singletonsswitch) =>
% 101.76/16.99 ((
% 101.76/16.99 (upairsetE) =>
% 101.76/16.99 ((
% 101.76/16.99 (upairsetIL) =>
% 101.76/16.99 ((
% 101.76/16.99 (upairsetIR) =>
% 101.76/16.99 ((
% 101.76/16.99 (emptyE1) =>
% 101.76/16.99 ((
% 101.76/16.99 (vacuousDall) =>
% 101.76/16.99 ((
% 101.76/16.99 (quantDeMorgan1) =>
% 101.76/16.99 ((
% 101.76/16.99 (quantDeMorgan2) =>
% 101.76/16.99 ((
% 101.76/16.99 (quantDeMorgan3) =>
% 101.76/16.99 ((
% 101.76/16.99 (quantDeMorgan4) =>
% 101.76/16.99 ((
% 101.76/16.99 (prop2setI) =>
% 101.76/16.99 ((
% 101.76/16.99 (prop2set2propI) =>
% 101.76/16.99 ((
% 101.76/16.99 (notdexE) =>
% 101.76/16.99 ((
% 101.76/16.99 (notdallE) =>
% 101.76/16.99 ((
% 101.76/16.99 (exuI1) =>
% 101.76/16.99 ((
% 101.76/16.99 (exuI3) =>
% 101.76/16.99 ((
% 101.76/16.99 (exuI2) =>
% 101.76/16.99 ((
% 101.76/16.99 (inCongP) =>
% 101.76/16.99 ((
% 101.76/16.99 (in__Cong) =>
% 101.76/16.99 ((
% 101.76/16.99 (exuE3u) =>
% 101.76/16.99 ((
% 101.76/16.99 (exu__Cong) =>
% 101.76/16.99 ((
% 101.76/16.99 (emptyset__Cong) =>
% 101.76/16.99 ((
% 101.76/16.99 (setadjoin__Cong) =>
% 101.76/16.99 ((
% 101.76/16.99 (powerset__Cong) =>
% 101.76/16.99 ((
% 101.76/16.99 (setunion__Cong) =>
% 101.76/16.99 ((
% 101.76/16.99 (omega__Cong) =>
% 101.76/16.99 ((
% 101.76/16.99 (exuEu) =>
% 101.76/16.99 ((
% 101.76/16.99 (descr__Cong) =>
% 101.76/16.99 ((
% 101.76/16.99 (dsetconstr__Cong) =>
% 101.76/16.99 ((
% 101.76/16.99 (subsetI1) =>
% 101.76/16.99 ((
% 101.76/16.99 (eqimpsubset2) =>
% 101.76/16.99 ((
% 101.76/16.99 (eqimpsubset1) =>
% 101.76/16.99 ((
% 101.76/16.99 (subsetI2) =>
% 101.76/16.99 ((
% 101.76/16.99 (emptysetsubset) =>
% 101.76/16.99 ((
% 101.76/16.99 (subsetE) =>
% 101.76/16.99 ((
% 101.76/16.99 (subsetE2) =>
% 101.76/16.99 ((
% 101.76/16.99 (notsubsetI) =>
% 101.76/16.99 ((
% 101.76/16.99 (notequalI1) =>
% 101.76/16.99 ((
% 101.76/16.99 (notequalI2) =>
% 101.76/16.99 ((
% 101.76/16.99 (subsetRefl) =>
% 101.76/16.99 ((
% 101.76/16.99 (subsetTrans) =>
% 101.76/16.99 ((
% 101.76/16.99 (setadjoinSub) =>
% 101.76/16.99 ((
% 101.76/16.99 (setadjoinSub2) =>
% 101.76/16.99 ((
% 101.76/16.99 (subset2powerset) =>
% 101.76/16.99 ((
% 101.76/16.99 (setextsub) =>
% 101.76/16.99 ((
% 101.76/16.99 (subsetemptysetimpeq) =>
% 101.76/16.99 ((
% 101.76/16.99 (powersetI1) =>
% 101.76/16.99 ((
% 101.76/16.99 (powersetE1) =>
% 101.76/16.99 ((
% 101.76/16.99 (inPowerset) =>
% 101.76/16.99 ((
% 101.76/16.99 (powersetsubset) =>
% 101.76/16.99 ((
% 101.76/16.99 (sepInPowerset) =>
% 101.76/16.99 ((
% 101.76/16.99 (sepSubset) =>
% 101.76/16.99 ((
% 101.76/16.99 (binunionIL) =>
% 101.76/16.99 ((
% 101.76/16.99 (upairset2IR) =>
% 101.76/16.99 ((
% 101.76/16.99 (binunionIR) =>
% 101.76/16.99 ((
% 101.76/16.99 (binunionEcases) =>
% 101.76/16.99 ((
% 101.76/16.99 (binunionE) =>
% 101.76/16.99 ((
% 101.76/16.99 (binunionLsub) =>
% 101.76/16.99 ((
% 101.76/16.99 (binunionRsub) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintersectI) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintersectSubset5) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintersectEL) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintersectLsub) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintersectSubset2) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintersectSubset3) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintersectER) =>
% 101.76/16.99 ((
% 101.76/16.99 (disjointsetsI1) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintersectRsub) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintersectSubset4) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintersectSubset1) =>
% 101.76/16.99 ((
% 101.76/16.99 (bs114d) =>
% 101.76/16.99 ((
% 101.76/16.99 (setminusI) =>
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% 101.76/16.99 (setminusLsub) =>
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% 101.76/16.99 (symdiffE) =>
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% 101.76/16.99 ((
% 101.76/16.99 (symdiffI2) =>
% 101.76/16.99 ((
% 101.76/16.99 (symdiffIneg1) =>
% 101.76/16.99 ((
% 101.76/16.99 (symdiffIneg2) =>
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% 101.76/16.99 (secondinupair) =>
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% 101.76/16.99 ((
% 101.76/16.99 (kpairiskpair) =>
% 101.76/16.99 ((
% 101.76/16.99 (kpairp) =>
% 101.76/16.99 ((
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% 101.76/16.99 ((
% 101.76/16.99 (singletoninpowerset) =>
% 101.76/16.99 ((
% 101.76/16.99 (singletoninpowunion) =>
% 101.76/16.99 ((
% 101.76/16.99 (upairset2E) =>
% 101.76/16.99 ((
% 101.76/16.99 (upairsubunion) =>
% 101.76/16.99 ((
% 101.76/16.99 (upairinpowunion) =>
% 101.76/16.99 ((
% 101.76/16.99 (ubforcartprodlem1) =>
% 101.76/16.99 ((
% 101.76/16.99 (ubforcartprodlem2) =>
% 101.76/16.99 ((
% 101.76/16.99 (ubforcartprodlem3) =>
% 101.76/16.99 ((
% 101.76/16.99 (cartprodpairin) =>
% 101.76/16.99 ((
% 101.76/16.99 (cartprodmempair1) =>
% 101.76/16.99 ((
% 101.76/16.99 (cartprodmempair) =>
% 101.76/16.99 ((
% 101.76/16.99 (setunionE2) =>
% 101.76/16.99 ((
% 101.76/16.99 (setunionsingleton1) =>
% 101.76/16.99 ((
% 101.76/16.99 (setunionsingleton2) =>
% 101.76/16.99 ((
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% 101.76/16.99 ((
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% 101.76/16.99 (ex1I) =>
% 101.76/16.99 ((
% 101.76/16.99 (ex1I2) =>
% 101.76/16.99 ((
% 101.76/16.99 (singletonsuniq) =>
% 101.76/16.99 ((
% 101.76/16.99 (setukpairinjL1) =>
% 101.76/16.99 ((
% 101.76/16.99 (kfstsingleton) =>
% 101.76/16.99 ((
% 101.76/16.99 (theprop) =>
% 101.76/16.99 ((
% 101.76/16.99 (kfstpairEq) =>
% 101.76/16.99 ((
% 101.76/16.99 (cartprodfstin) =>
% 101.76/16.99 ((
% 101.76/16.99 (setukpairinjL2) =>
% 101.76/16.99 ((
% 101.76/16.99 (setukpairinjL) =>
% 101.76/16.99 ((
% 101.76/16.99 (setukpairinjR11) =>
% 101.76/16.99 ((
% 101.76/16.99 (setukpairinjR12) =>
% 101.76/16.99 ((
% 101.76/16.99 (setukpairinjR1) =>
% 101.76/16.99 ((
% 101.76/16.99 (upairequniteq) =>
% 101.76/16.99 ((
% 101.76/16.99 (setukpairinjR2) =>
% 101.76/16.99 ((
% 101.76/16.99 (setukpairinjR) =>
% 101.76/16.99 ((
% 101.76/16.99 (ksndsingleton) =>
% 101.76/16.99 ((
% 101.76/16.99 (ksndpairEq) =>
% 101.76/16.99 ((
% 101.76/16.99 (kpairsurjEq) =>
% 101.76/16.99 ((
% 101.76/16.99 (cartprodsndin) =>
% 101.76/16.99 ((
% 101.76/16.99 (cartprodpairmemEL) =>
% 101.76/16.99 ((
% 101.76/16.99 (cartprodpairmemER) =>
% 101.76/16.99 ((
% 101.76/16.99 (cartprodmempaircEq) =>
% 101.76/16.99 ((
% 101.76/16.99 (cartprodfstpairEq) =>
% 101.76/16.99 ((
% 101.76/16.99 (cartprodsndpairEq) =>
% 101.76/16.99 ((
% 101.76/16.99 (cartprodpairsurjEq) =>
% 101.76/16.99 ((
% 101.76/16.99 (dpsetconstrI) =>
% 101.76/16.99 ((
% 101.76/16.99 (dpsetconstrSub) =>
% 101.76/16.99 ((
% 101.76/16.99 (setOfPairsIsBReln) =>
% 101.76/16.99 ((
% 101.76/16.99 (dpsetconstrERa) =>
% 101.76/16.99 ((
% 101.76/16.99 (dpsetconstrEL1) =>
% 101.76/16.99 ((
% 101.76/16.99 (dpsetconstrEL2) =>
% 101.76/16.99 ((
% 101.76/16.99 (dpsetconstrER) =>
% 101.76/16.99 ((
% 101.76/16.99 (funcImageSingleton) =>
% 101.76/16.99 ((
% 101.76/16.99 (apProp) =>
% 101.76/16.99 ((
% 101.76/16.99 (app) =>
% 101.76/16.99 ((
% 101.76/16.99 (infuncsetfunc) =>
% 101.76/16.99 ((
% 101.76/16.99 (ap2p) =>
% 101.76/16.99 ((
% 101.76/16.99 (funcinfuncset) =>
% 101.76/16.99 ((
% 101.76/16.99 (lamProp) =>
% 101.76/16.99 ((
% 101.76/16.99 (lamp) =>
% 101.76/16.99 ((
% 101.76/16.99 (lam2p) =>
% 101.76/16.99 ((
% 101.76/16.99 (brelnall1) =>
% 101.76/16.99 ((
% 101.76/16.99 (brelnall2) =>
% 101.76/16.99 ((
% 101.76/16.99 (ex1E2) =>
% 101.76/16.99 ((
% 101.76/16.99 (funcGraphProp1) =>
% 101.76/16.99 ((
% 101.76/16.99 (funcGraphProp3) =>
% 101.76/16.99 ((
% 101.76/16.99 (funcGraphProp2) =>
% 101.76/16.99 ((
% 101.76/16.99 (funcextLem) =>
% 101.76/16.99 ((
% 101.76/16.99 (funcGraphProp4) =>
% 101.76/16.99 ((
% 101.76/16.99 (subbreln) =>
% 101.76/16.99 ((
% 101.76/16.99 (eqbreln) =>
% 101.76/16.99 ((
% 101.76/16.99 (funcext) =>
% 101.76/16.99 ((
% 101.76/16.99 (funcext2) =>
% 101.76/16.99 ((
% 101.76/16.99 (ap2apEq1) =>
% 101.76/16.99 ((
% 101.76/16.99 (ap2apEq2) =>
% 101.76/16.99 ((
% 101.76/16.99 (beta1) =>
% 101.76/16.99 ((
% 101.76/16.99 (eta1) =>
% 101.76/16.99 ((
% 101.76/16.99 (lam2lamEq) =>
% 101.76/16.99 ((
% 101.76/16.99 (beta2) =>
% 101.76/16.99 ((
% 101.76/16.99 (eta2) =>
% 101.76/16.99 ((
% 101.76/16.99 (iffalseProp1) =>
% 101.76/16.99 ((
% 101.76/16.99 (iffalseProp2) =>
% 101.76/16.99 ((
% 101.76/16.99 (iftrueProp1) =>
% 101.76/16.99 ((
% 101.76/16.99 (iftrueProp2) =>
% 101.76/16.99 ((
% 101.76/16.99 (ifSingleton) =>
% 101.76/16.99 ((
% 101.76/16.99 (ifp) =>
% 101.76/16.99 ((
% 101.76/16.99 (theeq) =>
% 101.76/16.99 ((
% 101.76/16.99 (iftrue) =>
% 101.76/16.99 ((
% 101.76/16.99 (iffalse) =>
% 101.76/16.99 ((
% 101.76/16.99 (iftrueorfalse) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintersectT_lem) =>
% 101.76/16.99 ((
% 101.76/16.99 (binunionT_lem) =>
% 101.76/16.99 ((
% 101.76/16.99 (powersetT_lem) =>
% 101.76/16.99 ((
% 101.76/16.99 (setminusT_lem) =>
% 101.76/16.99 ((
% 101.76/16.99 (complementT_lem) =>
% 101.76/16.99 ((
% 101.76/16.99 (setextT) =>
% 101.76/16.99 ((
% 101.76/16.99 (subsetTI) =>
% 101.76/16.99 ((
% 101.76/16.99 (powersetTI1) =>
% 101.76/16.99 ((
% 101.76/16.99 (powersetTE1) =>
% 101.76/16.99 ((
% 101.76/16.99 (complementTI1) =>
% 101.76/16.99 ((
% 101.76/16.99 (complementTE1) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintersectTELcontra) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintersectTERcontra) =>
% 101.76/16.99 ((
% 101.76/16.99 (contrasubsetT) =>
% 101.76/16.99 ((
% 101.76/16.99 (contrasubsetT1) =>
% 101.76/16.99 ((
% 101.76/16.99 (contrasubsetT2) =>
% 101.76/16.99 ((
% 101.76/16.99 (contrasubsetT3) =>
% 101.76/16.99 ((
% 101.76/16.99 (doubleComplementI1) =>
% 101.76/16.99 ((
% 101.76/16.99 (doubleComplementE1) =>
% 101.76/16.99 ((
% 101.76/16.99 (doubleComplementSub1) =>
% 101.76/16.99 ((
% 101.76/16.99 (doubleComplementSub2) =>
% 101.76/16.99 ((
% 101.76/16.99 (doubleComplementEq) =>
% 101.76/16.99 ((
% 101.76/16.99 (complementTnotintersectT) =>
% 101.76/16.99 ((
% 101.76/16.99 (complementImpComplementIntersect) =>
% 101.76/16.99 ((
% 101.76/16.99 (complementSubsetComplementIntersect) =>
% 101.76/16.99 ((
% 101.76/16.99 (complementInPowersetComplementIntersect) =>
% 101.76/16.99 ((
% 101.76/16.99 (contraSubsetComplement) =>
% 101.76/16.99 ((
% 101.76/16.99 (complementTcontraSubset) =>
% 101.76/16.99 ((
% 101.76/16.99 (binunionTILcontra) =>
% 101.76/16.99 ((
% 101.76/16.99 (binunionTIRcontra) =>
% 101.76/16.99 ((
% 101.76/16.99 (inIntersectImpInUnion) =>
% 101.76/16.99 ((
% 101.76/16.99 (inIntersectImpInUnion2) =>
% 101.76/16.99 ((
% 101.76/16.99 (inIntersectImpInIntersectUnions) =>
% 101.76/16.99 ((
% 101.76/16.99 (intersectInPowersetIntersectUnions) =>
% 101.76/16.99 ((
% 101.76/16.99 (inComplementUnionImpNotIn1) =>
% 101.76/16.99 ((
% 101.76/16.99 (inComplementUnionImpInComplement1) =>
% 101.76/16.99 ((
% 101.76/16.99 (binunionTE) =>
% 101.76/16.99 ((
% 101.76/16.99 (binunionTEcontra) =>
% 101.76/16.99 ((
% 101.76/16.99 (demorgan2a1) =>
% 101.76/16.99 ((
% 101.76/16.99 (complementUnionInPowersetComplement) =>
% 101.76/16.99 ((
% 101.76/16.99 (demorgan2a2) =>
% 101.76/16.99 ((
% 101.76/16.99 (demorgan1a) =>
% 101.76/16.99 ((
% 101.76/16.99 (demorgan1b) =>
% 101.76/16.99 ((
% 101.76/16.99 (demorgan1) =>
% 101.76/16.99 ((
% 101.76/16.99 (demorgan2a) =>
% 101.76/16.99 ((
% 101.76/16.99 (demorgan2b2) =>
% 101.76/16.99 ((
% 101.76/16.99 (demorgan2b) =>
% 101.76/16.99 ((
% 101.76/16.99 (demorgan2) =>
% 101.76/16.99 ((
% 101.76/16.99 (woz13rule0) =>
% 101.76/16.99 ((
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% 101.76/16.99 ((
% 101.76/16.99 (woz13rule2) =>
% 101.76/16.99 ((
% 101.76/16.99 (woz13rule3) =>
% 101.76/16.99 ((
% 101.76/16.99 (woz13rule4) =>
% 101.76/16.99 ((
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% 101.76/16.99 ((
% 101.76/16.99 (woz1_2) =>
% 101.76/16.99 ((
% 101.76/16.99 (woz1_3) =>
% 101.76/16.99 ((
% 101.76/16.99 (woz1_4) =>
% 101.76/16.99 ((
% 101.76/16.99 (woz1_5) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1all2) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1SetBreln1) =>
% 101.76/16.99 ((
% 101.76/16.99 (choice2fnsingleton) =>
% 101.76/16.99 ((
% 101.76/16.99 (setOfPairsIsBReln1) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1all1) =>
% 101.76/16.99 ((
% 101.76/16.99 (subbreln1) =>
% 101.76/16.99 ((
% 101.76/16.99 (eqbreln1) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1invprop) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1invI) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1invE) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1compprop) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1compI) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1compE) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1compEex) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1unionprop) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1unionIL) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1unionIR) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1unionI) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1unionE) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1unionEcases) =>
% 101.76/16.99 ((
% 101.76/16.99 (breln1unionCommutes) =>
% 101.76/16.99 ((
% 101.76/16.99 (woz2Ex) =>
% 101.76/16.99 ((
% 101.76/16.99 (woz2W) =>
% 101.76/16.99 ((
% 101.76/16.99 (woz2A) =>
% 101.76/16.99 ((
% 101.76/16.99 (woz2B) =>
% 101.76/16.99 ((
% 101.76/16.99 (image1Ex) =>
% 101.76/16.99 ((
% 101.76/16.99 (image1Ex1) =>
% 101.76/16.99 ((
% 101.76/16.99 (image1Equiv) =>
% 101.76/16.99 ((
% 101.76/16.99 (image1E) =>
% 101.76/16.99 ((
% 101.76/16.99 (image1I) =>
% 101.76/16.99 ((
% 101.76/16.99 (injFuncInInjFuncSet) =>
% 101.76/16.99 ((
% 101.76/16.99 (injFuncSetFuncIn) =>
% 101.76/16.99 ((
% 101.76/16.99 (injFuncSetFuncInj) =>
% 101.76/16.99 ((
% 101.76/16.99 (surjFuncSetFuncIn) =>
% 101.76/16.99 ((
% 101.76/16.99 (surjFuncSetFuncSurj) =>
% 101.76/16.99 ((
% 101.76/16.99 (leftInvIsSurj) =>
% 101.76/16.99 ((
% 101.76/16.99 (surjCantorThm) =>
% 101.76/16.99 ((
% 101.76/16.99 (foundation2) =>
% 101.76/16.99 ((
% 101.76/16.99 (notinself) =>
% 101.76/16.99 ((
% 101.76/16.99 (notinself2) =>
% 101.76/16.99 ((
% 101.76/16.99 (omegaSp) =>
% 101.76/16.99 ((
% 101.76/16.99 (omegaSclos) =>
% 101.76/16.99 ((
% 101.76/16.99 (peano0notS) =>
% 101.76/16.99 ((
% 101.76/16.99 (peanoSinj) =>
% 101.76/16.99 ((
% 101.76/16.99 (transitivesetOp1) =>
% 101.76/16.99 ((
% 101.76/16.99 (binintTransitive) =>
% 101.76/16.99 ((
% 101.76/16.99 (transitivesetOp2) =>
% 101.76/16.99 ((
% 101.76/16.99 (setunionTransitive) =>
% 101.76/16.99 ((
% 101.76/16.99 (ordinalMinLem1) =>
% 101.76/16.99 ((
% 101.76/16.99 (!!) @ (
% 101.76/16.99 ^[Y0 : $i]:
% 101.76/16.99 ((
% 101.76/16.99 (ordinal @
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% 101.76/16.99 ((
% 101.76/16.99 (!!) @ (
% 101.76/16.99 ^[Y1 : $i]:
% 101.76/16.99 ((
% 101.76/16.99 (!!) @ (
% 101.76/16.99 ^[Y2 : $i]:
% 101.76/16.99 ((
% 101.76/16.99 (in @
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% 101.76/16.99 Y0) =>
% 101.76/16.99 ((
% 101.76/16.99 (in @
% 101.76/16.99 Y1 @
% 101.76/16.99 Y2) =>
% 101.76/16.99 (in @
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% 101.76/16.99 inference('cnf', [status(esa)], [zf_stmt_0])).
% 101.76/16.99 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 101.76/16.99 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 101.76/16.99 define([status(thm)])).
% 101.76/16.99 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 101.76/16.99 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 101.76/16.99 thf('1', plain,
% 101.76/16.99 (( emptyinunitempty ) =
% 101.76/16.99 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 101.76/16.99 define([status(thm)])).
% 101.76/16.99 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 101.76/16.99 ((((emptyset) = (emptyset)))))).
% 101.76/16.99 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 101.76/16.99 define([status(thm)])).
% 101.76/16.99 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 101.76/16.99 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 101.76/16.99 define([status(thm)])).
% 101.76/16.99 thf(zip_derived_cl1, plain,
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% 101.76/16.99 (((emptysetAx) =>
% 101.76/16.99 (((setadjoinAx) =>
% 101.76/16.99 (((powersetAx) =>
% 101.76/16.99 (((setunionAx) =>
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% 101.76/16.99 (((omegaIndAx) =>
% 101.76/16.99 (((replAx) =>
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% 101.76/16.99 emptyset)) =>
% 101.76/16.99 ((
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% 101.76/16.99 ((
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% 101.76/16.99 ((
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% 101.76/16.99 ((
% 101.76/16.99 (setoftrueEq) =>
% 101.76/16.99 ((
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% 101.76/16.99 ((
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% 101.76/16.99 ((
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% 101.76/16.99 ((
% 101.76/16.99 (setunionE) =>
% 101.76/16.99 ((
% 101.76/16.99 (subPowSU) =>
% 101.76/16.99 ((
% 101.76/16.99 (exuE2) =>
% 101.76/16.99 ((
% 101.76/16.99 (nonemptyImpWitness) =>
% 101.76/16.99 ((
% 101.76/16.99 (uniqinunit) =>
% 101.76/16.99 ((
% 101.76/16.99 (notinsingleton) =>
% 101.76/16.99 ((
% 101.76/16.99 (eqinunit) =>
% 101.76/16.99 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (breln1unionE) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (injFuncSetFuncIn) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncSetFuncInj) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjFuncSetFuncIn) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (setminusIRneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusLsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusSubset1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffE) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffIneg1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffIneg2) =>
% 101.76/17.00 ((
% 101.76/17.00 (secondinupair) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairiskpair) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairp) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonsubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletoninpowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletoninpowunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairset2E) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairsubunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairinpowunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem1) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem2) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem3) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairin) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempair1) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempair) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionE2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton1) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1E1) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1I) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1I2) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonsuniq) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL1) =>
% 101.76/17.00 ((
% 101.76/17.00 (kfstsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (theprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (kfstpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodfstin) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR11) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR12) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR1) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairequniteq) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR) =>
% 101.76/17.00 ((
% 101.76/17.00 (ksndsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (ksndpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairsurjEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodsndin) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairmemEL) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairmemER) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempaircEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodfstpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodsndpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairsurjEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrI) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrSub) =>
% 101.76/17.00 ((
% 101.76/17.00 (setOfPairsIsBReln) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrERa) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrEL1) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrEL2) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrER) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcImageSingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (apProp) =>
% 101.76/17.00 ((
% 101.76/17.00 (app) =>
% 101.76/17.00 ((
% 101.76/17.00 (infuncsetfunc) =>
% 101.76/17.00 ((
% 101.76/17.00 (ap2p) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcinfuncset) =>
% 101.76/17.00 ((
% 101.76/17.00 (lamProp) =>
% 101.76/17.00 ((
% 101.76/17.00 (lamp) =>
% 101.76/17.00 ((
% 101.76/17.00 (lam2p) =>
% 101.76/17.00 ((
% 101.76/17.00 (brelnall1) =>
% 101.76/17.00 ((
% 101.76/17.00 (brelnall2) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1E2) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcGraphProp1) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcGraphProp3) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcGraphProp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcextLem) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcGraphProp4) =>
% 101.76/17.00 ((
% 101.76/17.00 (subbreln) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqbreln) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcext) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcext2) =>
% 101.76/17.00 ((
% 101.76/17.00 (ap2apEq1) =>
% 101.76/17.00 ((
% 101.76/17.00 (ap2apEq2) =>
% 101.76/17.00 ((
% 101.76/17.00 (beta1) =>
% 101.76/17.00 ((
% 101.76/17.00 (eta1) =>
% 101.76/17.00 ((
% 101.76/17.00 (lam2lamEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (beta2) =>
% 101.76/17.00 ((
% 101.76/17.00 (eta2) =>
% 101.76/17.00 ((
% 101.76/17.00 (iffalseProp1) =>
% 101.76/17.00 ((
% 101.76/17.00 (iffalseProp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (iftrueProp1) =>
% 101.76/17.00 ((
% 101.76/17.00 (iftrueProp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (ifSingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (ifp) =>
% 101.76/17.00 ((
% 101.76/17.00 (theeq) =>
% 101.76/17.00 ((
% 101.76/17.00 (iftrue) =>
% 101.76/17.00 ((
% 101.76/17.00 (iffalse) =>
% 101.76/17.00 ((
% 101.76/17.00 (iftrueorfalse) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (setextT) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetTI) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetTI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetTE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectTELcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectTERcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT1) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT2) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT3) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementSub1) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementSub2) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTnotintersectT) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementImpComplementIntersect) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementSubsetComplementIntersect) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementInPowersetComplementIntersect) =>
% 101.76/17.00 ((
% 101.76/17.00 (contraSubsetComplement) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTcontraSubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTILcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTIRcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (inIntersectImpInUnion) =>
% 101.76/17.00 ((
% 101.76/17.00 (inIntersectImpInUnion2) =>
% 101.76/17.00 ((
% 101.76/17.00 (inIntersectImpInIntersectUnions) =>
% 101.76/17.00 ((
% 101.76/17.00 (intersectInPowersetIntersectUnions) =>
% 101.76/17.00 ((
% 101.76/17.00 (inComplementUnionImpNotIn1) =>
% 101.76/17.00 ((
% 101.76/17.00 (inComplementUnionImpInComplement1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTE) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTEcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a1) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementUnionInPowersetComplement) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a2) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1a) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1b) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2b2) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2b) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule0) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule1) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule3) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule4) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_1) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_3) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_4) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_5) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1all2) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1SetBreln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (choice2fnsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (setOfPairsIsBReln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1all1) =>
% 101.76/17.00 ((
% 101.76/17.00 (subbreln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqbreln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1invprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1invI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1invE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compEex) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionEcases) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionCommutes) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2Ex) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2W) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2A) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2B) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Ex) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Ex1) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Equiv) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1E) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1I) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncInInjFuncSet) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncSetFuncIn) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncSetFuncInj) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjFuncSetFuncIn) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjFuncSetFuncSurj) =>
% 101.76/17.00 ((
% 101.76/17.00 (leftInvIsSurj) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjCantorThm) =>
% 101.76/17.00 ((
% 101.76/17.00 (foundation2) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinself) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinself2) =>
% 101.76/17.00 ((
% 101.76/17.00 (omegaSp) =>
% 101.76/17.00 ((
% 101.76/17.00 (omegaSclos) =>
% 101.76/17.00 ((
% 101.76/17.00 (peano0notS) =>
% 101.76/17.00 ((
% 101.76/17.00 (peanoSinj) =>
% 101.76/17.00 ((
% 101.76/17.00 (transitivesetOp1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintTransitive) =>
% 101.76/17.00 ((
% 101.76/17.00 (transitivesetOp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionTransitive) =>
% 101.76/17.00 ((
% 101.76/17.00 (ordinalMinLem1) =>
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y0 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (ordinal @
% 101.76/17.00 Y0) =>
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y1 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y2 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (in @
% 101.76/17.00 Y2 @
% 101.76/17.00 Y0) =>
% 101.76/17.00 ((
% 101.76/17.00 (in @
% 101.76/17.00 Y1 @
% 101.76/17.00 Y2) =>
% 101.76/17.00 (in @
% 101.76/17.00 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 101.76/17.00 thf(zip_derived_cl16, plain,
% 101.76/17.00 (~ (((setunionAx) =>
% 101.76/17.00 (((in @ emptyset @ omega) =>
% 101.76/17.00 (((omegaSAx) =>
% 101.76/17.00 (((omegaIndAx) =>
% 101.76/17.00 (((replAx) =>
% 101.76/17.00 (((foundationAx) =>
% 101.76/17.00 (((wellorderingAx) =>
% 101.76/17.00 (((descrp) =>
% 101.76/17.00 (((dsetconstrI) =>
% 101.76/17.00 (((dsetconstrEL) =>
% 101.76/17.00 (((dsetconstrER) =>
% 101.76/17.00 (((exuE1) =>
% 101.76/17.00 (((prop2setE) =>
% 101.76/17.00 (((emptysetE) =>
% 101.76/17.00 (((emptysetimpfalse) =>
% 101.76/17.00 (((notinemptyset) =>
% 101.76/17.00 (((exuE3e) =>
% 101.76/17.00 (((setext) =>
% 101.76/17.00 (((emptyI) =>
% 101.76/17.00 (((noeltsimpempty) =>
% 101.76/17.00 (((setbeta) =>
% 101.76/17.00 (((nonemptyE1) =>
% 101.76/17.00 (((nonemptyI) =>
% 101.76/17.00 (((nonemptyI1) =>
% 101.76/17.00 (((setadjoinIL) =>
% 101.76/17.00 (((in @ emptyset @
% 101.76/17.00 (setadjoin @
% 101.76/17.00 emptyset @
% 101.76/17.00 emptyset)) =>
% 101.76/17.00 (((setadjoinIR) =>
% 101.76/17.00 (((setadjoinE) =>
% 101.76/17.00 (((setadjoinOr) =>
% 101.76/17.00 (((setoftrueEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetI) =>
% 101.76/17.00 ((
% 101.76/17.00 (emptyinPowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (emptyInPowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetE) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionI) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionE) =>
% 101.76/17.00 ((
% 101.76/17.00 (subPowSU) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuE2) =>
% 101.76/17.00 ((
% 101.76/17.00 (nonemptyImpWitness) =>
% 101.76/17.00 ((
% 101.76/17.00 (uniqinunit) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqinunit) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonsswitch) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairsetE) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairsetIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairsetIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (emptyE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (vacuousDall) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan1) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan2) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan3) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan4) =>
% 101.76/17.00 ((
% 101.76/17.00 (prop2setI) =>
% 101.76/17.00 ((
% 101.76/17.00 (prop2set2propI) =>
% 101.76/17.00 ((
% 101.76/17.00 (notdexE) =>
% 101.76/17.00 ((
% 101.76/17.00 (notdallE) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuI3) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (inCongP) =>
% 101.76/17.00 ((
% 101.76/17.00 (in__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuE3u) =>
% 101.76/17.00 ((
% 101.76/17.00 (exu__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (setadjoin__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (powerset__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunion__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuEu) =>
% 101.76/17.00 ((
% 101.76/17.00 (descr__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (dsetconstr__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqimpsubset2) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqimpsubset1) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (emptysetsubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetE) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetE2) =>
% 101.76/17.00 ((
% 101.76/17.00 (notsubsetI) =>
% 101.76/17.00 ((
% 101.76/17.00 (notequalI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (notequalI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetRefl) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetTrans) =>
% 101.76/17.00 ((
% 101.76/17.00 (setadjoinSub) =>
% 101.76/17.00 ((
% 101.76/17.00 (setadjoinSub2) =>
% 101.76/17.00 ((
% 101.76/17.00 (subset2powerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (setextsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetemptysetimpeq) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (inPowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetsubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (sepInPowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (sepSubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairset2IR) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionEcases) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionE) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionLsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionRsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectI) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset5) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectEL) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectLsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset2) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset3) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectER) =>
% 101.76/17.00 ((
% 101.76/17.00 (disjointsetsI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectRsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset4) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset1) =>
% 101.76/17.00 ((
% 101.76/17.00 (bs114d) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusI) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusEL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusER) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusSubset2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusERneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusELneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusILneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusIRneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusLsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusSubset1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffE) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffIneg1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffIneg2) =>
% 101.76/17.00 ((
% 101.76/17.00 (secondinupair) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairiskpair) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairp) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonsubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletoninpowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletoninpowunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairset2E) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairsubunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairinpowunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem1) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem2) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem3) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairin) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempair1) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempair) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionE2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton1) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1E1) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1I) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1I2) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonsuniq) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL1) =>
% 101.76/17.00 ((
% 101.76/17.00 (kfstsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (theprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (kfstpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodfstin) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR11) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR12) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR1) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairequniteq) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR) =>
% 101.76/17.00 ((
% 101.76/17.00 (ksndsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (ksndpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairsurjEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodsndin) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairmemEL) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairmemER) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempaircEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodfstpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodsndpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairsurjEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrI) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrSub) =>
% 101.76/17.00 ((
% 101.76/17.00 (setOfPairsIsBReln) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrERa) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrEL1) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrEL2) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrER) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcImageSingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (apProp) =>
% 101.76/17.00 ((
% 101.76/17.00 (app) =>
% 101.76/17.00 ((
% 101.76/17.00 (infuncsetfunc) =>
% 101.76/17.00 ((
% 101.76/17.00 (ap2p) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcinfuncset) =>
% 101.76/17.00 ((
% 101.76/17.00 (lamProp) =>
% 101.76/17.00 ((
% 101.76/17.00 (lamp) =>
% 101.76/17.00 ((
% 101.76/17.00 (lam2p) =>
% 101.76/17.00 ((
% 101.76/17.00 (brelnall1) =>
% 101.76/17.00 ((
% 101.76/17.00 (brelnall2) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1E2) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcGraphProp1) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcGraphProp3) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcGraphProp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcextLem) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcGraphProp4) =>
% 101.76/17.00 ((
% 101.76/17.00 (subbreln) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqbreln) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcext) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcext2) =>
% 101.76/17.00 ((
% 101.76/17.00 (ap2apEq1) =>
% 101.76/17.00 ((
% 101.76/17.00 (ap2apEq2) =>
% 101.76/17.00 ((
% 101.76/17.00 (beta1) =>
% 101.76/17.00 ((
% 101.76/17.00 (eta1) =>
% 101.76/17.00 ((
% 101.76/17.00 (lam2lamEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (beta2) =>
% 101.76/17.00 ((
% 101.76/17.00 (eta2) =>
% 101.76/17.00 ((
% 101.76/17.00 (iffalseProp1) =>
% 101.76/17.00 ((
% 101.76/17.00 (iffalseProp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (iftrueProp1) =>
% 101.76/17.00 ((
% 101.76/17.00 (iftrueProp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (ifSingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (ifp) =>
% 101.76/17.00 ((
% 101.76/17.00 (theeq) =>
% 101.76/17.00 ((
% 101.76/17.00 (iftrue) =>
% 101.76/17.00 ((
% 101.76/17.00 (iffalse) =>
% 101.76/17.00 ((
% 101.76/17.00 (iftrueorfalse) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (setextT) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetTI) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetTI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetTE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectTELcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectTERcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT1) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT2) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT3) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementSub1) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementSub2) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTnotintersectT) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementImpComplementIntersect) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementSubsetComplementIntersect) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementInPowersetComplementIntersect) =>
% 101.76/17.00 ((
% 101.76/17.00 (contraSubsetComplement) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTcontraSubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTILcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTIRcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (inIntersectImpInUnion) =>
% 101.76/17.00 ((
% 101.76/17.00 (inIntersectImpInUnion2) =>
% 101.76/17.00 ((
% 101.76/17.00 (inIntersectImpInIntersectUnions) =>
% 101.76/17.00 ((
% 101.76/17.00 (intersectInPowersetIntersectUnions) =>
% 101.76/17.00 ((
% 101.76/17.00 (inComplementUnionImpNotIn1) =>
% 101.76/17.00 ((
% 101.76/17.00 (inComplementUnionImpInComplement1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTE) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTEcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a1) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementUnionInPowersetComplement) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a2) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1a) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1b) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2b2) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2b) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule0) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule1) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule3) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule4) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_1) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_3) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_4) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_5) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1all2) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1SetBreln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (choice2fnsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (setOfPairsIsBReln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1all1) =>
% 101.76/17.00 ((
% 101.76/17.00 (subbreln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqbreln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1invprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1invI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1invE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compEex) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionEcases) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionCommutes) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2Ex) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2W) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2A) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2B) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Ex) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Ex1) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Equiv) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1E) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1I) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncInInjFuncSet) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncSetFuncIn) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncSetFuncInj) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjFuncSetFuncIn) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjFuncSetFuncSurj) =>
% 101.76/17.00 ((
% 101.76/17.00 (leftInvIsSurj) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjCantorThm) =>
% 101.76/17.00 ((
% 101.76/17.00 (foundation2) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinself) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinself2) =>
% 101.76/17.00 ((
% 101.76/17.00 (omegaSp) =>
% 101.76/17.00 ((
% 101.76/17.00 (omegaSclos) =>
% 101.76/17.00 ((
% 101.76/17.00 (peano0notS) =>
% 101.76/17.00 ((
% 101.76/17.00 (peanoSinj) =>
% 101.76/17.00 ((
% 101.76/17.00 (transitivesetOp1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintTransitive) =>
% 101.76/17.00 ((
% 101.76/17.00 (transitivesetOp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionTransitive) =>
% 101.76/17.00 ((
% 101.76/17.00 (ordinalMinLem1) =>
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y0 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (ordinal @
% 101.76/17.00 Y0) =>
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y1 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y2 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (in @
% 101.76/17.00 Y2 @
% 101.76/17.00 Y0) =>
% 101.76/17.00 ((
% 101.76/17.00 (in @
% 101.76/17.00 Y1 @
% 101.76/17.00 Y2) =>
% 101.76/17.00 (in @
% 101.76/17.00 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])).
% 101.76/17.00 thf(zip_derived_cl21, plain,
% 101.76/17.00 (~ (((in @ emptyset @ omega) =>
% 101.76/17.00 (((omegaSAx) =>
% 101.76/17.00 (((omegaIndAx) =>
% 101.76/17.00 (((replAx) =>
% 101.76/17.00 (((foundationAx) =>
% 101.76/17.00 (((wellorderingAx) =>
% 101.76/17.00 (((descrp) =>
% 101.76/17.00 (((dsetconstrI) =>
% 101.76/17.00 (((dsetconstrEL) =>
% 101.76/17.00 (((dsetconstrER) =>
% 101.76/17.00 (((exuE1) =>
% 101.76/17.00 (((prop2setE) =>
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% 101.76/17.00 (((noeltsimpempty) =>
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% 101.76/17.00 (((nonemptyI) =>
% 101.76/17.00 (((nonemptyI1) =>
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% 101.76/17.00 (((setadjoinIR) =>
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% 101.76/17.00 ((
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% 101.76/17.00 (quantDeMorgan2) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan3) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan4) =>
% 101.76/17.00 ((
% 101.76/17.00 (prop2setI) =>
% 101.76/17.00 ((
% 101.76/17.00 (prop2set2propI) =>
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% 101.76/17.00 (setunion__Cong) =>
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% 101.76/17.00 (descr__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (dsetconstr__Cong) =>
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% 101.76/17.00 (subsetI1) =>
% 101.76/17.00 ((
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% 101.76/17.00 (subsetE2) =>
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% 101.76/17.00 (notsubsetI) =>
% 101.76/17.00 ((
% 101.76/17.00 (notequalI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (notequalI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetRefl) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetTrans) =>
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% 101.76/17.00 ((
% 101.76/17.00 (setadjoinSub2) =>
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% 101.76/17.00 (sepInPowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (sepSubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairset2IR) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionIR) =>
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% 101.76/17.00 (binunionEcases) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionE) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionLsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionRsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectI) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset5) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectEL) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectLsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset2) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset3) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectER) =>
% 101.76/17.00 ((
% 101.76/17.00 (disjointsetsI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectRsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset4) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset1) =>
% 101.76/17.00 ((
% 101.76/17.00 (bs114d) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusI) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusEL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusER) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusSubset2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusERneg) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (setminusILneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusIRneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusLsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusSubset1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffE) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffIneg1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffIneg2) =>
% 101.76/17.00 ((
% 101.76/17.00 (secondinupair) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairiskpair) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairp) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonsubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletoninpowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletoninpowunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairset2E) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairsubunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairinpowunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem1) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem2) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem3) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairin) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempair1) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempair) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionE2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton1) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1E1) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1I) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1I2) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonsuniq) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL1) =>
% 101.76/17.00 ((
% 101.76/17.00 (kfstsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (theprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (kfstpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodfstin) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR11) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR12) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR1) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairequniteq) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR) =>
% 101.76/17.00 ((
% 101.76/17.00 (ksndsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (ksndpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairsurjEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodsndin) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairmemEL) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairmemER) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempaircEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodfstpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodsndpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairsurjEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrI) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrSub) =>
% 101.76/17.00 ((
% 101.76/17.00 (setOfPairsIsBReln) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrERa) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrEL1) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrEL2) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrER) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcImageSingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (apProp) =>
% 101.76/17.00 ((
% 101.76/17.00 (app) =>
% 101.76/17.00 ((
% 101.76/17.00 (infuncsetfunc) =>
% 101.76/17.00 ((
% 101.76/17.00 (ap2p) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcinfuncset) =>
% 101.76/17.00 ((
% 101.76/17.00 (lamProp) =>
% 101.76/17.00 ((
% 101.76/17.00 (lamp) =>
% 101.76/17.00 ((
% 101.76/17.00 (lam2p) =>
% 101.76/17.00 ((
% 101.76/17.00 (brelnall1) =>
% 101.76/17.00 ((
% 101.76/17.00 (brelnall2) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (funcGraphProp3) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (funcextLem) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcGraphProp4) =>
% 101.76/17.00 ((
% 101.76/17.00 (subbreln) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqbreln) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (funcext2) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (ap2apEq2) =>
% 101.76/17.00 ((
% 101.76/17.00 (beta1) =>
% 101.76/17.00 ((
% 101.76/17.00 (eta1) =>
% 101.76/17.00 ((
% 101.76/17.00 (lam2lamEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (beta2) =>
% 101.76/17.00 ((
% 101.76/17.00 (eta2) =>
% 101.76/17.00 ((
% 101.76/17.00 (iffalseProp1) =>
% 101.76/17.00 ((
% 101.76/17.00 (iffalseProp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (iftrueProp1) =>
% 101.76/17.00 ((
% 101.76/17.00 (iftrueProp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (ifSingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (ifp) =>
% 101.76/17.00 ((
% 101.76/17.00 (theeq) =>
% 101.76/17.00 ((
% 101.76/17.00 (iftrue) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (iftrueorfalse) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (binunionT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetT_lem) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (complementT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (setextT) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetTI) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (complementTI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectTELcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectTERcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT1) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT2) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT3) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementSub1) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementSub2) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTnotintersectT) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementImpComplementIntersect) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementSubsetComplementIntersect) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementInPowersetComplementIntersect) =>
% 101.76/17.00 ((
% 101.76/17.00 (contraSubsetComplement) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTcontraSubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTILcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTIRcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (inIntersectImpInUnion) =>
% 101.76/17.00 ((
% 101.76/17.00 (inIntersectImpInUnion2) =>
% 101.76/17.00 ((
% 101.76/17.00 (inIntersectImpInIntersectUnions) =>
% 101.76/17.00 ((
% 101.76/17.00 (intersectInPowersetIntersectUnions) =>
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% 101.76/17.00 (inComplementUnionImpNotIn1) =>
% 101.76/17.00 ((
% 101.76/17.00 (inComplementUnionImpInComplement1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTE) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTEcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a1) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementUnionInPowersetComplement) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a2) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1a) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1b) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2b2) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2b) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule0) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (woz13rule2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule3) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule4) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (woz1_2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_3) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_4) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_5) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1all2) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1SetBreln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (choice2fnsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (setOfPairsIsBReln1) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (breln1invI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1invE) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (breln1compI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compEex) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionEcases) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionCommutes) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2Ex) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2W) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (woz2B) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Ex) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Ex1) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Equiv) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1E) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1I) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncInInjFuncSet) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncSetFuncIn) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncSetFuncInj) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjFuncSetFuncIn) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjFuncSetFuncSurj) =>
% 101.76/17.00 ((
% 101.76/17.00 (leftInvIsSurj) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjCantorThm) =>
% 101.76/17.00 ((
% 101.76/17.00 (foundation2) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinself) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinself2) =>
% 101.76/17.00 ((
% 101.76/17.00 (omegaSp) =>
% 101.76/17.00 ((
% 101.76/17.00 (omegaSclos) =>
% 101.76/17.00 ((
% 101.76/17.00 (peano0notS) =>
% 101.76/17.00 ((
% 101.76/17.00 (peanoSinj) =>
% 101.76/17.00 ((
% 101.76/17.00 (transitivesetOp1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintTransitive) =>
% 101.76/17.00 ((
% 101.76/17.00 (transitivesetOp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionTransitive) =>
% 101.76/17.00 ((
% 101.76/17.00 (ordinalMinLem1) =>
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y0 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (ordinal @
% 101.76/17.00 Y0) =>
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y1 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y2 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (in @
% 101.76/17.00 Y2 @
% 101.76/17.00 Y0) =>
% 101.76/17.00 ((
% 101.76/17.00 (in @
% 101.76/17.00 Y1 @
% 101.76/17.00 Y2) =>
% 101.76/17.00 (in @
% 101.76/17.00 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])).
% 101.76/17.00 thf(zip_derived_cl28, plain,
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% 101.76/17.00 (((omegaIndAx) =>
% 101.76/17.00 (((replAx) =>
% 101.76/17.00 (((foundationAx) =>
% 101.76/17.00 (((wellorderingAx) =>
% 101.76/17.00 (((descrp) =>
% 101.76/17.00 (((dsetconstrI) =>
% 101.76/17.00 (((dsetconstrEL) =>
% 101.76/17.00 (((dsetconstrER) =>
% 101.76/17.00 (((exuE1) =>
% 101.76/17.00 (((prop2setE) =>
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% 101.76/17.00 (((notinemptyset) =>
% 101.76/17.00 (((exuE3e) =>
% 101.76/17.00 (((setext) =>
% 101.76/17.00 (((emptyI) =>
% 101.76/17.00 (((noeltsimpempty) =>
% 101.76/17.00 (((setbeta) =>
% 101.76/17.00 (((nonemptyE1) =>
% 101.76/17.00 (((nonemptyI) =>
% 101.76/17.00 (((nonemptyI1) =>
% 101.76/17.00 (((setadjoinIL) =>
% 101.76/17.00 (((in @ emptyset @
% 101.76/17.00 (setadjoin @
% 101.76/17.00 emptyset @ emptyset)) =>
% 101.76/17.00 (((setadjoinIR) =>
% 101.76/17.00 (((setadjoinE) =>
% 101.76/17.00 (((setadjoinOr) =>
% 101.76/17.00 (((setoftrueEq) =>
% 101.76/17.00 (((powersetI) =>
% 101.76/17.00 (((emptyinPowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (emptyInPowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetE) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionI) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionE) =>
% 101.76/17.00 ((
% 101.76/17.00 (subPowSU) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuE2) =>
% 101.76/17.00 ((
% 101.76/17.00 (nonemptyImpWitness) =>
% 101.76/17.00 ((
% 101.76/17.00 (uniqinunit) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqinunit) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (upairsetE) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairsetIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairsetIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (emptyE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (vacuousDall) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan1) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan2) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan3) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan4) =>
% 101.76/17.00 ((
% 101.76/17.00 (prop2setI) =>
% 101.76/17.00 ((
% 101.76/17.00 (prop2set2propI) =>
% 101.76/17.00 ((
% 101.76/17.00 (notdexE) =>
% 101.76/17.00 ((
% 101.76/17.00 (notdallE) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuI3) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (inCongP) =>
% 101.76/17.00 ((
% 101.76/17.00 (in__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuE3u) =>
% 101.76/17.00 ((
% 101.76/17.00 (exu__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (setadjoin__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (powerset__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunion__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuEu) =>
% 101.76/17.00 ((
% 101.76/17.00 (descr__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (dsetconstr__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqimpsubset2) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqimpsubset1) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (emptysetsubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetE) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetE2) =>
% 101.76/17.00 ((
% 101.76/17.00 (notsubsetI) =>
% 101.76/17.00 ((
% 101.76/17.00 (notequalI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (notequalI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetRefl) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetTrans) =>
% 101.76/17.00 ((
% 101.76/17.00 (setadjoinSub) =>
% 101.76/17.00 ((
% 101.76/17.00 (setadjoinSub2) =>
% 101.76/17.00 ((
% 101.76/17.00 (subset2powerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (setextsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetemptysetimpeq) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (inPowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetsubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (sepInPowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (sepSubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairset2IR) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionEcases) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionE) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionLsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionRsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectI) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset5) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectEL) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectLsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset2) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset3) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectER) =>
% 101.76/17.00 ((
% 101.76/17.00 (disjointsetsI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectRsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset4) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset1) =>
% 101.76/17.00 ((
% 101.76/17.00 (bs114d) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusI) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusEL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusER) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusSubset2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusERneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusELneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusILneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusIRneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusLsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusSubset1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffE) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffIneg1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffIneg2) =>
% 101.76/17.00 ((
% 101.76/17.00 (secondinupair) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairiskpair) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairp) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonsubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletoninpowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletoninpowunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairset2E) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairsubunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairinpowunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem1) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem2) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem3) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairin) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempair1) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempair) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionE2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton1) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1E1) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1I) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1I2) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonsuniq) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL1) =>
% 101.76/17.00 ((
% 101.76/17.00 (kfstsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (theprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (kfstpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodfstin) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR11) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR12) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR1) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairequniteq) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR) =>
% 101.76/17.00 ((
% 101.76/17.00 (ksndsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (ksndpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairsurjEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodsndin) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairmemEL) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairmemER) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempaircEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodfstpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodsndpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairsurjEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrI) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrSub) =>
% 101.76/17.00 ((
% 101.76/17.00 (setOfPairsIsBReln) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrER) =>
% 101.76/17.00 ((
% 101.76/17.00 (funcImageSingleton) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (funcGraphProp3) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (complementUnionInPowersetComplement) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a2) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1a) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1b) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2b2) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2b) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule0) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule1) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule3) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule4) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_1) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_3) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_4) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_5) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1all2) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1SetBreln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (choice2fnsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (setOfPairsIsBReln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1all1) =>
% 101.76/17.00 ((
% 101.76/17.00 (subbreln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqbreln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1invprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1invI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1invE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compEex) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionEcases) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionCommutes) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2Ex) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2W) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2A) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2B) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Ex) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Ex1) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Equiv) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1E) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1I) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncInInjFuncSet) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncSetFuncIn) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncSetFuncInj) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjFuncSetFuncIn) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjFuncSetFuncSurj) =>
% 101.76/17.00 ((
% 101.76/17.00 (leftInvIsSurj) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjCantorThm) =>
% 101.76/17.00 ((
% 101.76/17.00 (foundation2) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinself) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinself2) =>
% 101.76/17.00 ((
% 101.76/17.00 (omegaSp) =>
% 101.76/17.00 ((
% 101.76/17.00 (omegaSclos) =>
% 101.76/17.00 ((
% 101.76/17.00 (peano0notS) =>
% 101.76/17.00 ((
% 101.76/17.00 (peanoSinj) =>
% 101.76/17.00 ((
% 101.76/17.00 (transitivesetOp1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintTransitive) =>
% 101.76/17.00 ((
% 101.76/17.00 (transitivesetOp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionTransitive) =>
% 101.76/17.00 ((
% 101.76/17.00 (ordinalMinLem1) =>
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y0 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (ordinal @
% 101.76/17.00 Y0) =>
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y1 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y2 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (in @
% 101.76/17.00 Y2 @
% 101.76/17.00 Y0) =>
% 101.76/17.00 ((
% 101.76/17.00 (in @
% 101.76/17.00 Y1 @
% 101.76/17.00 Y2) =>
% 101.76/17.00 (in @
% 101.76/17.00 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])).
% 101.76/17.00 thf(zip_derived_cl34, plain,
% 101.76/17.00 (~ (((omegaIndAx) =>
% 101.76/17.00 (((replAx) =>
% 101.76/17.00 (((foundationAx) =>
% 101.76/17.00 (((wellorderingAx) =>
% 101.76/17.00 (((descrp) =>
% 101.76/17.00 (((dsetconstrI) =>
% 101.76/17.00 (((dsetconstrEL) =>
% 101.76/17.00 (((dsetconstrER) =>
% 101.76/17.00 (((exuE1) =>
% 101.76/17.00 (((prop2setE) =>
% 101.76/17.00 (((emptysetE) =>
% 101.76/17.00 (((emptysetimpfalse) =>
% 101.76/17.00 (((notinemptyset) =>
% 101.76/17.00 (((exuE3e) =>
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% 101.76/17.00 (((emptyI) =>
% 101.76/17.00 (((noeltsimpempty) =>
% 101.76/17.00 (((setbeta) =>
% 101.76/17.00 (((nonemptyE1) =>
% 101.76/17.00 (((nonemptyI) =>
% 101.76/17.00 (((nonemptyI1) =>
% 101.76/17.00 (((setadjoinIL) =>
% 101.76/17.00 (((in @ emptyset @
% 101.76/17.00 (setadjoin @ emptyset @
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% 101.76/17.00 (((setadjoinIR) =>
% 101.76/17.00 (((setadjoinE) =>
% 101.76/17.00 (((setadjoinOr) =>
% 101.76/17.00 (((setoftrueEq) =>
% 101.76/17.00 (((powersetI) =>
% 101.76/17.00 (((emptyinPowerset) =>
% 101.76/17.00 (((emptyInPowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetE) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionI) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionE) =>
% 101.76/17.00 ((
% 101.76/17.00 (subPowSU) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuE2) =>
% 101.76/17.00 ((
% 101.76/17.00 (nonemptyImpWitness) =>
% 101.76/17.00 ((
% 101.76/17.00 (uniqinunit) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqinunit) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonsswitch) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairsetE) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairsetIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairsetIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (emptyE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (vacuousDall) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan1) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan2) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan3) =>
% 101.76/17.00 ((
% 101.76/17.00 (quantDeMorgan4) =>
% 101.76/17.00 ((
% 101.76/17.00 (prop2setI) =>
% 101.76/17.00 ((
% 101.76/17.00 (prop2set2propI) =>
% 101.76/17.00 ((
% 101.76/17.00 (notdexE) =>
% 101.76/17.00 ((
% 101.76/17.00 (notdallE) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuI3) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (inCongP) =>
% 101.76/17.00 ((
% 101.76/17.00 (in__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuE3u) =>
% 101.76/17.00 ((
% 101.76/17.00 (exu__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (setadjoin__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (powerset__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunion__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuEu) =>
% 101.76/17.00 ((
% 101.76/17.00 (descr__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (dsetconstr__Cong) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqimpsubset2) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqimpsubset1) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (emptysetsubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetE) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetE2) =>
% 101.76/17.00 ((
% 101.76/17.00 (notsubsetI) =>
% 101.76/17.00 ((
% 101.76/17.00 (notequalI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (notequalI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetRefl) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetTrans) =>
% 101.76/17.00 ((
% 101.76/17.00 (setadjoinSub) =>
% 101.76/17.00 ((
% 101.76/17.00 (setadjoinSub2) =>
% 101.76/17.00 ((
% 101.76/17.00 (subset2powerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (setextsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetemptysetimpeq) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (inPowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetsubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (sepInPowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (sepSubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairset2IR) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionEcases) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionE) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionLsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionRsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectI) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset5) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectEL) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectLsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset2) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset3) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectER) =>
% 101.76/17.00 ((
% 101.76/17.00 (disjointsetsI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectRsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset4) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectSubset1) =>
% 101.76/17.00 ((
% 101.76/17.00 (bs114d) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusI) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusEL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusER) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusSubset2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusERneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusELneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusILneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusIRneg) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusLsub) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusSubset1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffE) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffI2) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffIneg1) =>
% 101.76/17.00 ((
% 101.76/17.00 (symdiffIneg2) =>
% 101.76/17.00 ((
% 101.76/17.00 (secondinupair) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairiskpair) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairp) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonsubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletoninpowerset) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletoninpowunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairset2E) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairsubunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairinpowunion) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem1) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem2) =>
% 101.76/17.00 ((
% 101.76/17.00 (ubforcartprodlem3) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairin) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempair1) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempair) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionE2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton1) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1E1) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1I) =>
% 101.76/17.00 ((
% 101.76/17.00 (ex1I2) =>
% 101.76/17.00 ((
% 101.76/17.00 (singletonsuniq) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL1) =>
% 101.76/17.00 ((
% 101.76/17.00 (kfstsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (theprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (kfstpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodfstin) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjL) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR11) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR12) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR1) =>
% 101.76/17.00 ((
% 101.76/17.00 (upairequniteq) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setukpairinjR) =>
% 101.76/17.00 ((
% 101.76/17.00 (ksndsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (ksndpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (kpairsurjEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodsndin) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairmemEL) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairmemER) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodmempaircEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodfstpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodsndpairEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (cartprodpairsurjEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrI) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrSub) =>
% 101.76/17.00 ((
% 101.76/17.00 (setOfPairsIsBReln) =>
% 101.76/17.00 ((
% 101.76/17.00 (dpsetconstrERa) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (ap2apEq2) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
% 101.76/17.00 (eta1) =>
% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 ((
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% 101.76/17.00 (iftrueProp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (ifSingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (ifp) =>
% 101.76/17.00 ((
% 101.76/17.00 (theeq) =>
% 101.76/17.00 ((
% 101.76/17.00 (iftrue) =>
% 101.76/17.00 ((
% 101.76/17.00 (iffalse) =>
% 101.76/17.00 ((
% 101.76/17.00 (iftrueorfalse) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (setminusT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementT_lem) =>
% 101.76/17.00 ((
% 101.76/17.00 (setextT) =>
% 101.76/17.00 ((
% 101.76/17.00 (subsetTI) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetTI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (powersetTE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectTELcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintersectTERcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT1) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT2) =>
% 101.76/17.00 ((
% 101.76/17.00 (contrasubsetT3) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementI1) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementE1) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementSub1) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementSub2) =>
% 101.76/17.00 ((
% 101.76/17.00 (doubleComplementEq) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTnotintersectT) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementImpComplementIntersect) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementSubsetComplementIntersect) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementInPowersetComplementIntersect) =>
% 101.76/17.00 ((
% 101.76/17.00 (contraSubsetComplement) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementTcontraSubset) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTILcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTIRcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (inIntersectImpInUnion) =>
% 101.76/17.00 ((
% 101.76/17.00 (inIntersectImpInUnion2) =>
% 101.76/17.00 ((
% 101.76/17.00 (inIntersectImpInIntersectUnions) =>
% 101.76/17.00 ((
% 101.76/17.00 (intersectInPowersetIntersectUnions) =>
% 101.76/17.00 ((
% 101.76/17.00 (inComplementUnionImpNotIn1) =>
% 101.76/17.00 ((
% 101.76/17.00 (inComplementUnionImpInComplement1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTE) =>
% 101.76/17.00 ((
% 101.76/17.00 (binunionTEcontra) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a1) =>
% 101.76/17.00 ((
% 101.76/17.00 (complementUnionInPowersetComplement) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a2) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1a) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1b) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan1) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2a) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2b2) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2b) =>
% 101.76/17.00 ((
% 101.76/17.00 (demorgan2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule0) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule1) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule3) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz13rule4) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_1) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_2) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_3) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_4) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz1_5) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1all2) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1SetBreln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (choice2fnsingleton) =>
% 101.76/17.00 ((
% 101.76/17.00 (setOfPairsIsBReln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1all1) =>
% 101.76/17.00 ((
% 101.76/17.00 (subbreln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (eqbreln1) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1invprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1invI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1invE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1compEex) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionprop) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionIL) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionIR) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionI) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionE) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionEcases) =>
% 101.76/17.00 ((
% 101.76/17.00 (breln1unionCommutes) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2Ex) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2W) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2A) =>
% 101.76/17.00 ((
% 101.76/17.00 (woz2B) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Ex) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Ex1) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1Equiv) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1E) =>
% 101.76/17.00 ((
% 101.76/17.00 (image1I) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncInInjFuncSet) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncSetFuncIn) =>
% 101.76/17.00 ((
% 101.76/17.00 (injFuncSetFuncInj) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjFuncSetFuncIn) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjFuncSetFuncSurj) =>
% 101.76/17.00 ((
% 101.76/17.00 (leftInvIsSurj) =>
% 101.76/17.00 ((
% 101.76/17.00 (surjCantorThm) =>
% 101.76/17.00 ((
% 101.76/17.00 (foundation2) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinself) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinself2) =>
% 101.76/17.00 ((
% 101.76/17.00 (omegaSp) =>
% 101.76/17.00 ((
% 101.76/17.00 (omegaSclos) =>
% 101.76/17.00 ((
% 101.76/17.00 (peano0notS) =>
% 101.76/17.00 ((
% 101.76/17.00 (peanoSinj) =>
% 101.76/17.00 ((
% 101.76/17.00 (transitivesetOp1) =>
% 101.76/17.00 ((
% 101.76/17.00 (binintTransitive) =>
% 101.76/17.00 ((
% 101.76/17.00 (transitivesetOp2) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionTransitive) =>
% 101.76/17.00 ((
% 101.76/17.00 (ordinalMinLem1) =>
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y0 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (ordinal @
% 101.76/17.00 Y0) =>
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y1 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (!!) @ (
% 101.76/17.00 ^[Y2 : $i]:
% 101.76/17.00 ((
% 101.76/17.00 (in @
% 101.76/17.00 Y2 @
% 101.76/17.00 Y0) =>
% 101.76/17.00 ((
% 101.76/17.00 (in @
% 101.76/17.00 Y1 @
% 101.76/17.00 Y2) =>
% 101.76/17.00 (in @
% 101.76/17.00 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl28])).
% 101.76/17.00 thf(zip_derived_cl40, plain,
% 101.76/17.00 (~ (((replAx) =>
% 101.76/17.00 (((foundationAx) =>
% 101.76/17.00 (((wellorderingAx) =>
% 101.76/17.00 (((descrp) =>
% 101.76/17.00 (((dsetconstrI) =>
% 101.76/17.00 (((dsetconstrEL) =>
% 101.76/17.00 (((dsetconstrER) =>
% 101.76/17.00 (((exuE1) =>
% 101.76/17.00 (((prop2setE) =>
% 101.76/17.00 (((emptysetE) =>
% 101.76/17.00 (((emptysetimpfalse) =>
% 101.76/17.00 (((notinemptyset) =>
% 101.76/17.00 (((exuE3e) =>
% 101.76/17.00 (((setext) =>
% 101.76/17.00 (((emptyI) =>
% 101.76/17.00 (((noeltsimpempty) =>
% 101.76/17.00 (((setbeta) =>
% 101.76/17.00 (((nonemptyE1) =>
% 101.76/17.00 (((nonemptyI) =>
% 101.76/17.00 (((nonemptyI1) =>
% 101.76/17.00 (((setadjoinIL) =>
% 101.76/17.00 (((in @ emptyset @
% 101.76/17.00 (setadjoin @ emptyset @
% 101.76/17.00 emptyset)) =>
% 101.76/17.00 (((setadjoinIR) =>
% 101.76/17.00 (((setadjoinE) =>
% 101.76/17.00 (((setadjoinOr) =>
% 101.76/17.00 (((setoftrueEq) =>
% 101.76/17.00 (((powersetI) =>
% 101.76/17.00 (((emptyinPowerset) =>
% 101.76/17.00 (((emptyInPowerset) =>
% 101.76/17.00 (((powersetE) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionI) =>
% 101.76/17.00 ((
% 101.76/17.00 (setunionE) =>
% 101.76/17.00 ((
% 101.76/17.00 (subPowSU) =>
% 101.76/17.00 ((
% 101.76/17.00 (exuE2) =>
% 101.76/17.00 ((
% 101.76/17.00 (nonemptyImpWitness) =>
% 101.76/17.00 ((
% 101.76/17.00 (uniqinunit) =>
% 101.76/17.00 ((
% 101.76/17.00 (notinsingleton) =>
% 101.76/17.00 ((
% 101.76/17.01 (eqinunit) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletonsswitch) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairsetE) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairsetIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairsetIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (emptyE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (vacuousDall) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan1) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan2) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan3) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan4) =>
% 101.76/17.01 ((
% 101.76/17.01 (prop2setI) =>
% 101.76/17.01 ((
% 101.76/17.01 (prop2set2propI) =>
% 101.76/17.01 ((
% 101.76/17.01 (notdexE) =>
% 101.76/17.01 ((
% 101.76/17.01 (notdallE) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuI3) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuI2) =>
% 101.76/17.01 ((
% 101.76/17.01 (inCongP) =>
% 101.76/17.01 ((
% 101.76/17.01 (in__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuE3u) =>
% 101.76/17.01 ((
% 101.76/17.01 (exu__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (setadjoin__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (powerset__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunion__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuEu) =>
% 101.76/17.01 ((
% 101.76/17.01 (descr__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (dsetconstr__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqimpsubset2) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqimpsubset1) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetI2) =>
% 101.76/17.01 ((
% 101.76/17.01 (emptysetsubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetE) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetE2) =>
% 101.76/17.01 ((
% 101.76/17.01 (notsubsetI) =>
% 101.76/17.01 ((
% 101.76/17.01 (notequalI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (notequalI2) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetRefl) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetTrans) =>
% 101.76/17.01 ((
% 101.76/17.01 (setadjoinSub) =>
% 101.76/17.01 ((
% 101.76/17.01 (setadjoinSub2) =>
% 101.76/17.01 ((
% 101.76/17.01 (subset2powerset) =>
% 101.76/17.01 ((
% 101.76/17.01 (setextsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetemptysetimpeq) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (inPowerset) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetsubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (sepInPowerset) =>
% 101.76/17.01 ((
% 101.76/17.01 (sepSubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairset2IR) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionEcases) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionE) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionLsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionRsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectI) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset5) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectEL) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectLsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset2) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset3) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectER) =>
% 101.76/17.01 ((
% 101.76/17.01 (disjointsetsI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectRsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset4) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset1) =>
% 101.76/17.01 ((
% 101.76/17.01 (bs114d) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusI) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusEL) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusER) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusSubset2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusERneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusELneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusILneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusIRneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusLsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusSubset1) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffE) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffI2) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffIneg1) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffIneg2) =>
% 101.76/17.01 ((
% 101.76/17.01 (secondinupair) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (kpairiskpair) =>
% 101.76/17.01 ((
% 101.76/17.01 (kpairp) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletonsubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletoninpowerset) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletoninpowunion) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairset2E) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairsubunion) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairinpowunion) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem1) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem3) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairin) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodmempair1) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodmempair) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionE2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionsingleton1) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionsingleton2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletonprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (ex1E1) =>
% 101.76/17.01 ((
% 101.76/17.01 (ex1I) =>
% 101.76/17.01 ((
% 101.76/17.01 (ex1I2) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletonsuniq) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL1) =>
% 101.76/17.01 ((
% 101.76/17.01 (kfstsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (theprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (kfstpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodfstin) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR11) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR12) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR1) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairequniteq) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR) =>
% 101.76/17.01 ((
% 101.76/17.01 (ksndsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (ksndpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (kpairsurjEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodsndin) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairmemEL) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairmemER) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodmempaircEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodfstpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodsndpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairsurjEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrI) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrSub) =>
% 101.76/17.01 ((
% 101.76/17.01 (setOfPairsIsBReln) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrERa) =>
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% 101.76/17.01 (dpsetconstrEL1) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrEL2) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrER) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcImageSingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (apProp) =>
% 101.76/17.01 ((
% 101.76/17.01 (app) =>
% 101.76/17.01 ((
% 101.76/17.01 (infuncsetfunc) =>
% 101.76/17.01 ((
% 101.76/17.01 (ap2p) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcinfuncset) =>
% 101.76/17.01 ((
% 101.76/17.01 (lamProp) =>
% 101.76/17.01 ((
% 101.76/17.01 (lamp) =>
% 101.76/17.01 ((
% 101.76/17.01 (lam2p) =>
% 101.76/17.01 ((
% 101.76/17.01 (brelnall1) =>
% 101.76/17.01 ((
% 101.76/17.01 (brelnall2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ex1E2) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp1) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp3) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp2) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcextLem) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp4) =>
% 101.76/17.01 ((
% 101.76/17.01 (subbreln) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqbreln) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcext) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcext2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ap2apEq1) =>
% 101.76/17.01 ((
% 101.76/17.01 (ap2apEq2) =>
% 101.76/17.01 ((
% 101.76/17.01 (beta1) =>
% 101.76/17.01 ((
% 101.76/17.01 (eta1) =>
% 101.76/17.01 ((
% 101.76/17.01 (lam2lamEq) =>
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% 101.76/17.01 (beta2) =>
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% 101.76/17.01 (iffalseProp2) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrueProp1) =>
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% 101.76/17.01 (iftrueProp2) =>
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% 101.76/17.01 (ifp) =>
% 101.76/17.01 ((
% 101.76/17.01 (theeq) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrue) =>
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% 101.76/17.01 (iffalse) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrueorfalse) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetT_lem) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (complementT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (setextT) =>
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% 101.76/17.01 (subsetTI) =>
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% 101.76/17.01 (complementTI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementTE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectTELcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectTERcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT1) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT2) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT3) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementSub1) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementSub2) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementTnotintersectT) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementImpComplementIntersect) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementSubsetComplementIntersect) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementInPowersetComplementIntersect) =>
% 101.76/17.01 ((
% 101.76/17.01 (contraSubsetComplement) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementTcontraSubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTILcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTIRcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (inIntersectImpInUnion) =>
% 101.76/17.01 ((
% 101.76/17.01 (inIntersectImpInUnion2) =>
% 101.76/17.01 ((
% 101.76/17.01 (inIntersectImpInIntersectUnions) =>
% 101.76/17.01 ((
% 101.76/17.01 (intersectInPowersetIntersectUnions) =>
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% 101.76/17.01 (inComplementUnionImpNotIn1) =>
% 101.76/17.01 ((
% 101.76/17.01 (inComplementUnionImpInComplement1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTE) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTEcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan2a1) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementUnionInPowersetComplement) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan2a2) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan1a) =>
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% 101.76/17.01 (demorgan1b) =>
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% 101.76/17.01 (demorgan1) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan2a) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan2b2) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan2b) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan2) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz13rule0) =>
% 101.76/17.01 ((
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% 101.76/17.01 (woz13rule2) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz13rule3) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz13rule4) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (woz1_2) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz1_3) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz1_4) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz1_5) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1all2) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1SetBreln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (choice2fnsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (setOfPairsIsBReln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1all1) =>
% 101.76/17.01 ((
% 101.76/17.01 (subbreln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqbreln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1invprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1invI) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1invE) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1compprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1compI) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1compE) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1compEex) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionI) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionE) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionEcases) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionCommutes) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2Ex) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2W) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2A) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2B) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1Ex) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1Ex1) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1Equiv) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1E) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1I) =>
% 101.76/17.01 ((
% 101.76/17.01 (injFuncInInjFuncSet) =>
% 101.76/17.01 ((
% 101.76/17.01 (injFuncSetFuncIn) =>
% 101.76/17.01 ((
% 101.76/17.01 (injFuncSetFuncInj) =>
% 101.76/17.01 ((
% 101.76/17.01 (surjFuncSetFuncIn) =>
% 101.76/17.01 ((
% 101.76/17.01 (surjFuncSetFuncSurj) =>
% 101.76/17.01 ((
% 101.76/17.01 (leftInvIsSurj) =>
% 101.76/17.01 ((
% 101.76/17.01 (surjCantorThm) =>
% 101.76/17.01 ((
% 101.76/17.01 (foundation2) =>
% 101.76/17.01 ((
% 101.76/17.01 (notinself) =>
% 101.76/17.01 ((
% 101.76/17.01 (notinself2) =>
% 101.76/17.01 ((
% 101.76/17.01 (omegaSp) =>
% 101.76/17.01 ((
% 101.76/17.01 (omegaSclos) =>
% 101.76/17.01 ((
% 101.76/17.01 (peano0notS) =>
% 101.76/17.01 ((
% 101.76/17.01 (peanoSinj) =>
% 101.76/17.01 ((
% 101.76/17.01 (transitivesetOp1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintTransitive) =>
% 101.76/17.01 ((
% 101.76/17.01 (transitivesetOp2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionTransitive) =>
% 101.76/17.01 ((
% 101.76/17.01 (ordinalMinLem1) =>
% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
% 101.76/17.01 ^[Y0 : $i]:
% 101.76/17.01 ((
% 101.76/17.01 (ordinal @
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% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
% 101.76/17.01 ^[Y1 : $i]:
% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
% 101.76/17.01 ^[Y2 : $i]:
% 101.76/17.01 ((
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% 101.76/17.01 Y0) =>
% 101.76/17.01 ((
% 101.76/17.01 (in @
% 101.76/17.01 Y1 @
% 101.76/17.01 Y2) =>
% 101.76/17.01 (in @
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% 101.76/17.01 (((setadjoinIR) =>
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan1) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan2) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan3) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (powerset__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunion__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuEu) =>
% 101.76/17.01 ((
% 101.76/17.01 (descr__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (dsetconstr__Cong) =>
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (binintersectLsub) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset3) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectER) =>
% 101.76/17.01 ((
% 101.76/17.01 (disjointsetsI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectRsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset4) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (bs114d) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (setminusSubset2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusERneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusELneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusILneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusIRneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusLsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusSubset1) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffE) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffI2) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffIneg1) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffIneg2) =>
% 101.76/17.01 ((
% 101.76/17.01 (secondinupair) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (kpairiskpair) =>
% 101.76/17.01 ((
% 101.76/17.01 (kpairp) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletonsubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletoninpowerset) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletoninpowunion) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairset2E) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairsubunion) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairinpowunion) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem1) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem3) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairin) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodmempair1) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodmempair) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionE2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionsingleton1) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionsingleton2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletonprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (ex1E1) =>
% 101.76/17.01 ((
% 101.76/17.01 (ex1I) =>
% 101.76/17.01 ((
% 101.76/17.01 (ex1I2) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletonsuniq) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL1) =>
% 101.76/17.01 ((
% 101.76/17.01 (kfstsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (theprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (kfstpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodfstin) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR11) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR12) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR1) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairequniteq) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR) =>
% 101.76/17.01 ((
% 101.76/17.01 (ksndsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (ksndpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (kpairsurjEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodsndin) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairmemEL) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairmemER) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodmempaircEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodfstpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodsndpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairsurjEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrI) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrSub) =>
% 101.76/17.01 ((
% 101.76/17.01 (setOfPairsIsBReln) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrERa) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrEL1) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrEL2) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrER) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcImageSingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (apProp) =>
% 101.76/17.01 ((
% 101.76/17.01 (app) =>
% 101.76/17.01 ((
% 101.76/17.01 (infuncsetfunc) =>
% 101.76/17.01 ((
% 101.76/17.01 (ap2p) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcinfuncset) =>
% 101.76/17.01 ((
% 101.76/17.01 (lamProp) =>
% 101.76/17.01 ((
% 101.76/17.01 (lamp) =>
% 101.76/17.01 ((
% 101.76/17.01 (lam2p) =>
% 101.76/17.01 ((
% 101.76/17.01 (brelnall1) =>
% 101.76/17.01 ((
% 101.76/17.01 (brelnall2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ex1E2) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp1) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp3) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp2) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcextLem) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp4) =>
% 101.76/17.01 ((
% 101.76/17.01 (subbreln) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqbreln) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcext) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcext2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ap2apEq1) =>
% 101.76/17.01 ((
% 101.76/17.01 (ap2apEq2) =>
% 101.76/17.01 ((
% 101.76/17.01 (beta1) =>
% 101.76/17.01 ((
% 101.76/17.01 (eta1) =>
% 101.76/17.01 ((
% 101.76/17.01 (lam2lamEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (beta2) =>
% 101.76/17.01 ((
% 101.76/17.01 (eta2) =>
% 101.76/17.01 ((
% 101.76/17.01 (iffalseProp1) =>
% 101.76/17.01 ((
% 101.76/17.01 (iffalseProp2) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrueProp1) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrueProp2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ifSingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (ifp) =>
% 101.76/17.01 ((
% 101.76/17.01 (theeq) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrue) =>
% 101.76/17.01 ((
% 101.76/17.01 (iffalse) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrueorfalse) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (setextT) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetTI) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetTI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetTE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementTI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementTE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectTELcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectTERcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT1) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT2) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT3) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementSub1) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementSub2) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementTnotintersectT) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementImpComplementIntersect) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementSubsetComplementIntersect) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementInPowersetComplementIntersect) =>
% 101.76/17.01 ((
% 101.76/17.01 (contraSubsetComplement) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementTcontraSubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTILcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTIRcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (inIntersectImpInUnion) =>
% 101.76/17.01 ((
% 101.76/17.01 (inIntersectImpInUnion2) =>
% 101.76/17.01 ((
% 101.76/17.01 (inIntersectImpInIntersectUnions) =>
% 101.76/17.01 ((
% 101.76/17.01 (intersectInPowersetIntersectUnions) =>
% 101.76/17.01 ((
% 101.76/17.01 (inComplementUnionImpNotIn1) =>
% 101.76/17.01 ((
% 101.76/17.01 (inComplementUnionImpInComplement1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTE) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTEcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan2a1) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementUnionInPowersetComplement) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan2a2) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan1a) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan1b) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan1) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan2a) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan2b2) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan2b) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan2) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz13rule0) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz13rule1) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz13rule2) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz13rule3) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz13rule4) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz1_1) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz1_2) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz1_3) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz1_4) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz1_5) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1all2) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1SetBreln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (choice2fnsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (setOfPairsIsBReln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1all1) =>
% 101.76/17.01 ((
% 101.76/17.01 (subbreln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqbreln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1invprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1invI) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1invE) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1compprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1compI) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1compE) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1compEex) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionI) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionE) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionEcases) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionCommutes) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2Ex) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2W) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2A) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2B) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1Ex) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1Ex1) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1Equiv) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1E) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1I) =>
% 101.76/17.01 ((
% 101.76/17.01 (injFuncInInjFuncSet) =>
% 101.76/17.01 ((
% 101.76/17.01 (injFuncSetFuncIn) =>
% 101.76/17.01 ((
% 101.76/17.01 (injFuncSetFuncInj) =>
% 101.76/17.01 ((
% 101.76/17.01 (surjFuncSetFuncIn) =>
% 101.76/17.01 ((
% 101.76/17.01 (surjFuncSetFuncSurj) =>
% 101.76/17.01 ((
% 101.76/17.01 (leftInvIsSurj) =>
% 101.76/17.01 ((
% 101.76/17.01 (surjCantorThm) =>
% 101.76/17.01 ((
% 101.76/17.01 (foundation2) =>
% 101.76/17.01 ((
% 101.76/17.01 (notinself) =>
% 101.76/17.01 ((
% 101.76/17.01 (notinself2) =>
% 101.76/17.01 ((
% 101.76/17.01 (omegaSp) =>
% 101.76/17.01 ((
% 101.76/17.01 (omegaSclos) =>
% 101.76/17.01 ((
% 101.76/17.01 (peano0notS) =>
% 101.76/17.01 ((
% 101.76/17.01 (peanoSinj) =>
% 101.76/17.01 ((
% 101.76/17.01 (transitivesetOp1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintTransitive) =>
% 101.76/17.01 ((
% 101.76/17.01 (transitivesetOp2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionTransitive) =>
% 101.76/17.01 ((
% 101.76/17.01 (ordinalMinLem1) =>
% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
% 101.76/17.01 ^[Y0 : $i]:
% 101.76/17.01 ((
% 101.76/17.01 (ordinal @
% 101.76/17.01 Y0) =>
% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
% 101.76/17.01 ^[Y1 : $i]:
% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
% 101.76/17.01 ^[Y2 : $i]:
% 101.76/17.01 ((
% 101.76/17.01 (in @
% 101.76/17.01 Y2 @
% 101.76/17.01 Y0) =>
% 101.76/17.01 ((
% 101.76/17.01 (in @
% 101.76/17.01 Y1 @
% 101.76/17.01 Y2) =>
% 101.76/17.01 (in @
% 101.76/17.01 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
% 101.76/17.01 thf(zip_derived_cl50, plain,
% 101.76/17.01 (~ (((wellorderingAx) =>
% 101.76/17.01 (((descrp) =>
% 101.76/17.01 (((dsetconstrI) =>
% 101.76/17.01 (((dsetconstrEL) =>
% 101.76/17.01 (((dsetconstrER) =>
% 101.76/17.01 (((exuE1) =>
% 101.76/17.01 (((prop2setE) =>
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% 101.76/17.01 (((emptysetimpfalse) =>
% 101.76/17.01 (((notinemptyset) =>
% 101.76/17.01 (((exuE3e) =>
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% 101.76/17.01 (((emptyI) =>
% 101.76/17.01 (((noeltsimpempty) =>
% 101.76/17.01 (((setbeta) =>
% 101.76/17.01 (((nonemptyE1) =>
% 101.76/17.01 (((nonemptyI) =>
% 101.76/17.01 (((nonemptyI1) =>
% 101.76/17.01 (((setadjoinIL) =>
% 101.76/17.01 (((in @ emptyset @
% 101.76/17.01 (setadjoin @ emptyset @
% 101.76/17.01 emptyset)) =>
% 101.76/17.01 (((setadjoinIR) =>
% 101.76/17.01 (((setadjoinE) =>
% 101.76/17.01 (((setadjoinOr) =>
% 101.76/17.01 (((setoftrueEq) =>
% 101.76/17.01 (((powersetI) =>
% 101.76/17.01 (((emptyinPowerset) =>
% 101.76/17.01 (((emptyInPowerset) =>
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% 101.76/17.01 (((setunionI) =>
% 101.76/17.01 (((setunionE) =>
% 101.76/17.01 ((
% 101.76/17.01 (subPowSU) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuE2) =>
% 101.76/17.01 ((
% 101.76/17.01 (nonemptyImpWitness) =>
% 101.76/17.01 ((
% 101.76/17.01 (uniqinunit) =>
% 101.76/17.01 ((
% 101.76/17.01 (notinsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqinunit) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (upairsetE) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairsetIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairsetIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (emptyE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (vacuousDall) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan1) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan2) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan3) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan4) =>
% 101.76/17.01 ((
% 101.76/17.01 (prop2setI) =>
% 101.76/17.01 ((
% 101.76/17.01 (prop2set2propI) =>
% 101.76/17.01 ((
% 101.76/17.01 (notdexE) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (exuI3) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuI2) =>
% 101.76/17.01 ((
% 101.76/17.01 (inCongP) =>
% 101.76/17.01 ((
% 101.76/17.01 (in__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuE3u) =>
% 101.76/17.01 ((
% 101.76/17.01 (exu__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (setadjoin__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (powerset__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunion__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuEu) =>
% 101.76/17.01 ((
% 101.76/17.01 (descr__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (dsetconstr__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqimpsubset2) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqimpsubset1) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetI2) =>
% 101.76/17.01 ((
% 101.76/17.01 (emptysetsubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetE) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetE2) =>
% 101.76/17.01 ((
% 101.76/17.01 (notsubsetI) =>
% 101.76/17.01 ((
% 101.76/17.01 (notequalI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (notequalI2) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetRefl) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetTrans) =>
% 101.76/17.01 ((
% 101.76/17.01 (setadjoinSub) =>
% 101.76/17.01 ((
% 101.76/17.01 (setadjoinSub2) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 (binunionRsub) =>
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% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset5) =>
% 101.76/17.01 ((
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% 101.76/17.01 (binintersectSubset3) =>
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (setminusSubset1) =>
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% 101.76/17.01 (symdiffE) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (symdiffI2) =>
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% 101.76/17.01 ((
% 101.76/17.01 (symdiffIneg2) =>
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% 101.76/17.01 (upairinpowunion) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem1) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem3) =>
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% 101.76/17.01 (kfstpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodfstin) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR11) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR12) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR1) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairequniteq) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR) =>
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% 101.76/17.01 (ksndsingleton) =>
% 101.76/17.01 ((
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% 101.76/17.01 (kpairsurjEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodsndin) =>
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% 101.76/17.01 (cartprodpairmemER) =>
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% 101.76/17.01 (cartprodmempaircEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodfstpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodsndpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairsurjEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrI) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrSub) =>
% 101.76/17.01 ((
% 101.76/17.01 (setOfPairsIsBReln) =>
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% 101.76/17.01 (dpsetconstrERa) =>
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% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrEL2) =>
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% 101.76/17.01 (dpsetconstrER) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcImageSingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (apProp) =>
% 101.76/17.01 ((
% 101.76/17.01 (app) =>
% 101.76/17.01 ((
% 101.76/17.01 (infuncsetfunc) =>
% 101.76/17.01 ((
% 101.76/17.01 (ap2p) =>
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% 101.76/17.01 (funcinfuncset) =>
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% 101.76/17.01 (lamProp) =>
% 101.76/17.01 ((
% 101.76/17.01 (lamp) =>
% 101.76/17.01 ((
% 101.76/17.01 (lam2p) =>
% 101.76/17.01 ((
% 101.76/17.01 (brelnall1) =>
% 101.76/17.01 ((
% 101.76/17.01 (brelnall2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ex1E2) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp1) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp3) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp2) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcextLem) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp4) =>
% 101.76/17.01 ((
% 101.76/17.01 (subbreln) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqbreln) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcext) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcext2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ap2apEq1) =>
% 101.76/17.01 ((
% 101.76/17.01 (ap2apEq2) =>
% 101.76/17.01 ((
% 101.76/17.01 (beta1) =>
% 101.76/17.01 ((
% 101.76/17.01 (eta1) =>
% 101.76/17.01 ((
% 101.76/17.01 (lam2lamEq) =>
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% 101.76/17.01 (beta2) =>
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% 101.76/17.01 ((
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% 101.76/17.01 (iftrueProp1) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrueProp2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ifSingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (ifp) =>
% 101.76/17.01 ((
% 101.76/17.01 (theeq) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrue) =>
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% 101.76/17.01 (iffalse) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrueorfalse) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetT_lem) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 (binintersectTELcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectTERcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT2) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT3) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementSub1) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementSub2) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementTnotintersectT) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementImpComplementIntersect) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementSubsetComplementIntersect) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementInPowersetComplementIntersect) =>
% 101.76/17.01 ((
% 101.76/17.01 (contraSubsetComplement) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementTcontraSubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTILcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTIRcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (inIntersectImpInUnion) =>
% 101.76/17.01 ((
% 101.76/17.01 (inIntersectImpInUnion2) =>
% 101.76/17.01 ((
% 101.76/17.01 (inIntersectImpInIntersectUnions) =>
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% 101.76/17.01 (intersectInPowersetIntersectUnions) =>
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% 101.76/17.01 (inComplementUnionImpNotIn1) =>
% 101.76/17.01 ((
% 101.76/17.01 (inComplementUnionImpInComplement1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTE) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTEcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (demorgan2a1) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementUnionInPowersetComplement) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (demorgan2) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 (woz13rule4) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (woz1_3) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz1_4) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz1_5) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1all2) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1SetBreln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (choice2fnsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (setOfPairsIsBReln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1all1) =>
% 101.76/17.01 ((
% 101.76/17.01 (subbreln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqbreln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1invprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1invI) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1invE) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (breln1compE) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1compEex) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionI) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionE) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionEcases) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionCommutes) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2Ex) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2W) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2A) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2B) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (image1Ex1) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1Equiv) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1E) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1I) =>
% 101.76/17.01 ((
% 101.76/17.01 (injFuncInInjFuncSet) =>
% 101.76/17.01 ((
% 101.76/17.01 (injFuncSetFuncIn) =>
% 101.76/17.01 ((
% 101.76/17.01 (injFuncSetFuncInj) =>
% 101.76/17.01 ((
% 101.76/17.01 (surjFuncSetFuncIn) =>
% 101.76/17.01 ((
% 101.76/17.01 (surjFuncSetFuncSurj) =>
% 101.76/17.01 ((
% 101.76/17.01 (leftInvIsSurj) =>
% 101.76/17.01 ((
% 101.76/17.01 (surjCantorThm) =>
% 101.76/17.01 ((
% 101.76/17.01 (foundation2) =>
% 101.76/17.01 ((
% 101.76/17.01 (notinself) =>
% 101.76/17.01 ((
% 101.76/17.01 (notinself2) =>
% 101.76/17.01 ((
% 101.76/17.01 (omegaSp) =>
% 101.76/17.01 ((
% 101.76/17.01 (omegaSclos) =>
% 101.76/17.01 ((
% 101.76/17.01 (peano0notS) =>
% 101.76/17.01 ((
% 101.76/17.01 (peanoSinj) =>
% 101.76/17.01 ((
% 101.76/17.01 (transitivesetOp1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintTransitive) =>
% 101.76/17.01 ((
% 101.76/17.01 (transitivesetOp2) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ^[Y0 : $i]:
% 101.76/17.01 ((
% 101.76/17.01 (ordinal @
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% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
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% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
% 101.76/17.01 ^[Y2 : $i]:
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (in @
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% 101.76/17.01 Y2) =>
% 101.76/17.01 (in @
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% 101.76/17.01 (binintersectSubset3) =>
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% 101.76/17.01 (binintersectER) =>
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% 101.76/17.01 (bs114d) =>
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% 101.76/17.01 (symdiffE) =>
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% 101.76/17.01 (symdiffI1) =>
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% 101.76/17.01 (symdiffI2) =>
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% 101.76/17.01 (symdiffIneg1) =>
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% 101.76/17.01 ((
% 101.76/17.01 (secondinupair) =>
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% 101.76/17.01 (setukpairIL) =>
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% 101.76/17.01 (setukpairIR) =>
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% 101.76/17.01 (kpairiskpair) =>
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% 101.76/17.01 (kpairp) =>
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% 101.76/17.01 (singletoninpowerset) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletoninpowunion) =>
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% 101.76/17.01 (upairset2E) =>
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% 101.76/17.01 (upairsubunion) =>
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% 101.76/17.01 (upairinpowunion) =>
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% 101.76/17.01 (ubforcartprodlem1) =>
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% 101.76/17.01 (ubforcartprodlem2) =>
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% 101.76/17.01 (ubforcartprodlem3) =>
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% 101.76/17.01 (setunionsingleton2) =>
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% 101.76/17.01 (ex1I2) =>
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% 101.76/17.01 (singletonsuniq) =>
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% 101.76/17.01 (setukpairinjL1) =>
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% 101.76/17.01 (setukpairinjL2) =>
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% 101.76/17.01 (setukpairinjL) =>
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% 101.76/17.01 (setukpairinjR11) =>
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% 101.76/17.01 (setukpairinjR12) =>
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% 101.76/17.01 (setukpairinjR1) =>
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% 101.76/17.01 (upairequniteq) =>
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% 101.76/17.01 (setukpairinjR2) =>
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% 101.76/17.01 (setukpairinjR) =>
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% 101.76/17.01 (ksndsingleton) =>
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% 101.76/17.01 (ksndpairEq) =>
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% 101.76/17.01 (kpairsurjEq) =>
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% 101.76/17.01 (cartprodsndin) =>
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% 101.76/17.01 (cartprodpairmemEL) =>
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% 101.76/17.01 (cartprodpairmemER) =>
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% 101.76/17.01 (cartprodmempaircEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodfstpairEq) =>
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% 101.76/17.01 (cartprodsndpairEq) =>
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% 101.76/17.01 (cartprodpairsurjEq) =>
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% 101.76/17.01 (dpsetconstrI) =>
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% 101.76/17.01 (dpsetconstrSub) =>
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% 101.76/17.01 (dpsetconstrEL2) =>
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% 101.76/17.01 (lamp) =>
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% 101.76/17.01 (complementImpComplementIntersect) =>
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% 101.76/17.01 (inComplementUnionImpNotIn1) =>
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% 101.76/17.01 ((
% 101.76/17.01 (binintTransitive) =>
% 101.76/17.01 ((
% 101.76/17.01 (transitivesetOp2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionTransitive) =>
% 101.76/17.01 ((
% 101.76/17.01 (ordinalMinLem1) =>
% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
% 101.76/17.01 ^[Y0 : $i]:
% 101.76/17.01 ((
% 101.76/17.01 (ordinal @
% 101.76/17.01 Y0) =>
% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
% 101.76/17.01 ^[Y1 : $i]:
% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
% 101.76/17.01 ^[Y2 : $i]:
% 101.76/17.01 ((
% 101.76/17.01 (in @
% 101.76/17.01 Y2 @
% 101.76/17.01 Y0) =>
% 101.76/17.01 ((
% 101.76/17.01 (in @
% 101.76/17.01 Y1 @
% 101.76/17.01 Y2) =>
% 101.76/17.01 (in @
% 101.76/17.01 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])).
% 101.76/17.01 thf(zip_derived_cl62, plain,
% 101.76/17.01 (~ (((dsetconstrI) =>
% 101.76/17.01 (((dsetconstrEL) =>
% 101.76/17.01 (((dsetconstrER) =>
% 101.76/17.01 (((exuE1) =>
% 101.76/17.01 (((prop2setE) =>
% 101.76/17.01 (((emptysetE) =>
% 101.76/17.01 (((emptysetimpfalse) =>
% 101.76/17.01 (((notinemptyset) =>
% 101.76/17.01 (((exuE3e) =>
% 101.76/17.01 (((setext) =>
% 101.76/17.01 (((emptyI) =>
% 101.76/17.01 (((noeltsimpempty) =>
% 101.76/17.01 (((setbeta) =>
% 101.76/17.01 (((nonemptyE1) =>
% 101.76/17.01 (((nonemptyI) =>
% 101.76/17.01 (((nonemptyI1) =>
% 101.76/17.01 (((setadjoinIL) =>
% 101.76/17.01 (((in @ emptyset @
% 101.76/17.01 (setadjoin @ emptyset @ emptyset)) =>
% 101.76/17.01 (((setadjoinIR) =>
% 101.76/17.01 (((setadjoinE) =>
% 101.76/17.01 (((setadjoinOr) =>
% 101.76/17.01 (((setoftrueEq) =>
% 101.76/17.01 (((powersetI) =>
% 101.76/17.01 (((emptyinPowerset) =>
% 101.76/17.01 (((emptyInPowerset) =>
% 101.76/17.01 (((powersetE) =>
% 101.76/17.01 (((setunionI) =>
% 101.76/17.01 (((setunionE) =>
% 101.76/17.01 (((subPowSU) =>
% 101.76/17.01 (((exuE2) =>
% 101.76/17.01 ((
% 101.76/17.01 (nonemptyImpWitness) =>
% 101.76/17.01 ((
% 101.76/17.01 (uniqinunit) =>
% 101.76/17.01 ((
% 101.76/17.01 (notinsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqinunit) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletonsswitch) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairsetE) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairsetIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairsetIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (emptyE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (vacuousDall) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan1) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan2) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan3) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan4) =>
% 101.76/17.01 ((
% 101.76/17.01 (prop2setI) =>
% 101.76/17.01 ((
% 101.76/17.01 (prop2set2propI) =>
% 101.76/17.01 ((
% 101.76/17.01 (notdexE) =>
% 101.76/17.01 ((
% 101.76/17.01 (notdallE) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuI3) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuI2) =>
% 101.76/17.01 ((
% 101.76/17.01 (inCongP) =>
% 101.76/17.01 ((
% 101.76/17.01 (in__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuE3u) =>
% 101.76/17.01 ((
% 101.76/17.01 (exu__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (setadjoin__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (powerset__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunion__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuEu) =>
% 101.76/17.01 ((
% 101.76/17.01 (descr__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (dsetconstr__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqimpsubset2) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqimpsubset1) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetI2) =>
% 101.76/17.01 ((
% 101.76/17.01 (emptysetsubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetE) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetE2) =>
% 101.76/17.01 ((
% 101.76/17.01 (notsubsetI) =>
% 101.76/17.01 ((
% 101.76/17.01 (notequalI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (notequalI2) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetRefl) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetTrans) =>
% 101.76/17.01 ((
% 101.76/17.01 (setadjoinSub) =>
% 101.76/17.01 ((
% 101.76/17.01 (setadjoinSub2) =>
% 101.76/17.01 ((
% 101.76/17.01 (subset2powerset) =>
% 101.76/17.01 ((
% 101.76/17.01 (setextsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetemptysetimpeq) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (inPowerset) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetsubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (sepInPowerset) =>
% 101.76/17.01 ((
% 101.76/17.01 (sepSubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairset2IR) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionEcases) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionE) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionLsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionRsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectI) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset5) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectEL) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectLsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset2) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset3) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectER) =>
% 101.76/17.01 ((
% 101.76/17.01 (disjointsetsI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectRsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset4) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset1) =>
% 101.76/17.01 ((
% 101.76/17.01 (bs114d) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusI) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusEL) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusER) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusSubset2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusERneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusELneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusILneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusIRneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusLsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusSubset1) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffE) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffI2) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffIneg1) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffIneg2) =>
% 101.76/17.01 ((
% 101.76/17.01 (secondinupair) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (kpairiskpair) =>
% 101.76/17.01 ((
% 101.76/17.01 (kpairp) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletonsubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletoninpowerset) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletoninpowunion) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairset2E) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairsubunion) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairinpowunion) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem1) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem3) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairin) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodmempair1) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodmempair) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionE2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionsingleton1) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionsingleton2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletonprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (ex1E1) =>
% 101.76/17.01 ((
% 101.76/17.01 (ex1I) =>
% 101.76/17.01 ((
% 101.76/17.01 (ex1I2) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletonsuniq) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL1) =>
% 101.76/17.01 ((
% 101.76/17.01 (kfstsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (theprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (kfstpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodfstin) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR11) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR12) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR1) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairequniteq) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjR) =>
% 101.76/17.01 ((
% 101.76/17.01 (ksndsingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (ksndpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (kpairsurjEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodsndin) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairmemEL) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairmemER) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodmempaircEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodfstpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodsndpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairsurjEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrI) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrSub) =>
% 101.76/17.01 ((
% 101.76/17.01 (setOfPairsIsBReln) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrERa) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrEL1) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrEL2) =>
% 101.76/17.01 ((
% 101.76/17.01 (dpsetconstrER) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcImageSingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (apProp) =>
% 101.76/17.01 ((
% 101.76/17.01 (app) =>
% 101.76/17.01 ((
% 101.76/17.01 (infuncsetfunc) =>
% 101.76/17.01 ((
% 101.76/17.01 (ap2p) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcinfuncset) =>
% 101.76/17.01 ((
% 101.76/17.01 (lamProp) =>
% 101.76/17.01 ((
% 101.76/17.01 (lamp) =>
% 101.76/17.01 ((
% 101.76/17.01 (lam2p) =>
% 101.76/17.01 ((
% 101.76/17.01 (brelnall1) =>
% 101.76/17.01 ((
% 101.76/17.01 (brelnall2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ex1E2) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp1) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp3) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp2) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcextLem) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcGraphProp4) =>
% 101.76/17.01 ((
% 101.76/17.01 (subbreln) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqbreln) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcext) =>
% 101.76/17.01 ((
% 101.76/17.01 (funcext2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ap2apEq1) =>
% 101.76/17.01 ((
% 101.76/17.01 (ap2apEq2) =>
% 101.76/17.01 ((
% 101.76/17.01 (beta1) =>
% 101.76/17.01 ((
% 101.76/17.01 (eta1) =>
% 101.76/17.01 ((
% 101.76/17.01 (lam2lamEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (beta2) =>
% 101.76/17.01 ((
% 101.76/17.01 (eta2) =>
% 101.76/17.01 ((
% 101.76/17.01 (iffalseProp1) =>
% 101.76/17.01 ((
% 101.76/17.01 (iffalseProp2) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrueProp1) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrueProp2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ifSingleton) =>
% 101.76/17.01 ((
% 101.76/17.01 (ifp) =>
% 101.76/17.01 ((
% 101.76/17.01 (theeq) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrue) =>
% 101.76/17.01 ((
% 101.76/17.01 (iffalse) =>
% 101.76/17.01 ((
% 101.76/17.01 (iftrueorfalse) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementT_lem) =>
% 101.76/17.01 ((
% 101.76/17.01 (setextT) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetTI) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetTI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetTE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementTI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementTE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectTELcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectTERcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT1) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT2) =>
% 101.76/17.01 ((
% 101.76/17.01 (contrasubsetT3) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementE1) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementSub1) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementSub2) =>
% 101.76/17.01 ((
% 101.76/17.01 (doubleComplementEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementTnotintersectT) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementImpComplementIntersect) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementSubsetComplementIntersect) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementInPowersetComplementIntersect) =>
% 101.76/17.01 ((
% 101.76/17.01 (contraSubsetComplement) =>
% 101.76/17.01 ((
% 101.76/17.01 (complementTcontraSubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTILcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTIRcontra) =>
% 101.76/17.01 ((
% 101.76/17.01 (inIntersectImpInUnion) =>
% 101.76/17.01 ((
% 101.76/17.01 (inIntersectImpInUnion2) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (intersectInPowersetIntersectUnions) =>
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% 101.76/17.01 (inComplementUnionImpNotIn1) =>
% 101.76/17.01 ((
% 101.76/17.01 (inComplementUnionImpInComplement1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTE) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionTEcontra) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (subbreln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqbreln1) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1invprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1invI) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1invE) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1compprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1compI) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1compE) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1compEex) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionI) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionE) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionEcases) =>
% 101.76/17.01 ((
% 101.76/17.01 (breln1unionCommutes) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2Ex) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2W) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2A) =>
% 101.76/17.01 ((
% 101.76/17.01 (woz2B) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1Ex) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1Ex1) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1Equiv) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1E) =>
% 101.76/17.01 ((
% 101.76/17.01 (image1I) =>
% 101.76/17.01 ((
% 101.76/17.01 (injFuncInInjFuncSet) =>
% 101.76/17.01 ((
% 101.76/17.01 (injFuncSetFuncIn) =>
% 101.76/17.01 ((
% 101.76/17.01 (injFuncSetFuncInj) =>
% 101.76/17.01 ((
% 101.76/17.01 (surjFuncSetFuncIn) =>
% 101.76/17.01 ((
% 101.76/17.01 (surjFuncSetFuncSurj) =>
% 101.76/17.01 ((
% 101.76/17.01 (leftInvIsSurj) =>
% 101.76/17.01 ((
% 101.76/17.01 (surjCantorThm) =>
% 101.76/17.01 ((
% 101.76/17.01 (foundation2) =>
% 101.76/17.01 ((
% 101.76/17.01 (notinself) =>
% 101.76/17.01 ((
% 101.76/17.01 (notinself2) =>
% 101.76/17.01 ((
% 101.76/17.01 (omegaSp) =>
% 101.76/17.01 ((
% 101.76/17.01 (omegaSclos) =>
% 101.76/17.01 ((
% 101.76/17.01 (peano0notS) =>
% 101.76/17.01 ((
% 101.76/17.01 (peanoSinj) =>
% 101.76/17.01 ((
% 101.76/17.01 (transitivesetOp1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintTransitive) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
% 101.76/17.01 ^[Y0 : $i]:
% 101.76/17.01 ((
% 101.76/17.01 (ordinal @
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% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
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% 101.76/17.01 ((
% 101.76/17.01 (!!) @ (
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (in @
% 101.76/17.01 Y1 @
% 101.76/17.01 Y2) =>
% 101.76/17.01 (in @
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% 101.76/17.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl56])).
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% 101.76/17.01 (((setadjoinIR) =>
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% 101.76/17.01 (((setoftrueEq) =>
% 101.76/17.01 (((powersetI) =>
% 101.76/17.01 (((emptyinPowerset) =>
% 101.76/17.01 (((emptyInPowerset) =>
% 101.76/17.01 (((powersetE) =>
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% 101.76/17.01 (((setunionE) =>
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% 101.76/17.01 (notinsingleton) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (upairsetIL) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan2) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan3) =>
% 101.76/17.01 ((
% 101.76/17.01 (quantDeMorgan4) =>
% 101.76/17.01 ((
% 101.76/17.01 (prop2setI) =>
% 101.76/17.01 ((
% 101.76/17.01 (prop2set2propI) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (notdallE) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (exuE3u) =>
% 101.76/17.01 ((
% 101.76/17.01 (exu__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (setadjoin__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (powerset__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunion__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (exuEu) =>
% 101.76/17.01 ((
% 101.76/17.01 (descr__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (dsetconstr__Cong) =>
% 101.76/17.01 ((
% 101.76/17.01 (subsetI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (eqimpsubset2) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (subsetI2) =>
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (notequalI2) =>
% 101.76/17.01 ((
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% 101.76/17.01 (subsetTrans) =>
% 101.76/17.01 ((
% 101.76/17.01 (setadjoinSub) =>
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% 101.76/17.01 (inPowerset) =>
% 101.76/17.01 ((
% 101.76/17.01 (powersetsubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (sepInPowerset) =>
% 101.76/17.01 ((
% 101.76/17.01 (sepSubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairset2IR) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionEcases) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionE) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionLsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (binunionRsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectI) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset5) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectEL) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectLsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset2) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset3) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectER) =>
% 101.76/17.01 ((
% 101.76/17.01 (disjointsetsI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectRsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset4) =>
% 101.76/17.01 ((
% 101.76/17.01 (binintersectSubset1) =>
% 101.76/17.01 ((
% 101.76/17.01 (bs114d) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusI) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusEL) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusER) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusSubset2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusERneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusELneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusILneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusIRneg) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusLsub) =>
% 101.76/17.01 ((
% 101.76/17.01 (setminusSubset1) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffE) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffI1) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffI2) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffIneg1) =>
% 101.76/17.01 ((
% 101.76/17.01 (symdiffIneg2) =>
% 101.76/17.01 ((
% 101.76/17.01 (secondinupair) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairIL) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairIR) =>
% 101.76/17.01 ((
% 101.76/17.01 (kpairiskpair) =>
% 101.76/17.01 ((
% 101.76/17.01 (kpairp) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletonsubset) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletoninpowerset) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletoninpowunion) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairset2E) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairsubunion) =>
% 101.76/17.01 ((
% 101.76/17.01 (upairinpowunion) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem1) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem2) =>
% 101.76/17.01 ((
% 101.76/17.01 (ubforcartprodlem3) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodpairin) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (cartprodmempair) =>
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% 101.76/17.01 ((
% 101.76/17.01 (setunionsingleton2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setunionsingleton) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
% 101.76/17.01 (ex1I2) =>
% 101.76/17.01 ((
% 101.76/17.01 (singletonsuniq) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL1) =>
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% 101.76/17.01 ((
% 101.76/17.01 (theprop) =>
% 101.76/17.01 ((
% 101.76/17.01 (kfstpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodfstin) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL2) =>
% 101.76/17.01 ((
% 101.76/17.01 (setukpairinjL) =>
% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 ((
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% 101.76/17.01 (setukpairinjR) =>
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% 101.76/17.01 (ksndpairEq) =>
% 101.76/17.01 ((
% 101.76/17.01 (kpairsurjEq) =>
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% 101.76/17.01 ((
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% 101.76/17.01 (cartprodpairmemER) =>
% 101.76/17.01 ((
% 101.76/17.01 (cartprodmempaircEq) =>
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% 101.76/17.01 (cartprodpairsurjEq) =>
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% 101.76/17.01 ((
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% 101.76/17.02 ((
% 101.76/17.02 (contraSubsetComplement) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTcontraSubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTILcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTIRcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInUnion) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInUnion2) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInIntersectUnions) =>
% 101.76/17.02 ((
% 101.76/17.02 (intersectInPowersetIntersectUnions) =>
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% 101.76/17.02 (inComplementUnionImpNotIn1) =>
% 101.76/17.02 ((
% 101.76/17.02 (inComplementUnionImpInComplement1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTE) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTEcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a1) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementUnionInPowersetComplement) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a2) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (demorgan1b) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan1) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2b2) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2b) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (woz13rule1) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule3) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule4) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (woz1_2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_3) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_4) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_5) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1all2) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1SetBreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (choice2fnsingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (setOfPairsIsBReln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1all1) =>
% 101.76/17.02 ((
% 101.76/17.02 (subbreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqbreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compEex) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionEcases) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionCommutes) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2Ex) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2W) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2A) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2B) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Ex) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Ex1) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Equiv) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1E) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1I) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncInInjFuncSet) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncSetFuncIn) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncSetFuncInj) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjFuncSetFuncIn) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjFuncSetFuncSurj) =>
% 101.76/17.02 ((
% 101.76/17.02 (leftInvIsSurj) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjCantorThm) =>
% 101.76/17.02 ((
% 101.76/17.02 (foundation2) =>
% 101.76/17.02 ((
% 101.76/17.02 (notinself) =>
% 101.76/17.02 ((
% 101.76/17.02 (notinself2) =>
% 101.76/17.02 ((
% 101.76/17.02 (omegaSp) =>
% 101.76/17.02 ((
% 101.76/17.02 (omegaSclos) =>
% 101.76/17.02 ((
% 101.76/17.02 (peano0notS) =>
% 101.76/17.02 ((
% 101.76/17.02 (peanoSinj) =>
% 101.76/17.02 ((
% 101.76/17.02 (transitivesetOp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintTransitive) =>
% 101.76/17.02 ((
% 101.76/17.02 (transitivesetOp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setunionTransitive) =>
% 101.76/17.02 ((
% 101.76/17.02 (ordinalMinLem1) =>
% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y0 : $i]:
% 101.76/17.02 ((
% 101.76/17.02 (ordinal @
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% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y1 : $i]:
% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y2 : $i]:
% 101.76/17.02 ((
% 101.76/17.02 (in @
% 101.76/17.02 Y2 @
% 101.76/17.02 Y0) =>
% 101.76/17.02 ((
% 101.76/17.02 (in @
% 101.76/17.02 Y1 @
% 101.76/17.02 Y2) =>
% 101.76/17.02 (in @
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% 101.76/17.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])).
% 101.76/17.02 thf(zip_derived_cl79, plain,
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% 101.76/17.02 (((noeltsimpempty) =>
% 101.76/17.02 (((setbeta) =>
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% 101.76/17.02 (((nonemptyI1) =>
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% 101.76/17.02 (((setadjoinIR) =>
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% 101.76/17.02 (((setoftrueEq) =>
% 101.76/17.02 (((powersetI) =>
% 101.76/17.02 (((emptyinPowerset) =>
% 101.76/17.02 (((emptyInPowerset) =>
% 101.76/17.02 (((powersetE) =>
% 101.76/17.02 (((setunionI) =>
% 101.76/17.02 (((setunionE) =>
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% 101.76/17.02 ((
% 101.76/17.02 (eqinunit) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (upairsetE) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairsetIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairsetIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (emptyE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (vacuousDall) =>
% 101.76/17.02 ((
% 101.76/17.02 (quantDeMorgan1) =>
% 101.76/17.02 ((
% 101.76/17.02 (quantDeMorgan2) =>
% 101.76/17.02 ((
% 101.76/17.02 (quantDeMorgan3) =>
% 101.76/17.02 ((
% 101.76/17.02 (quantDeMorgan4) =>
% 101.76/17.02 ((
% 101.76/17.02 (prop2setI) =>
% 101.76/17.02 ((
% 101.76/17.02 (prop2set2propI) =>
% 101.76/17.02 ((
% 101.76/17.02 (notdexE) =>
% 101.76/17.02 ((
% 101.76/17.02 (notdallE) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuI3) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (inCongP) =>
% 101.76/17.02 ((
% 101.76/17.02 (in__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuE3u) =>
% 101.76/17.02 ((
% 101.76/17.02 (exu__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (setadjoin__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (powerset__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (setunion__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuEu) =>
% 101.76/17.02 ((
% 101.76/17.02 (descr__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (dsetconstr__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqimpsubset2) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqimpsubset1) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (emptysetsubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetE) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetE2) =>
% 101.76/17.02 ((
% 101.76/17.02 (notsubsetI) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (notequalI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetRefl) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetTrans) =>
% 101.76/17.02 ((
% 101.76/17.02 (setadjoinSub) =>
% 101.76/17.02 ((
% 101.76/17.02 (setadjoinSub2) =>
% 101.76/17.02 ((
% 101.76/17.02 (subset2powerset) =>
% 101.76/17.02 ((
% 101.76/17.02 (setextsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetemptysetimpeq) =>
% 101.76/17.02 ((
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% 101.76/17.02 (powersetE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (inPowerset) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetsubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (sepInPowerset) =>
% 101.76/17.02 ((
% 101.76/17.02 (sepSubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairset2IR) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionEcases) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionE) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionLsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionRsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectI) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset5) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectEL) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectLsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset2) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset3) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectER) =>
% 101.76/17.02 ((
% 101.76/17.02 (disjointsetsI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectRsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset4) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset1) =>
% 101.76/17.02 ((
% 101.76/17.02 (bs114d) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusI) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusEL) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusER) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusSubset2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusERneg) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (setminusILneg) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusIRneg) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusLsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusSubset1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffE) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffIneg1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffIneg2) =>
% 101.76/17.02 ((
% 101.76/17.02 (secondinupair) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (kpairiskpair) =>
% 101.76/17.02 ((
% 101.76/17.02 (kpairp) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletonsubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletoninpowerset) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletoninpowunion) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairset2E) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairsubunion) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairinpowunion) =>
% 101.76/17.02 ((
% 101.76/17.02 (ubforcartprodlem1) =>
% 101.76/17.02 ((
% 101.76/17.02 (ubforcartprodlem2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ubforcartprodlem3) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairin) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (cartprodmempair) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (ex1I) =>
% 101.76/17.02 ((
% 101.76/17.02 (ex1I2) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletonsuniq) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (kfstpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodfstin) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjL2) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR) =>
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% 101.76/17.02 (ksndsingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (ksndpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (kpairsurjEq) =>
% 101.76/17.02 ((
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% 101.76/17.02 (cartprodpairmemEL) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairmemER) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodmempaircEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodfstpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodsndpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairsurjEq) =>
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (lam2lamEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (beta2) =>
% 101.76/17.02 ((
% 101.76/17.02 (eta2) =>
% 101.76/17.02 ((
% 101.76/17.02 (iffalseProp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (iffalseProp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrueProp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrueProp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ifSingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (ifp) =>
% 101.76/17.02 ((
% 101.76/17.02 (theeq) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrue) =>
% 101.76/17.02 ((
% 101.76/17.02 (iffalse) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrueorfalse) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (setextT) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetTI) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetTI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetTE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectTELcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectTERcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT1) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT2) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT3) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementSub1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementSub2) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTnotintersectT) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementImpComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementSubsetComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementInPowersetComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (contraSubsetComplement) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTcontraSubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTILcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTIRcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInUnion) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInUnion2) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInIntersectUnions) =>
% 101.76/17.02 ((
% 101.76/17.02 (intersectInPowersetIntersectUnions) =>
% 101.76/17.02 ((
% 101.76/17.02 (inComplementUnionImpNotIn1) =>
% 101.76/17.02 ((
% 101.76/17.02 (inComplementUnionImpInComplement1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTE) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTEcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a1) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementUnionInPowersetComplement) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a2) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan1a) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan1b) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan1) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2b2) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2b) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule0) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule1) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule3) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule4) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_1) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_3) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_4) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_5) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1all2) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1SetBreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (choice2fnsingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (setOfPairsIsBReln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1all1) =>
% 101.76/17.02 ((
% 101.76/17.02 (subbreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqbreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compEex) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionEcases) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionCommutes) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2Ex) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2W) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2A) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2B) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Ex) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Ex1) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Equiv) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1E) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1I) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncInInjFuncSet) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncSetFuncIn) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncSetFuncInj) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjFuncSetFuncIn) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjFuncSetFuncSurj) =>
% 101.76/17.02 ((
% 101.76/17.02 (leftInvIsSurj) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjCantorThm) =>
% 101.76/17.02 ((
% 101.76/17.02 (foundation2) =>
% 101.76/17.02 ((
% 101.76/17.02 (notinself) =>
% 101.76/17.02 ((
% 101.76/17.02 (notinself2) =>
% 101.76/17.02 ((
% 101.76/17.02 (omegaSp) =>
% 101.76/17.02 ((
% 101.76/17.02 (omegaSclos) =>
% 101.76/17.02 ((
% 101.76/17.02 (peano0notS) =>
% 101.76/17.02 ((
% 101.76/17.02 (peanoSinj) =>
% 101.76/17.02 ((
% 101.76/17.02 (transitivesetOp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintTransitive) =>
% 101.76/17.02 ((
% 101.76/17.02 (transitivesetOp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setunionTransitive) =>
% 101.76/17.02 ((
% 101.76/17.02 (ordinalMinLem1) =>
% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y0 : $i]:
% 101.76/17.02 ((
% 101.76/17.02 (ordinal @
% 101.76/17.02 Y0) =>
% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y1 : $i]:
% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y2 : $i]:
% 101.76/17.02 ((
% 101.76/17.02 (in @
% 101.76/17.02 Y2 @
% 101.76/17.02 Y0) =>
% 101.76/17.02 ((
% 101.76/17.02 (in @
% 101.76/17.02 Y1 @
% 101.76/17.02 Y2) =>
% 101.76/17.02 (in @
% 101.76/17.02 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])).
% 101.76/17.02 thf(zip_derived_cl95, plain,
% 101.76/17.02 (~ (((exuE1) =>
% 101.76/17.02 (((prop2setE) =>
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% 101.76/17.02 (((emptysetimpfalse) =>
% 101.76/17.02 (((notinemptyset) =>
% 101.76/17.02 (((exuE3e) =>
% 101.76/17.02 (((setext) =>
% 101.76/17.02 (((emptyI) =>
% 101.76/17.02 (((noeltsimpempty) =>
% 101.76/17.02 (((setbeta) =>
% 101.76/17.02 (((nonemptyE1) =>
% 101.76/17.02 (((nonemptyI) =>
% 101.76/17.02 (((nonemptyI1) =>
% 101.76/17.02 (((setadjoinIL) =>
% 101.76/17.02 (((in @ emptyset @
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% 101.76/17.02 (((setadjoinIR) =>
% 101.76/17.02 (((setadjoinE) =>
% 101.76/17.02 (((setadjoinOr) =>
% 101.76/17.02 (((setoftrueEq) =>
% 101.76/17.02 (((powersetI) =>
% 101.76/17.02 (((emptyinPowerset) =>
% 101.76/17.02 (((emptyInPowerset) =>
% 101.76/17.02 (((powersetE) =>
% 101.76/17.02 (((setunionI) =>
% 101.76/17.02 (((setunionE) =>
% 101.76/17.02 (((subPowSU) =>
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% 101.76/17.02 (((nonemptyImpWitness) =>
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% 101.76/17.02 (((notinsingleton) =>
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% 101.76/17.02 ((
% 101.76/17.02 (upairsetE) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairsetIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairsetIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (emptyE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (vacuousDall) =>
% 101.76/17.02 ((
% 101.76/17.02 (quantDeMorgan1) =>
% 101.76/17.02 ((
% 101.76/17.02 (quantDeMorgan2) =>
% 101.76/17.02 ((
% 101.76/17.02 (quantDeMorgan3) =>
% 101.76/17.02 ((
% 101.76/17.02 (quantDeMorgan4) =>
% 101.76/17.02 ((
% 101.76/17.02 (prop2setI) =>
% 101.76/17.02 ((
% 101.76/17.02 (prop2set2propI) =>
% 101.76/17.02 ((
% 101.76/17.02 (notdexE) =>
% 101.76/17.02 ((
% 101.76/17.02 (notdallE) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuI3) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (inCongP) =>
% 101.76/17.02 ((
% 101.76/17.02 (in__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuE3u) =>
% 101.76/17.02 ((
% 101.76/17.02 (exu__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (setadjoin__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (powerset__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (setunion__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuEu) =>
% 101.76/17.02 ((
% 101.76/17.02 (descr__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (dsetconstr__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqimpsubset2) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqimpsubset1) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (emptysetsubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetE) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetE2) =>
% 101.76/17.02 ((
% 101.76/17.02 (notsubsetI) =>
% 101.76/17.02 ((
% 101.76/17.02 (notequalI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (notequalI2) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (subsetTrans) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (setadjoinSub2) =>
% 101.76/17.02 ((
% 101.76/17.02 (subset2powerset) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 (powersetE1) =>
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% 101.76/17.02 ((
% 101.76/17.02 (powersetsubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (sepInPowerset) =>
% 101.76/17.02 ((
% 101.76/17.02 (sepSubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairset2IR) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionEcases) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionE) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionLsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionRsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectI) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset5) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectEL) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectLsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset2) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset3) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectER) =>
% 101.76/17.02 ((
% 101.76/17.02 (disjointsetsI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectRsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset4) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset1) =>
% 101.76/17.02 ((
% 101.76/17.02 (bs114d) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusI) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusEL) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusER) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusSubset2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusERneg) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusELneg) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusILneg) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusIRneg) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusLsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusSubset1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffE) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffIneg1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffIneg2) =>
% 101.76/17.02 ((
% 101.76/17.02 (secondinupair) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (kpairiskpair) =>
% 101.76/17.02 ((
% 101.76/17.02 (kpairp) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletonsubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletoninpowerset) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletoninpowunion) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairset2E) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairsubunion) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairinpowunion) =>
% 101.76/17.02 ((
% 101.76/17.02 (ubforcartprodlem1) =>
% 101.76/17.02 ((
% 101.76/17.02 (ubforcartprodlem2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ubforcartprodlem3) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairin) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodmempair1) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodmempair) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (ex1I2) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletonsuniq) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjL1) =>
% 101.76/17.02 ((
% 101.76/17.02 (kfstsingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (theprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (kfstpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodfstin) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjL2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjL) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR11) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR12) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (upairequniteq) =>
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% 101.76/17.02 (setukpairinjR) =>
% 101.76/17.02 ((
% 101.76/17.02 (ksndsingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (ksndpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (kpairsurjEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodsndin) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairmemEL) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairmemER) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodmempaircEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodfstpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodsndpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairsurjEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrI) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrSub) =>
% 101.76/17.02 ((
% 101.76/17.02 (setOfPairsIsBReln) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrERa) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrEL1) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrEL2) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrER) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcImageSingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (apProp) =>
% 101.76/17.02 ((
% 101.76/17.02 (app) =>
% 101.76/17.02 ((
% 101.76/17.02 (infuncsetfunc) =>
% 101.76/17.02 ((
% 101.76/17.02 (ap2p) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcinfuncset) =>
% 101.76/17.02 ((
% 101.76/17.02 (lamProp) =>
% 101.76/17.02 ((
% 101.76/17.02 (lamp) =>
% 101.76/17.02 ((
% 101.76/17.02 (lam2p) =>
% 101.76/17.02 ((
% 101.76/17.02 (brelnall1) =>
% 101.76/17.02 ((
% 101.76/17.02 (brelnall2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ex1E2) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp3) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcextLem) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp4) =>
% 101.76/17.02 ((
% 101.76/17.02 (subbreln) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqbreln) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcext) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcext2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ap2apEq1) =>
% 101.76/17.02 ((
% 101.76/17.02 (ap2apEq2) =>
% 101.76/17.02 ((
% 101.76/17.02 (beta1) =>
% 101.76/17.02 ((
% 101.76/17.02 (eta1) =>
% 101.76/17.02 ((
% 101.76/17.02 (lam2lamEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (beta2) =>
% 101.76/17.02 ((
% 101.76/17.02 (eta2) =>
% 101.76/17.02 ((
% 101.76/17.02 (iffalseProp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (iffalseProp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrueProp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrueProp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ifSingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (ifp) =>
% 101.76/17.02 ((
% 101.76/17.02 (theeq) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrue) =>
% 101.76/17.02 ((
% 101.76/17.02 (iffalse) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrueorfalse) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (setextT) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetTI) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetTI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetTE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectTELcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectTERcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT1) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT2) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT3) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementSub1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementSub2) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTnotintersectT) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementImpComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementSubsetComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementInPowersetComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (contraSubsetComplement) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTcontraSubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTILcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTIRcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInUnion) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInUnion2) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInIntersectUnions) =>
% 101.76/17.02 ((
% 101.76/17.02 (intersectInPowersetIntersectUnions) =>
% 101.76/17.02 ((
% 101.76/17.02 (inComplementUnionImpNotIn1) =>
% 101.76/17.02 ((
% 101.76/17.02 (inComplementUnionImpInComplement1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTE) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTEcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a1) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementUnionInPowersetComplement) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a2) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan1a) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan1b) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan1) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2b2) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2b) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule0) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule1) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule3) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule4) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_1) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_3) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_4) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_5) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1all2) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1SetBreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (choice2fnsingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (setOfPairsIsBReln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1all1) =>
% 101.76/17.02 ((
% 101.76/17.02 (subbreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqbreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compEex) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionEcases) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionCommutes) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2Ex) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2W) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2A) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2B) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Ex) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Ex1) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Equiv) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1E) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1I) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncInInjFuncSet) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncSetFuncIn) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncSetFuncInj) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjFuncSetFuncIn) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjFuncSetFuncSurj) =>
% 101.76/17.02 ((
% 101.76/17.02 (leftInvIsSurj) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjCantorThm) =>
% 101.76/17.02 ((
% 101.76/17.02 (foundation2) =>
% 101.76/17.02 ((
% 101.76/17.02 (notinself) =>
% 101.76/17.02 ((
% 101.76/17.02 (notinself2) =>
% 101.76/17.02 ((
% 101.76/17.02 (omegaSp) =>
% 101.76/17.02 ((
% 101.76/17.02 (omegaSclos) =>
% 101.76/17.02 ((
% 101.76/17.02 (peano0notS) =>
% 101.76/17.02 ((
% 101.76/17.02 (peanoSinj) =>
% 101.76/17.02 ((
% 101.76/17.02 (transitivesetOp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintTransitive) =>
% 101.76/17.02 ((
% 101.76/17.02 (transitivesetOp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setunionTransitive) =>
% 101.76/17.02 ((
% 101.76/17.02 (ordinalMinLem1) =>
% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y0 : $i]:
% 101.76/17.02 ((
% 101.76/17.02 (ordinal @
% 101.76/17.02 Y0) =>
% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y1 : $i]:
% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y2 : $i]:
% 101.76/17.02 ((
% 101.76/17.02 (in @
% 101.76/17.02 Y2 @
% 101.76/17.02 Y0) =>
% 101.76/17.02 ((
% 101.76/17.02 (in @
% 101.76/17.02 Y1 @
% 101.76/17.02 Y2) =>
% 101.76/17.02 (in @
% 101.76/17.02 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 101.76/17.02 thf(zip_derived_cl115, plain,
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% 101.76/17.02 (((notinemptyset) =>
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% 101.76/17.02 (((setbeta) =>
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% 101.76/17.02 (((nonemptyI1) =>
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% 101.76/17.02 (((setadjoinIR) =>
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% 101.76/17.02 (((setunionE) =>
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% 101.76/17.02 ((
% 101.76/17.02 (upairsetIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairsetIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (emptyE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (vacuousDall) =>
% 101.76/17.02 ((
% 101.76/17.02 (quantDeMorgan1) =>
% 101.76/17.02 ((
% 101.76/17.02 (quantDeMorgan2) =>
% 101.76/17.02 ((
% 101.76/17.02 (quantDeMorgan3) =>
% 101.76/17.02 ((
% 101.76/17.02 (quantDeMorgan4) =>
% 101.76/17.02 ((
% 101.76/17.02 (prop2setI) =>
% 101.76/17.02 ((
% 101.76/17.02 (prop2set2propI) =>
% 101.76/17.02 ((
% 101.76/17.02 (notdexE) =>
% 101.76/17.02 ((
% 101.76/17.02 (notdallE) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuI3) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (inCongP) =>
% 101.76/17.02 ((
% 101.76/17.02 (in__Cong) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (exu__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (setadjoin__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (powerset__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (setunion__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuEu) =>
% 101.76/17.02 ((
% 101.76/17.02 (descr__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (dsetconstr__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqimpsubset2) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqimpsubset1) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (emptysetsubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetE) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetE2) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (notequalI2) =>
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (setextsub) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (sepInPowerset) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (upairset2IR) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionEcases) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionE) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionLsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionRsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectI) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset5) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset2) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset3) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectER) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset4) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset1) =>
% 101.76/17.02 ((
% 101.76/17.02 (bs114d) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusI) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusEL) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusER) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusSubset2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusERneg) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusELneg) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusILneg) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusIRneg) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (setminusSubset1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffE) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffIneg1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffIneg2) =>
% 101.76/17.02 ((
% 101.76/17.02 (secondinupair) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (kpairiskpair) =>
% 101.76/17.02 ((
% 101.76/17.02 (kpairp) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletonsubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletoninpowerset) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (upairsubunion) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairinpowunion) =>
% 101.76/17.02 ((
% 101.76/17.02 (ubforcartprodlem1) =>
% 101.76/17.02 ((
% 101.76/17.02 (ubforcartprodlem2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ubforcartprodlem3) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairin) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodmempair1) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodmempair) =>
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% 101.76/17.02 ((
% 101.76/17.02 (setunionsingleton2) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (kfstpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodfstin) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjL2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjL) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR11) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR12) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR1) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairequniteq) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR) =>
% 101.76/17.02 ((
% 101.76/17.02 (ksndsingleton) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (kpairsurjEq) =>
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% 101.76/17.02 (cartprodsndin) =>
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% 101.76/17.02 (cartprodpairmemEL) =>
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% 101.76/17.02 (cartprodpairmemER) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodmempaircEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodfstpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodsndpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairsurjEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrI) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrSub) =>
% 101.76/17.02 ((
% 101.76/17.02 (setOfPairsIsBReln) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrERa) =>
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% 101.76/17.02 (dpsetconstrEL1) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrEL2) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrER) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcImageSingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (apProp) =>
% 101.76/17.02 ((
% 101.76/17.02 (app) =>
% 101.76/17.02 ((
% 101.76/17.02 (infuncsetfunc) =>
% 101.76/17.02 ((
% 101.76/17.02 (ap2p) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcinfuncset) =>
% 101.76/17.02 ((
% 101.76/17.02 (lamProp) =>
% 101.76/17.02 ((
% 101.76/17.02 (lamp) =>
% 101.76/17.02 ((
% 101.76/17.02 (lam2p) =>
% 101.76/17.02 ((
% 101.76/17.02 (brelnall1) =>
% 101.76/17.02 ((
% 101.76/17.02 (brelnall2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ex1E2) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp3) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcextLem) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp4) =>
% 101.76/17.02 ((
% 101.76/17.02 (subbreln) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqbreln) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcext) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcext2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ap2apEq1) =>
% 101.76/17.02 ((
% 101.76/17.02 (ap2apEq2) =>
% 101.76/17.02 ((
% 101.76/17.02 (beta1) =>
% 101.76/17.02 ((
% 101.76/17.02 (eta1) =>
% 101.76/17.02 ((
% 101.76/17.02 (lam2lamEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (beta2) =>
% 101.76/17.02 ((
% 101.76/17.02 (eta2) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (iffalseProp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrueProp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrueProp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ifSingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (ifp) =>
% 101.76/17.02 ((
% 101.76/17.02 (theeq) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrue) =>
% 101.76/17.02 ((
% 101.76/17.02 (iffalse) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrueorfalse) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (setextT) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetTI) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (complementTI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectTELcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectTERcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT1) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT2) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT3) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementSub1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementSub2) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTnotintersectT) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementImpComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementSubsetComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementInPowersetComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (contraSubsetComplement) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTcontraSubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTILcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTIRcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInUnion) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInUnion2) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInIntersectUnions) =>
% 101.76/17.02 ((
% 101.76/17.02 (intersectInPowersetIntersectUnions) =>
% 101.76/17.02 ((
% 101.76/17.02 (inComplementUnionImpNotIn1) =>
% 101.76/17.02 ((
% 101.76/17.02 (inComplementUnionImpInComplement1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTE) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTEcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a1) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementUnionInPowersetComplement) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a2) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan1a) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan1b) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan1) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2b2) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2b) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule0) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (woz13rule2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule3) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule4) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_1) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_3) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_4) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_5) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1all2) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1SetBreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (choice2fnsingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (setOfPairsIsBReln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1all1) =>
% 101.76/17.02 ((
% 101.76/17.02 (subbreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqbreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compEex) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionEcases) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionCommutes) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2Ex) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2W) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2A) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2B) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Ex) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Ex1) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Equiv) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1E) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1I) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncInInjFuncSet) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncSetFuncIn) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncSetFuncInj) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjFuncSetFuncIn) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjFuncSetFuncSurj) =>
% 101.76/17.02 ((
% 101.76/17.02 (leftInvIsSurj) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjCantorThm) =>
% 101.76/17.02 ((
% 101.76/17.02 (foundation2) =>
% 101.76/17.02 ((
% 101.76/17.02 (notinself) =>
% 101.76/17.02 ((
% 101.76/17.02 (notinself2) =>
% 101.76/17.02 ((
% 101.76/17.02 (omegaSp) =>
% 101.76/17.02 ((
% 101.76/17.02 (omegaSclos) =>
% 101.76/17.02 ((
% 101.76/17.02 (peano0notS) =>
% 101.76/17.02 ((
% 101.76/17.02 (peanoSinj) =>
% 101.76/17.02 ((
% 101.76/17.02 (transitivesetOp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintTransitive) =>
% 101.76/17.02 ((
% 101.76/17.02 (transitivesetOp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setunionTransitive) =>
% 101.76/17.02 ((
% 101.76/17.02 (ordinalMinLem1) =>
% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y0 : $i]:
% 101.76/17.02 ((
% 101.76/17.02 (ordinal @
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% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
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% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y2 : $i]:
% 101.76/17.02 ((
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% 101.76/17.02 Y0) =>
% 101.76/17.02 ((
% 101.76/17.02 (in @
% 101.76/17.02 Y1 @
% 101.76/17.02 Y2) =>
% 101.76/17.02 (in @
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% 101.76/17.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])).
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% 101.76/17.02 (((setadjoinIR) =>
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (notdallE) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (exuI3) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (inCongP) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (setunion__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuEu) =>
% 101.76/17.02 ((
% 101.76/17.02 (descr__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (dsetconstr__Cong) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (subsetE) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetE2) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (binunionEcases) =>
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% 101.76/17.02 ((
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% 101.76/17.02 (binintersectSubset3) =>
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 (setminusIRneg) =>
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% 101.76/17.02 ((
% 101.76/17.02 (setminusSubset1) =>
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% 101.76/17.02 (symdiffE) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffIneg1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffIneg2) =>
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% 101.76/17.02 (ubforcartprodlem3) =>
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% 101.76/17.02 (setukpairinjL2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjL) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR11) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR12) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR1) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairequniteq) =>
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% 101.76/17.02 (setukpairinjR2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR) =>
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% 101.76/17.02 (cartprodmempaircEq) =>
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% 101.76/17.02 (cartprodfstpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodsndpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairsurjEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrI) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrSub) =>
% 101.76/17.02 ((
% 101.76/17.02 (setOfPairsIsBReln) =>
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% 101.76/17.02 (dpsetconstrERa) =>
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% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrEL2) =>
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% 101.76/17.02 (dpsetconstrER) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcImageSingleton) =>
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% 101.76/17.02 ((
% 101.76/17.02 (app) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (ap2p) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcinfuncset) =>
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% 101.76/17.02 (lamProp) =>
% 101.76/17.02 ((
% 101.76/17.02 (lamp) =>
% 101.76/17.02 ((
% 101.76/17.02 (lam2p) =>
% 101.76/17.02 ((
% 101.76/17.02 (brelnall1) =>
% 101.76/17.02 ((
% 101.76/17.02 (brelnall2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ex1E2) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp3) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp2) =>
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% 101.76/17.02 (funcextLem) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp4) =>
% 101.76/17.02 ((
% 101.76/17.02 (subbreln) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqbreln) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcext) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcext2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ap2apEq1) =>
% 101.76/17.02 ((
% 101.76/17.02 (ap2apEq2) =>
% 101.76/17.02 ((
% 101.76/17.02 (beta1) =>
% 101.76/17.02 ((
% 101.76/17.02 (eta1) =>
% 101.76/17.02 ((
% 101.76/17.02 (lam2lamEq) =>
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% 101.76/17.02 (beta2) =>
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% 101.76/17.02 ((
% 101.76/17.02 (iftrueProp2) =>
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% 101.76/17.02 (ifSingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (ifp) =>
% 101.76/17.02 ((
% 101.76/17.02 (theeq) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrue) =>
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (binintersectTERcontra) =>
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT2) =>
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% 101.76/17.02 (contrasubsetT3) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementSub1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementSub2) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTnotintersectT) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementImpComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementSubsetComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementInPowersetComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (contraSubsetComplement) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTcontraSubset) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (binunionTIRcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInUnion) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInUnion2) =>
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% 101.76/17.02 (inIntersectImpInIntersectUnions) =>
% 101.76/17.02 ((
% 101.76/17.02 (intersectInPowersetIntersectUnions) =>
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% 101.76/17.02 (inComplementUnionImpNotIn1) =>
% 101.76/17.02 ((
% 101.76/17.02 (inComplementUnionImpInComplement1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTE) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTEcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a1) =>
% 101.76/17.02 ((
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% 101.76/17.02 (demorgan2a2) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 (woz1_3) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_4) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_5) =>
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% 101.76/17.02 (breln1all2) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (choice2fnsingleton) =>
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (breln1unionIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionEcases) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionCommutes) =>
% 101.76/17.02 ((
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% 101.76/17.02 (woz2W) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (image1E) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1I) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncInInjFuncSet) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncSetFuncIn) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncSetFuncInj) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjFuncSetFuncIn) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjFuncSetFuncSurj) =>
% 101.76/17.02 ((
% 101.76/17.02 (leftInvIsSurj) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjCantorThm) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 ((
% 101.76/17.02 (peano0notS) =>
% 101.76/17.02 ((
% 101.76/17.02 (peanoSinj) =>
% 101.76/17.02 ((
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% 101.76/17.02 ((
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% 101.76/17.02 Y2) =>
% 101.76/17.02 (in @
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% 101.76/17.02 (in__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuE3u) =>
% 101.76/17.02 ((
% 101.76/17.02 (exu__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (setadjoin__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (powerset__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (setunion__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (exuEu) =>
% 101.76/17.02 ((
% 101.76/17.02 (descr__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (dsetconstr__Cong) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqimpsubset2) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqimpsubset1) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (emptysetsubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetE) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetE2) =>
% 101.76/17.02 ((
% 101.76/17.02 (notsubsetI) =>
% 101.76/17.02 ((
% 101.76/17.02 (notequalI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (notequalI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetRefl) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetTrans) =>
% 101.76/17.02 ((
% 101.76/17.02 (setadjoinSub) =>
% 101.76/17.02 ((
% 101.76/17.02 (setadjoinSub2) =>
% 101.76/17.02 ((
% 101.76/17.02 (subset2powerset) =>
% 101.76/17.02 ((
% 101.76/17.02 (setextsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetemptysetimpeq) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (inPowerset) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetsubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (sepInPowerset) =>
% 101.76/17.02 ((
% 101.76/17.02 (sepSubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairset2IR) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionEcases) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionE) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionLsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionRsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectI) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset5) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectEL) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectLsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset2) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset3) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectER) =>
% 101.76/17.02 ((
% 101.76/17.02 (disjointsetsI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectRsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset4) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectSubset1) =>
% 101.76/17.02 ((
% 101.76/17.02 (bs114d) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusI) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusEL) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusER) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusSubset2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusERneg) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusELneg) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusILneg) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusIRneg) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusLsub) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusSubset1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffE) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffI2) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffIneg1) =>
% 101.76/17.02 ((
% 101.76/17.02 (symdiffIneg2) =>
% 101.76/17.02 ((
% 101.76/17.02 (secondinupair) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (kpairiskpair) =>
% 101.76/17.02 ((
% 101.76/17.02 (kpairp) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletonsubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletoninpowerset) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletoninpowunion) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairset2E) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairsubunion) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairinpowunion) =>
% 101.76/17.02 ((
% 101.76/17.02 (ubforcartprodlem1) =>
% 101.76/17.02 ((
% 101.76/17.02 (ubforcartprodlem2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ubforcartprodlem3) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairin) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodmempair1) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodmempair) =>
% 101.76/17.02 ((
% 101.76/17.02 (setunionE2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setunionsingleton1) =>
% 101.76/17.02 ((
% 101.76/17.02 (setunionsingleton2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setunionsingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletonprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (ex1E1) =>
% 101.76/17.02 ((
% 101.76/17.02 (ex1I) =>
% 101.76/17.02 ((
% 101.76/17.02 (ex1I2) =>
% 101.76/17.02 ((
% 101.76/17.02 (singletonsuniq) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjL1) =>
% 101.76/17.02 ((
% 101.76/17.02 (kfstsingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (theprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (kfstpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodfstin) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjL2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjL) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR11) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR12) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR1) =>
% 101.76/17.02 ((
% 101.76/17.02 (upairequniteq) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setukpairinjR) =>
% 101.76/17.02 ((
% 101.76/17.02 (ksndsingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (ksndpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (kpairsurjEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodsndin) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairmemEL) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairmemER) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodmempaircEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodfstpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodsndpairEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (cartprodpairsurjEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrI) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrSub) =>
% 101.76/17.02 ((
% 101.76/17.02 (setOfPairsIsBReln) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrERa) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrEL1) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrEL2) =>
% 101.76/17.02 ((
% 101.76/17.02 (dpsetconstrER) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcImageSingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (apProp) =>
% 101.76/17.02 ((
% 101.76/17.02 (app) =>
% 101.76/17.02 ((
% 101.76/17.02 (infuncsetfunc) =>
% 101.76/17.02 ((
% 101.76/17.02 (ap2p) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcinfuncset) =>
% 101.76/17.02 ((
% 101.76/17.02 (lamProp) =>
% 101.76/17.02 ((
% 101.76/17.02 (lamp) =>
% 101.76/17.02 ((
% 101.76/17.02 (lam2p) =>
% 101.76/17.02 ((
% 101.76/17.02 (brelnall1) =>
% 101.76/17.02 ((
% 101.76/17.02 (brelnall2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ex1E2) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp3) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcextLem) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcGraphProp4) =>
% 101.76/17.02 ((
% 101.76/17.02 (subbreln) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqbreln) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcext) =>
% 101.76/17.02 ((
% 101.76/17.02 (funcext2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ap2apEq1) =>
% 101.76/17.02 ((
% 101.76/17.02 (ap2apEq2) =>
% 101.76/17.02 ((
% 101.76/17.02 (beta1) =>
% 101.76/17.02 ((
% 101.76/17.02 (eta1) =>
% 101.76/17.02 ((
% 101.76/17.02 (lam2lamEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (beta2) =>
% 101.76/17.02 ((
% 101.76/17.02 (eta2) =>
% 101.76/17.02 ((
% 101.76/17.02 (iffalseProp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (iffalseProp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrueProp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrueProp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (ifSingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (ifp) =>
% 101.76/17.02 ((
% 101.76/17.02 (theeq) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrue) =>
% 101.76/17.02 ((
% 101.76/17.02 (iffalse) =>
% 101.76/17.02 ((
% 101.76/17.02 (iftrueorfalse) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (setminusT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementT_lem) =>
% 101.76/17.02 ((
% 101.76/17.02 (setextT) =>
% 101.76/17.02 ((
% 101.76/17.02 (subsetTI) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetTI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (powersetTE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectTELcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintersectTERcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT1) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT2) =>
% 101.76/17.02 ((
% 101.76/17.02 (contrasubsetT3) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementI1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementE1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementSub1) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementSub2) =>
% 101.76/17.02 ((
% 101.76/17.02 (doubleComplementEq) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTnotintersectT) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementImpComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementSubsetComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementInPowersetComplementIntersect) =>
% 101.76/17.02 ((
% 101.76/17.02 (contraSubsetComplement) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementTcontraSubset) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTILcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTIRcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInUnion) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInUnion2) =>
% 101.76/17.02 ((
% 101.76/17.02 (inIntersectImpInIntersectUnions) =>
% 101.76/17.02 ((
% 101.76/17.02 (intersectInPowersetIntersectUnions) =>
% 101.76/17.02 ((
% 101.76/17.02 (inComplementUnionImpNotIn1) =>
% 101.76/17.02 ((
% 101.76/17.02 (inComplementUnionImpInComplement1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTE) =>
% 101.76/17.02 ((
% 101.76/17.02 (binunionTEcontra) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a1) =>
% 101.76/17.02 ((
% 101.76/17.02 (complementUnionInPowersetComplement) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a2) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan1a) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan1b) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan1) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2a) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2b2) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2b) =>
% 101.76/17.02 ((
% 101.76/17.02 (demorgan2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule0) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule1) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule3) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz13rule4) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_1) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_2) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_3) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_4) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz1_5) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1all2) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1SetBreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (choice2fnsingleton) =>
% 101.76/17.02 ((
% 101.76/17.02 (setOfPairsIsBReln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1all1) =>
% 101.76/17.02 ((
% 101.76/17.02 (subbreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (eqbreln1) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1invE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1compEex) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionprop) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionIL) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionIR) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionI) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionE) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionEcases) =>
% 101.76/17.02 ((
% 101.76/17.02 (breln1unionCommutes) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2Ex) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2W) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2A) =>
% 101.76/17.02 ((
% 101.76/17.02 (woz2B) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Ex) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Ex1) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1Equiv) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1E) =>
% 101.76/17.02 ((
% 101.76/17.02 (image1I) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncInInjFuncSet) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncSetFuncIn) =>
% 101.76/17.02 ((
% 101.76/17.02 (injFuncSetFuncInj) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjFuncSetFuncIn) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjFuncSetFuncSurj) =>
% 101.76/17.02 ((
% 101.76/17.02 (leftInvIsSurj) =>
% 101.76/17.02 ((
% 101.76/17.02 (surjCantorThm) =>
% 101.76/17.02 ((
% 101.76/17.02 (foundation2) =>
% 101.76/17.02 ((
% 101.76/17.02 (notinself) =>
% 101.76/17.02 ((
% 101.76/17.02 (notinself2) =>
% 101.76/17.02 ((
% 101.76/17.02 (omegaSp) =>
% 101.76/17.02 ((
% 101.76/17.02 (omegaSclos) =>
% 101.76/17.02 ((
% 101.76/17.02 (peano0notS) =>
% 101.76/17.02 ((
% 101.76/17.02 (peanoSinj) =>
% 101.76/17.02 ((
% 101.76/17.02 (transitivesetOp1) =>
% 101.76/17.02 ((
% 101.76/17.02 (binintTransitive) =>
% 101.76/17.02 ((
% 101.76/17.02 (transitivesetOp2) =>
% 101.76/17.02 ((
% 101.76/17.02 (setunionTransitive) =>
% 101.76/17.02 ((
% 101.76/17.02 (ordinalMinLem1) =>
% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y0 : $i]:
% 101.76/17.02 ((
% 101.76/17.02 (ordinal @
% 101.76/17.02 Y0) =>
% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y1 : $i]:
% 101.76/17.02 ((
% 101.76/17.02 (!!) @ (
% 101.76/17.02 ^[Y2 : $i]:
% 101.76/17.02 ((
% 101.76/17.02 (in @
% 101.76/17.02 Y2 @
% 101.76/17.02 Y0) =>
% 101.76/17.02 ((
% 101.76/17.02 (in @
% 101.76/17.02 Y1 @
% 101.76/17.02 Y2) =>
% 101.76/17.02 (in @
% 101.76/17.02 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl133])).
% 101.76/17.02 thf(zip_derived_cl164, plain,
% 101.76/17.02 (~ (((notinemptyset) =>
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% 101.76/17.03 (secondinupair) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairIL) =>
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% 101.76/17.03 (setukpairIR) =>
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% 101.76/17.03 (kpairp) =>
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% 101.76/17.03 (singletoninpowerset) =>
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% 101.76/17.03 (singletoninpowunion) =>
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% 101.76/17.03 (upairsubunion) =>
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% 101.76/17.03 (ubforcartprodlem1) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem2) =>
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% 101.76/17.03 (ubforcartprodlem3) =>
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% 101.76/17.03 (injFuncSetFuncInj) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjFuncSetFuncIn) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjFuncSetFuncSurj) =>
% 101.76/17.03 ((
% 101.76/17.03 (leftInvIsSurj) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjCantorThm) =>
% 101.76/17.03 ((
% 101.76/17.03 (foundation2) =>
% 101.76/17.03 ((
% 101.76/17.03 (notinself) =>
% 101.76/17.03 ((
% 101.76/17.03 (notinself2) =>
% 101.76/17.03 ((
% 101.76/17.03 (omegaSp) =>
% 101.76/17.03 ((
% 101.76/17.03 (omegaSclos) =>
% 101.76/17.03 ((
% 101.76/17.03 (peano0notS) =>
% 101.76/17.03 ((
% 101.76/17.03 (peanoSinj) =>
% 101.76/17.03 ((
% 101.76/17.03 (transitivesetOp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintTransitive) =>
% 101.76/17.03 ((
% 101.76/17.03 (transitivesetOp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionTransitive) =>
% 101.76/17.03 ((
% 101.76/17.03 (ordinalMinLem1) =>
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y0 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (ordinal @
% 101.76/17.03 Y0) =>
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y1 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y2 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (in @
% 101.76/17.03 Y2 @
% 101.76/17.03 Y0) =>
% 101.76/17.03 ((
% 101.76/17.03 (in @
% 101.76/17.03 Y1 @
% 101.76/17.03 Y2) =>
% 101.76/17.03 (in @
% 101.76/17.03 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl149])).
% 101.76/17.03 thf(zip_derived_cl177, plain,
% 101.76/17.03 (~ (((exuE3e) =>
% 101.76/17.03 (((setext) =>
% 101.76/17.03 (((emptyI) =>
% 101.76/17.03 (((noeltsimpempty) =>
% 101.76/17.03 (((setbeta) =>
% 101.76/17.03 (((nonemptyE1) =>
% 101.76/17.03 (((nonemptyI) =>
% 101.76/17.03 (((nonemptyI1) =>
% 101.76/17.03 (((setadjoinIL) =>
% 101.76/17.03 (((in @ emptyset @
% 101.76/17.03 (setadjoin @ emptyset @ emptyset)) =>
% 101.76/17.03 (((setadjoinIR) =>
% 101.76/17.03 (((setadjoinE) =>
% 101.76/17.03 (((setadjoinOr) =>
% 101.76/17.03 (((setoftrueEq) =>
% 101.76/17.03 (((powersetI) =>
% 101.76/17.03 (((emptyinPowerset) =>
% 101.76/17.03 (((emptyInPowerset) =>
% 101.76/17.03 (((powersetE) =>
% 101.76/17.03 (((setunionI) =>
% 101.76/17.03 (((setunionE) =>
% 101.76/17.03 (((subPowSU) =>
% 101.76/17.03 (((exuE2) =>
% 101.76/17.03 (((nonemptyImpWitness) =>
% 101.76/17.03 (((uniqinunit) =>
% 101.76/17.03 (((notinsingleton) =>
% 101.76/17.03 (((eqinunit) =>
% 101.76/17.03 (((singletonsswitch) =>
% 101.76/17.03 (((upairsetE) =>
% 101.76/17.03 (((upairsetIL) =>
% 101.76/17.03 (((upairsetIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (emptyE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (vacuousDall) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan1) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan2) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan3) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan4) =>
% 101.76/17.03 ((
% 101.76/17.03 (prop2setI) =>
% 101.76/17.03 ((
% 101.76/17.03 (prop2set2propI) =>
% 101.76/17.03 ((
% 101.76/17.03 (notdexE) =>
% 101.76/17.03 ((
% 101.76/17.03 (notdallE) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI3) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (inCongP) =>
% 101.76/17.03 ((
% 101.76/17.03 (in__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuE3u) =>
% 101.76/17.03 ((
% 101.76/17.03 (exu__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoin__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (powerset__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunion__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuEu) =>
% 101.76/17.03 ((
% 101.76/17.03 (descr__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (dsetconstr__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqimpsubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqimpsubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (emptysetsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetE) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetE2) =>
% 101.76/17.03 ((
% 101.76/17.03 (notsubsetI) =>
% 101.76/17.03 ((
% 101.76/17.03 (notequalI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (notequalI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetRefl) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetTrans) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoinSub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoinSub2) =>
% 101.76/17.03 ((
% 101.76/17.03 (subset2powerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (setextsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetemptysetimpeq) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (inPowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (sepInPowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (sepSubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairset2IR) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionEcases) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionE) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionRsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectI) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset5) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset3) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectER) =>
% 101.76/17.03 ((
% 101.76/17.03 (disjointsetsI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectRsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset4) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (bs114d) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusI) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusER) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusSubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusERneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusELneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusILneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusIRneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusSubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffE) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffIneg1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffIneg2) =>
% 101.76/17.03 ((
% 101.76/17.03 (secondinupair) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairiskpair) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairp) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletonsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletoninpowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletoninpowunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairset2E) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairsubunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairinpowunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem1) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem3) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairin) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempair1) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempair) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionE2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionsingleton1) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionsingleton2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletonprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1E1) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1I) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1I2) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletonsuniq) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjL1) =>
% 101.76/17.03 ((
% 101.76/17.03 (kfstsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (theprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (kfstpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodfstin) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjL2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR11) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR12) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR1) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairequniteq) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR) =>
% 101.76/17.03 ((
% 101.76/17.03 (ksndsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (ksndpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairsurjEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodsndin) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairmemEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairmemER) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempaircEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodfstpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodsndpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairsurjEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrI) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrSub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setOfPairsIsBReln) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrERa) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrEL1) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrEL2) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrER) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcImageSingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (apProp) =>
% 101.76/17.03 ((
% 101.76/17.03 (app) =>
% 101.76/17.03 ((
% 101.76/17.03 (infuncsetfunc) =>
% 101.76/17.03 ((
% 101.76/17.03 (ap2p) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcinfuncset) =>
% 101.76/17.03 ((
% 101.76/17.03 (lamProp) =>
% 101.76/17.03 ((
% 101.76/17.03 (lamp) =>
% 101.76/17.03 ((
% 101.76/17.03 (lam2p) =>
% 101.76/17.03 ((
% 101.76/17.03 (brelnall1) =>
% 101.76/17.03 ((
% 101.76/17.03 (brelnall2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1E2) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp3) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcextLem) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp4) =>
% 101.76/17.03 ((
% 101.76/17.03 (subbreln) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqbreln) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcext) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcext2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ap2apEq1) =>
% 101.76/17.03 ((
% 101.76/17.03 (ap2apEq2) =>
% 101.76/17.03 ((
% 101.76/17.03 (beta1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eta1) =>
% 101.76/17.03 ((
% 101.76/17.03 (lam2lamEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (beta2) =>
% 101.76/17.03 ((
% 101.76/17.03 (eta2) =>
% 101.76/17.03 ((
% 101.76/17.03 (iffalseProp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (iffalseProp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrueProp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrueProp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ifSingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (ifp) =>
% 101.76/17.03 ((
% 101.76/17.03 (theeq) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrue) =>
% 101.76/17.03 ((
% 101.76/17.03 (iffalse) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrueorfalse) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (setextT) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetTI) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetTI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetTE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectTELcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectTERcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT1) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT2) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT3) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementSub1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementSub2) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTnotintersectT) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementImpComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementSubsetComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementInPowersetComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (contraSubsetComplement) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTcontraSubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTILcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTIRcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInUnion) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInUnion2) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInIntersectUnions) =>
% 101.76/17.03 ((
% 101.76/17.03 (intersectInPowersetIntersectUnions) =>
% 101.76/17.03 ((
% 101.76/17.03 (inComplementUnionImpNotIn1) =>
% 101.76/17.03 ((
% 101.76/17.03 (inComplementUnionImpInComplement1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTE) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTEcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementUnionInPowersetComplement) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a2) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1a) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1b) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2b2) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2b) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule0) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule1) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule3) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule4) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_1) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_3) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_4) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_5) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1all2) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1SetBreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (choice2fnsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (setOfPairsIsBReln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1all1) =>
% 101.76/17.03 ((
% 101.76/17.03 (subbreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqbreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compEex) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionEcases) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionCommutes) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2Ex) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2W) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2A) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2B) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Ex) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Ex1) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Equiv) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1E) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1I) =>
% 101.76/17.03 ((
% 101.76/17.03 (injFuncInInjFuncSet) =>
% 101.76/17.03 ((
% 101.76/17.03 (injFuncSetFuncIn) =>
% 101.76/17.03 ((
% 101.76/17.03 (injFuncSetFuncInj) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjFuncSetFuncIn) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjFuncSetFuncSurj) =>
% 101.76/17.03 ((
% 101.76/17.03 (leftInvIsSurj) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjCantorThm) =>
% 101.76/17.03 ((
% 101.76/17.03 (foundation2) =>
% 101.76/17.03 ((
% 101.76/17.03 (notinself) =>
% 101.76/17.03 ((
% 101.76/17.03 (notinself2) =>
% 101.76/17.03 ((
% 101.76/17.03 (omegaSp) =>
% 101.76/17.03 ((
% 101.76/17.03 (omegaSclos) =>
% 101.76/17.03 ((
% 101.76/17.03 (peano0notS) =>
% 101.76/17.03 ((
% 101.76/17.03 (peanoSinj) =>
% 101.76/17.03 ((
% 101.76/17.03 (transitivesetOp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintTransitive) =>
% 101.76/17.03 ((
% 101.76/17.03 (transitivesetOp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionTransitive) =>
% 101.76/17.03 ((
% 101.76/17.03 (ordinalMinLem1) =>
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y0 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (ordinal @
% 101.76/17.03 Y0) =>
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y1 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y2 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (in @
% 101.76/17.03 Y2 @
% 101.76/17.03 Y0) =>
% 101.76/17.03 ((
% 101.76/17.03 (in @
% 101.76/17.03 Y1 @
% 101.76/17.03 Y2) =>
% 101.76/17.03 (in @
% 101.76/17.03 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])).
% 101.76/17.03 thf(zip_derived_cl191, plain,
% 101.76/17.03 (~ (((setext) =>
% 101.76/17.03 (((emptyI) =>
% 101.76/17.03 (((noeltsimpempty) =>
% 101.76/17.03 (((setbeta) =>
% 101.76/17.03 (((nonemptyE1) =>
% 101.76/17.03 (((nonemptyI) =>
% 101.76/17.03 (((nonemptyI1) =>
% 101.76/17.03 (((setadjoinIL) =>
% 101.76/17.03 (((in @ emptyset @
% 101.76/17.03 (setadjoin @ emptyset @ emptyset)) =>
% 101.76/17.03 (((setadjoinIR) =>
% 101.76/17.03 (((setadjoinE) =>
% 101.76/17.03 (((setadjoinOr) =>
% 101.76/17.03 (((setoftrueEq) =>
% 101.76/17.03 (((powersetI) =>
% 101.76/17.03 (((emptyinPowerset) =>
% 101.76/17.03 (((emptyInPowerset) =>
% 101.76/17.03 (((powersetE) =>
% 101.76/17.03 (((setunionI) =>
% 101.76/17.03 (((setunionE) =>
% 101.76/17.03 (((subPowSU) =>
% 101.76/17.03 (((exuE2) =>
% 101.76/17.03 (((nonemptyImpWitness) =>
% 101.76/17.03 (((uniqinunit) =>
% 101.76/17.03 (((notinsingleton) =>
% 101.76/17.03 (((eqinunit) =>
% 101.76/17.03 (((singletonsswitch) =>
% 101.76/17.03 (((upairsetE) =>
% 101.76/17.03 (((upairsetIL) =>
% 101.76/17.03 (((upairsetIR) =>
% 101.76/17.03 (((emptyE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (vacuousDall) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan1) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan2) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan3) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan4) =>
% 101.76/17.03 ((
% 101.76/17.03 (prop2setI) =>
% 101.76/17.03 ((
% 101.76/17.03 (prop2set2propI) =>
% 101.76/17.03 ((
% 101.76/17.03 (notdexE) =>
% 101.76/17.03 ((
% 101.76/17.03 (notdallE) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI3) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (inCongP) =>
% 101.76/17.03 ((
% 101.76/17.03 (in__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuE3u) =>
% 101.76/17.03 ((
% 101.76/17.03 (exu__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoin__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (powerset__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunion__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuEu) =>
% 101.76/17.03 ((
% 101.76/17.03 (descr__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (dsetconstr__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqimpsubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqimpsubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (emptysetsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetE) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetE2) =>
% 101.76/17.03 ((
% 101.76/17.03 (notsubsetI) =>
% 101.76/17.03 ((
% 101.76/17.03 (notequalI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (notequalI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetRefl) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetTrans) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoinSub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoinSub2) =>
% 101.76/17.03 ((
% 101.76/17.03 (subset2powerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (setextsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetemptysetimpeq) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (inPowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (sepInPowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (sepSubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairset2IR) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionEcases) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionE) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionRsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectI) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset5) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset3) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectER) =>
% 101.76/17.03 ((
% 101.76/17.03 (disjointsetsI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectRsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset4) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (bs114d) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusI) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusER) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusSubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusERneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusELneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusILneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusIRneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusSubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffE) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffIneg1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffIneg2) =>
% 101.76/17.03 ((
% 101.76/17.03 (secondinupair) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairiskpair) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairp) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletonsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletoninpowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletoninpowunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairset2E) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairsubunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairinpowunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem1) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem3) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairin) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempair1) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempair) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionE2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionsingleton1) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionsingleton2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletonprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1E1) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1I) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1I2) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletonsuniq) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjL1) =>
% 101.76/17.03 ((
% 101.76/17.03 (kfstsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (theprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (kfstpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodfstin) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjL2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR11) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR12) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR1) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairequniteq) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR) =>
% 101.76/17.03 ((
% 101.76/17.03 (ksndsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (ksndpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairsurjEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodsndin) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairmemEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairmemER) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempaircEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodfstpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodsndpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairsurjEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrI) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrSub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setOfPairsIsBReln) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrERa) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrEL1) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrEL2) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrER) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcImageSingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (apProp) =>
% 101.76/17.03 ((
% 101.76/17.03 (app) =>
% 101.76/17.03 ((
% 101.76/17.03 (infuncsetfunc) =>
% 101.76/17.03 ((
% 101.76/17.03 (ap2p) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcinfuncset) =>
% 101.76/17.03 ((
% 101.76/17.03 (lamProp) =>
% 101.76/17.03 ((
% 101.76/17.03 (lamp) =>
% 101.76/17.03 ((
% 101.76/17.03 (lam2p) =>
% 101.76/17.03 ((
% 101.76/17.03 (brelnall1) =>
% 101.76/17.03 ((
% 101.76/17.03 (brelnall2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1E2) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp3) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcextLem) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp4) =>
% 101.76/17.03 ((
% 101.76/17.03 (subbreln) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqbreln) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcext) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcext2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ap2apEq1) =>
% 101.76/17.03 ((
% 101.76/17.03 (ap2apEq2) =>
% 101.76/17.03 ((
% 101.76/17.03 (beta1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eta1) =>
% 101.76/17.03 ((
% 101.76/17.03 (lam2lamEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (beta2) =>
% 101.76/17.03 ((
% 101.76/17.03 (eta2) =>
% 101.76/17.03 ((
% 101.76/17.03 (iffalseProp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (iffalseProp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrueProp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrueProp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ifSingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (ifp) =>
% 101.76/17.03 ((
% 101.76/17.03 (theeq) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrue) =>
% 101.76/17.03 ((
% 101.76/17.03 (iffalse) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrueorfalse) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (setextT) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetTI) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetTI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetTE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectTELcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectTERcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT1) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT2) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT3) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementSub1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementSub2) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTnotintersectT) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementImpComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementSubsetComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementInPowersetComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (contraSubsetComplement) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTcontraSubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTILcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTIRcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInUnion) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInUnion2) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInIntersectUnions) =>
% 101.76/17.03 ((
% 101.76/17.03 (intersectInPowersetIntersectUnions) =>
% 101.76/17.03 ((
% 101.76/17.03 (inComplementUnionImpNotIn1) =>
% 101.76/17.03 ((
% 101.76/17.03 (inComplementUnionImpInComplement1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTE) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTEcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementUnionInPowersetComplement) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a2) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1a) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1b) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2b2) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2b) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule0) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule1) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule3) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule4) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_1) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_3) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_4) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_5) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1all2) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1SetBreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (choice2fnsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (setOfPairsIsBReln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1all1) =>
% 101.76/17.03 ((
% 101.76/17.03 (subbreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqbreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compEex) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionEcases) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionCommutes) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2Ex) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2W) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2A) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2B) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Ex) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Ex1) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Equiv) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1E) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1I) =>
% 101.76/17.03 ((
% 101.76/17.03 (injFuncInInjFuncSet) =>
% 101.76/17.03 ((
% 101.76/17.03 (injFuncSetFuncIn) =>
% 101.76/17.03 ((
% 101.76/17.03 (injFuncSetFuncInj) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjFuncSetFuncIn) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjFuncSetFuncSurj) =>
% 101.76/17.03 ((
% 101.76/17.03 (leftInvIsSurj) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjCantorThm) =>
% 101.76/17.03 ((
% 101.76/17.03 (foundation2) =>
% 101.76/17.03 ((
% 101.76/17.03 (notinself) =>
% 101.76/17.03 ((
% 101.76/17.03 (notinself2) =>
% 101.76/17.03 ((
% 101.76/17.03 (omegaSp) =>
% 101.76/17.03 ((
% 101.76/17.03 (omegaSclos) =>
% 101.76/17.03 ((
% 101.76/17.03 (peano0notS) =>
% 101.76/17.03 ((
% 101.76/17.03 (peanoSinj) =>
% 101.76/17.03 ((
% 101.76/17.03 (transitivesetOp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintTransitive) =>
% 101.76/17.03 ((
% 101.76/17.03 (transitivesetOp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionTransitive) =>
% 101.76/17.03 ((
% 101.76/17.03 (ordinalMinLem1) =>
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y0 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (ordinal @
% 101.76/17.03 Y0) =>
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y1 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y2 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (in @
% 101.76/17.03 Y2 @
% 101.76/17.03 Y0) =>
% 101.76/17.03 ((
% 101.76/17.03 (in @
% 101.76/17.03 Y1 @
% 101.76/17.03 Y2) =>
% 101.76/17.03 (in @
% 101.76/17.03 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl177])).
% 101.76/17.03 thf(zip_derived_cl205, plain,
% 101.76/17.03 (~ (((emptyI) =>
% 101.76/17.03 (((noeltsimpempty) =>
% 101.76/17.03 (((setbeta) =>
% 101.76/17.03 (((nonemptyE1) =>
% 101.76/17.03 (((nonemptyI) =>
% 101.76/17.03 (((nonemptyI1) =>
% 101.76/17.03 (((setadjoinIL) =>
% 101.76/17.03 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 101.76/17.03 (((setadjoinIR) =>
% 101.76/17.03 (((setadjoinE) =>
% 101.76/17.03 (((setadjoinOr) =>
% 101.76/17.03 (((setoftrueEq) =>
% 101.76/17.03 (((powersetI) =>
% 101.76/17.03 (((emptyinPowerset) =>
% 101.76/17.03 (((emptyInPowerset) =>
% 101.76/17.03 (((powersetE) =>
% 101.76/17.03 (((setunionI) =>
% 101.76/17.03 (((setunionE) =>
% 101.76/17.03 (((subPowSU) =>
% 101.76/17.03 (((exuE2) =>
% 101.76/17.03 (((nonemptyImpWitness) =>
% 101.76/17.03 (((uniqinunit) =>
% 101.76/17.03 (((notinsingleton) =>
% 101.76/17.03 (((eqinunit) =>
% 101.76/17.03 (((singletonsswitch) =>
% 101.76/17.03 (((upairsetE) =>
% 101.76/17.03 (((upairsetIL) =>
% 101.76/17.03 (((upairsetIR) =>
% 101.76/17.03 (((emptyE1) =>
% 101.76/17.03 (((vacuousDall) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan1) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan2) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan3) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan4) =>
% 101.76/17.03 ((
% 101.76/17.03 (prop2setI) =>
% 101.76/17.03 ((
% 101.76/17.03 (prop2set2propI) =>
% 101.76/17.03 ((
% 101.76/17.03 (notdexE) =>
% 101.76/17.03 ((
% 101.76/17.03 (notdallE) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI3) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (inCongP) =>
% 101.76/17.03 ((
% 101.76/17.03 (in__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuE3u) =>
% 101.76/17.03 ((
% 101.76/17.03 (exu__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoin__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (powerset__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunion__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuEu) =>
% 101.76/17.03 ((
% 101.76/17.03 (descr__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (dsetconstr__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqimpsubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqimpsubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (emptysetsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetE) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetE2) =>
% 101.76/17.03 ((
% 101.76/17.03 (notsubsetI) =>
% 101.76/17.03 ((
% 101.76/17.03 (notequalI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (notequalI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetRefl) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetTrans) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoinSub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoinSub2) =>
% 101.76/17.03 ((
% 101.76/17.03 (subset2powerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (setextsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetemptysetimpeq) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (inPowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (sepInPowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (sepSubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairset2IR) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionEcases) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionE) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionRsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectI) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset5) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset3) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectER) =>
% 101.76/17.03 ((
% 101.76/17.03 (disjointsetsI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectRsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset4) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (bs114d) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusI) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusER) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusSubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusERneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusELneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusILneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusIRneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusSubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffE) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffIneg1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffIneg2) =>
% 101.76/17.03 ((
% 101.76/17.03 (secondinupair) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairiskpair) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairp) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletonsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletoninpowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletoninpowunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairset2E) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairsubunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairinpowunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem1) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem3) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairin) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempair1) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempair) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionE2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionsingleton1) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionsingleton2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletonprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1E1) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1I) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1I2) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletonsuniq) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjL1) =>
% 101.76/17.03 ((
% 101.76/17.03 (kfstsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (theprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (kfstpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodfstin) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjL2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR11) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR12) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR1) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairequniteq) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR) =>
% 101.76/17.03 ((
% 101.76/17.03 (ksndsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (ksndpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairsurjEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodsndin) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairmemEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairmemER) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempaircEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodfstpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodsndpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairsurjEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrI) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrSub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setOfPairsIsBReln) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrERa) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrEL1) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrEL2) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrER) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcImageSingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (apProp) =>
% 101.76/17.03 ((
% 101.76/17.03 (app) =>
% 101.76/17.03 ((
% 101.76/17.03 (infuncsetfunc) =>
% 101.76/17.03 ((
% 101.76/17.03 (ap2p) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcinfuncset) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
% 101.76/17.03 (lamp) =>
% 101.76/17.03 ((
% 101.76/17.03 (lam2p) =>
% 101.76/17.03 ((
% 101.76/17.03 (brelnall1) =>
% 101.76/17.03 ((
% 101.76/17.03 (brelnall2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1E2) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp3) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp2) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp4) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
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% 101.76/17.03 (funcext) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcext2) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
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% 101.76/17.03 ((
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% 101.76/17.03 ((
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% 101.76/17.03 ((
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% 101.76/17.03 ((
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% 101.76/17.03 ((
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% 101.76/17.03 ((
% 101.76/17.03 (iffalseProp2) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
% 101.76/17.03 (iftrueProp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ifSingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (ifp) =>
% 101.76/17.03 ((
% 101.76/17.03 (theeq) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrue) =>
% 101.76/17.03 ((
% 101.76/17.03 (iffalse) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrueorfalse) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (setextT) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetTI) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetTI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetTE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectTELcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectTERcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT1) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT2) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT3) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementSub1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementSub2) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTnotintersectT) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementImpComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementSubsetComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementInPowersetComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (contraSubsetComplement) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTcontraSubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTILcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTIRcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInUnion) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInUnion2) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInIntersectUnions) =>
% 101.76/17.03 ((
% 101.76/17.03 (intersectInPowersetIntersectUnions) =>
% 101.76/17.03 ((
% 101.76/17.03 (inComplementUnionImpNotIn1) =>
% 101.76/17.03 ((
% 101.76/17.03 (inComplementUnionImpInComplement1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTE) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTEcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementUnionInPowersetComplement) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a2) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1a) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1b) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2b2) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2b) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule0) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule1) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule3) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule4) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_1) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_3) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_4) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_5) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1all2) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1SetBreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (choice2fnsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (setOfPairsIsBReln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1all1) =>
% 101.76/17.03 ((
% 101.76/17.03 (subbreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqbreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compEex) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionEcases) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionCommutes) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2Ex) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2W) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2A) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2B) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Ex) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Ex1) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Equiv) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1E) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1I) =>
% 101.76/17.03 ((
% 101.76/17.03 (injFuncInInjFuncSet) =>
% 101.76/17.03 ((
% 101.76/17.03 (injFuncSetFuncIn) =>
% 101.76/17.03 ((
% 101.76/17.03 (injFuncSetFuncInj) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjFuncSetFuncIn) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjFuncSetFuncSurj) =>
% 101.76/17.03 ((
% 101.76/17.03 (leftInvIsSurj) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjCantorThm) =>
% 101.76/17.03 ((
% 101.76/17.03 (foundation2) =>
% 101.76/17.03 ((
% 101.76/17.03 (notinself) =>
% 101.76/17.03 ((
% 101.76/17.03 (notinself2) =>
% 101.76/17.03 ((
% 101.76/17.03 (omegaSp) =>
% 101.76/17.03 ((
% 101.76/17.03 (omegaSclos) =>
% 101.76/17.03 ((
% 101.76/17.03 (peano0notS) =>
% 101.76/17.03 ((
% 101.76/17.03 (peanoSinj) =>
% 101.76/17.03 ((
% 101.76/17.03 (transitivesetOp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintTransitive) =>
% 101.76/17.03 ((
% 101.76/17.03 (transitivesetOp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionTransitive) =>
% 101.76/17.03 ((
% 101.76/17.03 (ordinalMinLem1) =>
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y0 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (ordinal @
% 101.76/17.03 Y0) =>
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y1 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y2 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (in @
% 101.76/17.03 Y2 @
% 101.76/17.03 Y0) =>
% 101.76/17.03 ((
% 101.76/17.03 (in @
% 101.76/17.03 Y1 @
% 101.76/17.03 Y2) =>
% 101.76/17.03 (in @
% 101.76/17.03 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])).
% 101.76/17.03 thf(zip_derived_cl219, plain,
% 101.76/17.03 (~ (((noeltsimpempty) =>
% 101.76/17.03 (((setbeta) =>
% 101.76/17.03 (((nonemptyE1) =>
% 101.76/17.03 (((nonemptyI) =>
% 101.76/17.03 (((nonemptyI1) =>
% 101.76/17.03 (((setadjoinIL) =>
% 101.76/17.03 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 101.76/17.03 (((setadjoinIR) =>
% 101.76/17.03 (((setadjoinE) =>
% 101.76/17.03 (((setadjoinOr) =>
% 101.76/17.03 (((setoftrueEq) =>
% 101.76/17.03 (((powersetI) =>
% 101.76/17.03 (((emptyinPowerset) =>
% 101.76/17.03 (((emptyInPowerset) =>
% 101.76/17.03 (((powersetE) =>
% 101.76/17.03 (((setunionI) =>
% 101.76/17.03 (((setunionE) =>
% 101.76/17.03 (((subPowSU) =>
% 101.76/17.03 (((exuE2) =>
% 101.76/17.03 (((nonemptyImpWitness) =>
% 101.76/17.03 (((uniqinunit) =>
% 101.76/17.03 (((notinsingleton) =>
% 101.76/17.03 (((eqinunit) =>
% 101.76/17.03 (((singletonsswitch) =>
% 101.76/17.03 (((upairsetE) =>
% 101.76/17.03 (((upairsetIL) =>
% 101.76/17.03 (((upairsetIR) =>
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% 101.76/17.03 (((quantDeMorgan1) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan2) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan3) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan4) =>
% 101.76/17.03 ((
% 101.76/17.03 (prop2setI) =>
% 101.76/17.03 ((
% 101.76/17.03 (prop2set2propI) =>
% 101.76/17.03 ((
% 101.76/17.03 (notdexE) =>
% 101.76/17.03 ((
% 101.76/17.03 (notdallE) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI3) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (inCongP) =>
% 101.76/17.03 ((
% 101.76/17.03 (in__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuE3u) =>
% 101.76/17.03 ((
% 101.76/17.03 (exu__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoin__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (powerset__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunion__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuEu) =>
% 101.76/17.03 ((
% 101.76/17.03 (descr__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (dsetconstr__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqimpsubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqimpsubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (emptysetsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetE) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetE2) =>
% 101.76/17.03 ((
% 101.76/17.03 (notsubsetI) =>
% 101.76/17.03 ((
% 101.76/17.03 (notequalI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (notequalI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetRefl) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetTrans) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoinSub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoinSub2) =>
% 101.76/17.03 ((
% 101.76/17.03 (subset2powerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (setextsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetemptysetimpeq) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
% 101.76/17.03 (powersetE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (inPowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (sepInPowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (sepSubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairset2IR) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionEcases) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionE) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionRsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectI) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset5) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset3) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectER) =>
% 101.76/17.03 ((
% 101.76/17.03 (disjointsetsI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectRsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset4) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (bs114d) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusI) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusER) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusSubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusERneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusELneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusILneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusIRneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusSubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffE) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffIneg1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffIneg2) =>
% 101.76/17.03 ((
% 101.76/17.03 (secondinupair) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairiskpair) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairp) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletonsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletoninpowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletoninpowunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairset2E) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairsubunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairinpowunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem1) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem3) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairin) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempair1) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempair) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionE2) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
% 101.76/17.03 (setunionsingleton2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletonprop) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
% 101.76/17.03 (ex1I) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1I2) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletonsuniq) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
% 101.76/17.03 (kfstsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (theprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (kfstpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodfstin) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjL2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR11) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR12) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR1) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairequniteq) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR) =>
% 101.76/17.03 ((
% 101.76/17.03 (ksndsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (ksndpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairsurjEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodsndin) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairmemEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairmemER) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempaircEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodfstpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodsndpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairsurjEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrI) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrSub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setOfPairsIsBReln) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrERa) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrEL1) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrEL2) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrER) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcImageSingleton) =>
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% 101.76/17.03 (apProp) =>
% 101.76/17.03 ((
% 101.76/17.03 (app) =>
% 101.76/17.03 ((
% 101.76/17.03 (infuncsetfunc) =>
% 101.76/17.03 ((
% 101.76/17.03 (ap2p) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcinfuncset) =>
% 101.76/17.03 ((
% 101.76/17.03 (lamProp) =>
% 101.76/17.03 ((
% 101.76/17.03 (lamp) =>
% 101.76/17.03 ((
% 101.76/17.03 (lam2p) =>
% 101.76/17.03 ((
% 101.76/17.03 (brelnall1) =>
% 101.76/17.03 ((
% 101.76/17.03 (brelnall2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1E2) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp3) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcextLem) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp4) =>
% 101.76/17.03 ((
% 101.76/17.03 (subbreln) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqbreln) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcext) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcext2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ap2apEq1) =>
% 101.76/17.03 ((
% 101.76/17.03 (ap2apEq2) =>
% 101.76/17.03 ((
% 101.76/17.03 (beta1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eta1) =>
% 101.76/17.03 ((
% 101.76/17.03 (lam2lamEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (beta2) =>
% 101.76/17.03 ((
% 101.76/17.03 (eta2) =>
% 101.76/17.03 ((
% 101.76/17.03 (iffalseProp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (iffalseProp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrueProp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrueProp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ifSingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (ifp) =>
% 101.76/17.03 ((
% 101.76/17.03 (theeq) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrue) =>
% 101.76/17.03 ((
% 101.76/17.03 (iffalse) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrueorfalse) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (setextT) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetTI) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetTI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetTE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectTELcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectTERcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT1) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT2) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT3) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementSub1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementSub2) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTnotintersectT) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementImpComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementSubsetComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementInPowersetComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (contraSubsetComplement) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTcontraSubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTILcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTIRcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInUnion) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInUnion2) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInIntersectUnions) =>
% 101.76/17.03 ((
% 101.76/17.03 (intersectInPowersetIntersectUnions) =>
% 101.76/17.03 ((
% 101.76/17.03 (inComplementUnionImpNotIn1) =>
% 101.76/17.03 ((
% 101.76/17.03 (inComplementUnionImpInComplement1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTE) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTEcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementUnionInPowersetComplement) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a2) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1a) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1b) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2b2) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2b) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule0) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule1) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule3) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule4) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_1) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_3) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_4) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_5) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1all2) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1SetBreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (choice2fnsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (setOfPairsIsBReln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1all1) =>
% 101.76/17.03 ((
% 101.76/17.03 (subbreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqbreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compEex) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionEcases) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionCommutes) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2Ex) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2W) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2A) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2B) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Ex) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Ex1) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Equiv) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1E) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1I) =>
% 101.76/17.03 ((
% 101.76/17.03 (injFuncInInjFuncSet) =>
% 101.76/17.03 ((
% 101.76/17.03 (injFuncSetFuncIn) =>
% 101.76/17.03 ((
% 101.76/17.03 (injFuncSetFuncInj) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjFuncSetFuncIn) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjFuncSetFuncSurj) =>
% 101.76/17.03 ((
% 101.76/17.03 (leftInvIsSurj) =>
% 101.76/17.03 ((
% 101.76/17.03 (surjCantorThm) =>
% 101.76/17.03 ((
% 101.76/17.03 (foundation2) =>
% 101.76/17.03 ((
% 101.76/17.03 (notinself) =>
% 101.76/17.03 ((
% 101.76/17.03 (notinself2) =>
% 101.76/17.03 ((
% 101.76/17.03 (omegaSp) =>
% 101.76/17.03 ((
% 101.76/17.03 (omegaSclos) =>
% 101.76/17.03 ((
% 101.76/17.03 (peano0notS) =>
% 101.76/17.03 ((
% 101.76/17.03 (peanoSinj) =>
% 101.76/17.03 ((
% 101.76/17.03 (transitivesetOp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintTransitive) =>
% 101.76/17.03 ((
% 101.76/17.03 (transitivesetOp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionTransitive) =>
% 101.76/17.03 ((
% 101.76/17.03 (ordinalMinLem1) =>
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y0 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (ordinal @
% 101.76/17.03 Y0) =>
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y1 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (!!) @ (
% 101.76/17.03 ^[Y2 : $i]:
% 101.76/17.03 ((
% 101.76/17.03 (in @
% 101.76/17.03 Y2 @
% 101.76/17.03 Y0) =>
% 101.76/17.03 ((
% 101.76/17.03 (in @
% 101.76/17.03 Y1 @
% 101.76/17.03 Y2) =>
% 101.76/17.03 (in @
% 101.76/17.03 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl205])).
% 101.76/17.03 thf(zip_derived_cl231, plain,
% 101.76/17.03 (~ (((setbeta) =>
% 101.76/17.03 (((nonemptyE1) =>
% 101.76/17.03 (((nonemptyI) =>
% 101.76/17.03 (((nonemptyI1) =>
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% 101.76/17.03 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 101.76/17.03 (((setadjoinIR) =>
% 101.76/17.03 (((setadjoinE) =>
% 101.76/17.03 (((setadjoinOr) =>
% 101.76/17.03 (((setoftrueEq) =>
% 101.76/17.03 (((powersetI) =>
% 101.76/17.03 (((emptyinPowerset) =>
% 101.76/17.03 (((emptyInPowerset) =>
% 101.76/17.03 (((powersetE) =>
% 101.76/17.03 (((setunionI) =>
% 101.76/17.03 (((setunionE) =>
% 101.76/17.03 (((subPowSU) =>
% 101.76/17.03 (((exuE2) =>
% 101.76/17.03 (((nonemptyImpWitness) =>
% 101.76/17.03 (((uniqinunit) =>
% 101.76/17.03 (((notinsingleton) =>
% 101.76/17.03 (((eqinunit) =>
% 101.76/17.03 (((singletonsswitch) =>
% 101.76/17.03 (((upairsetE) =>
% 101.76/17.03 (((upairsetIL) =>
% 101.76/17.03 (((upairsetIR) =>
% 101.76/17.03 (((emptyE1) =>
% 101.76/17.03 (((vacuousDall) =>
% 101.76/17.03 (((quantDeMorgan1) =>
% 101.76/17.03 (((quantDeMorgan2) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan3) =>
% 101.76/17.03 ((
% 101.76/17.03 (quantDeMorgan4) =>
% 101.76/17.03 ((
% 101.76/17.03 (prop2setI) =>
% 101.76/17.03 ((
% 101.76/17.03 (prop2set2propI) =>
% 101.76/17.03 ((
% 101.76/17.03 (notdexE) =>
% 101.76/17.03 ((
% 101.76/17.03 (notdallE) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI3) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (inCongP) =>
% 101.76/17.03 ((
% 101.76/17.03 (in__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuE3u) =>
% 101.76/17.03 ((
% 101.76/17.03 (exu__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoin__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (powerset__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunion__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (exuEu) =>
% 101.76/17.03 ((
% 101.76/17.03 (descr__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (dsetconstr__Cong) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqimpsubset2) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
% 101.76/17.03 (subsetI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (emptysetsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetE) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetE2) =>
% 101.76/17.03 ((
% 101.76/17.03 (notsubsetI) =>
% 101.76/17.03 ((
% 101.76/17.03 (notequalI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (notequalI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetRefl) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetTrans) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoinSub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setadjoinSub2) =>
% 101.76/17.03 ((
% 101.76/17.03 (subset2powerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (setextsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetemptysetimpeq) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
% 101.76/17.03 (powersetE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (inPowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (sepInPowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (sepSubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairset2IR) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionEcases) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionE) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionRsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectI) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset5) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset3) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectER) =>
% 101.76/17.03 ((
% 101.76/17.03 (disjointsetsI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectRsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset4) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectSubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (bs114d) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusI) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusER) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusSubset2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusERneg) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
% 101.76/17.03 (setminusILneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusIRneg) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusLsub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusSubset1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffE) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffI2) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffIneg1) =>
% 101.76/17.03 ((
% 101.76/17.03 (symdiffIneg2) =>
% 101.76/17.03 ((
% 101.76/17.03 (secondinupair) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairiskpair) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairp) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletonsubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletoninpowerset) =>
% 101.76/17.03 ((
% 101.76/17.03 (singletoninpowunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairset2E) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairsubunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairinpowunion) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem1) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ubforcartprodlem3) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairin) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempair1) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempair) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionE2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setunionsingleton1) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
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% 101.76/17.03 ((
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% 101.76/17.03 ((
% 101.76/17.03 (ex1I) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1I2) =>
% 101.76/17.03 ((
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% 101.76/17.03 ((
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% 101.76/17.03 ((
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% 101.76/17.03 ((
% 101.76/17.03 (kfstpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodfstin) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjL2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjL) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR11) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR12) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR1) =>
% 101.76/17.03 ((
% 101.76/17.03 (upairequniteq) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR2) =>
% 101.76/17.03 ((
% 101.76/17.03 (setukpairinjR) =>
% 101.76/17.03 ((
% 101.76/17.03 (ksndsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (ksndpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (kpairsurjEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodsndin) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairmemEL) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairmemER) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodmempaircEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodfstpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodsndpairEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (cartprodpairsurjEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrI) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrSub) =>
% 101.76/17.03 ((
% 101.76/17.03 (setOfPairsIsBReln) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrERa) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrEL1) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrEL2) =>
% 101.76/17.03 ((
% 101.76/17.03 (dpsetconstrER) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcImageSingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (apProp) =>
% 101.76/17.03 ((
% 101.76/17.03 (app) =>
% 101.76/17.03 ((
% 101.76/17.03 (infuncsetfunc) =>
% 101.76/17.03 ((
% 101.76/17.03 (ap2p) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcinfuncset) =>
% 101.76/17.03 ((
% 101.76/17.03 (lamProp) =>
% 101.76/17.03 ((
% 101.76/17.03 (lamp) =>
% 101.76/17.03 ((
% 101.76/17.03 (lam2p) =>
% 101.76/17.03 ((
% 101.76/17.03 (brelnall1) =>
% 101.76/17.03 ((
% 101.76/17.03 (brelnall2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ex1E2) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp3) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcextLem) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcGraphProp4) =>
% 101.76/17.03 ((
% 101.76/17.03 (subbreln) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqbreln) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcext) =>
% 101.76/17.03 ((
% 101.76/17.03 (funcext2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ap2apEq1) =>
% 101.76/17.03 ((
% 101.76/17.03 (ap2apEq2) =>
% 101.76/17.03 ((
% 101.76/17.03 (beta1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eta1) =>
% 101.76/17.03 ((
% 101.76/17.03 (lam2lamEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (beta2) =>
% 101.76/17.03 ((
% 101.76/17.03 (eta2) =>
% 101.76/17.03 ((
% 101.76/17.03 (iffalseProp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (iffalseProp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrueProp1) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrueProp2) =>
% 101.76/17.03 ((
% 101.76/17.03 (ifSingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (ifp) =>
% 101.76/17.03 ((
% 101.76/17.03 (theeq) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrue) =>
% 101.76/17.03 ((
% 101.76/17.03 (iffalse) =>
% 101.76/17.03 ((
% 101.76/17.03 (iftrueorfalse) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (setminusT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementT_lem) =>
% 101.76/17.03 ((
% 101.76/17.03 (setextT) =>
% 101.76/17.03 ((
% 101.76/17.03 (subsetTI) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetTI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (powersetTE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectTELcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (binintersectTERcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT1) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT2) =>
% 101.76/17.03 ((
% 101.76/17.03 (contrasubsetT3) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementI1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementE1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementSub1) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementSub2) =>
% 101.76/17.03 ((
% 101.76/17.03 (doubleComplementEq) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTnotintersectT) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementImpComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementSubsetComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementInPowersetComplementIntersect) =>
% 101.76/17.03 ((
% 101.76/17.03 (contraSubsetComplement) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementTcontraSubset) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTILcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTIRcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInUnion) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInUnion2) =>
% 101.76/17.03 ((
% 101.76/17.03 (inIntersectImpInIntersectUnions) =>
% 101.76/17.03 ((
% 101.76/17.03 (intersectInPowersetIntersectUnions) =>
% 101.76/17.03 ((
% 101.76/17.03 (inComplementUnionImpNotIn1) =>
% 101.76/17.03 ((
% 101.76/17.03 (inComplementUnionImpInComplement1) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTE) =>
% 101.76/17.03 ((
% 101.76/17.03 (binunionTEcontra) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a1) =>
% 101.76/17.03 ((
% 101.76/17.03 (complementUnionInPowersetComplement) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a2) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1a) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1b) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan1) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2a) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2b2) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2b) =>
% 101.76/17.03 ((
% 101.76/17.03 (demorgan2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule0) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule1) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule3) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz13rule4) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_1) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_2) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_3) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_4) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz1_5) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1all2) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1SetBreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (choice2fnsingleton) =>
% 101.76/17.03 ((
% 101.76/17.03 (setOfPairsIsBReln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1all1) =>
% 101.76/17.03 ((
% 101.76/17.03 (subbreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (eqbreln1) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1invE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1compEex) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionprop) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionIL) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionIR) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionI) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionE) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionEcases) =>
% 101.76/17.03 ((
% 101.76/17.03 (breln1unionCommutes) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2Ex) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2W) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2A) =>
% 101.76/17.03 ((
% 101.76/17.03 (woz2B) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Ex) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Ex1) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1Equiv) =>
% 101.76/17.03 ((
% 101.76/17.03 (image1E) =>
% 101.76/17.04 ((
% 101.76/17.04 (image1I) =>
% 101.76/17.04 ((
% 101.76/17.04 (injFuncInInjFuncSet) =>
% 101.76/17.04 ((
% 101.76/17.04 (injFuncSetFuncIn) =>
% 101.76/17.04 ((
% 101.76/17.04 (injFuncSetFuncInj) =>
% 101.76/17.04 ((
% 101.76/17.04 (surjFuncSetFuncIn) =>
% 101.76/17.04 ((
% 101.76/17.04 (surjFuncSetFuncSurj) =>
% 101.76/17.04 ((
% 101.76/17.04 (leftInvIsSurj) =>
% 101.76/17.04 ((
% 101.76/17.04 (surjCantorThm) =>
% 101.76/17.04 ((
% 101.76/17.04 (foundation2) =>
% 101.76/17.04 ((
% 101.76/17.04 (notinself) =>
% 101.76/17.04 ((
% 101.76/17.04 (notinself2) =>
% 101.76/17.04 ((
% 101.76/17.04 (omegaSp) =>
% 101.76/17.04 ((
% 101.76/17.04 (omegaSclos) =>
% 101.76/17.04 ((
% 101.76/17.04 (peano0notS) =>
% 101.76/17.04 ((
% 101.76/17.04 (peanoSinj) =>
% 101.76/17.04 ((
% 101.76/17.04 (transitivesetOp1) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintTransitive) =>
% 101.76/17.04 ((
% 101.76/17.04 (transitivesetOp2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionTransitive) =>
% 101.76/17.04 ((
% 101.76/17.04 (ordinalMinLem1) =>
% 101.76/17.04 ((
% 101.76/17.04 (!!) @ (
% 101.76/17.04 ^[Y0 : $i]:
% 101.76/17.04 ((
% 101.76/17.04 (ordinal @
% 101.76/17.04 Y0) =>
% 101.76/17.04 ((
% 101.76/17.04 (!!) @ (
% 101.76/17.04 ^[Y1 : $i]:
% 101.76/17.04 ((
% 101.76/17.04 (!!) @ (
% 101.76/17.04 ^[Y2 : $i]:
% 101.76/17.04 ((
% 101.76/17.04 (in @
% 101.76/17.04 Y2 @
% 101.76/17.04 Y0) =>
% 101.76/17.04 ((
% 101.76/17.04 (in @
% 101.76/17.04 Y1 @
% 101.76/17.04 Y2) =>
% 101.76/17.04 (in @
% 101.76/17.04 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl219])).
% 101.76/17.04 thf(zip_derived_cl244, plain,
% 101.76/17.04 (~ (((nonemptyE1) =>
% 101.76/17.04 (((nonemptyI) =>
% 101.76/17.04 (((nonemptyI1) =>
% 101.76/17.04 (((setadjoinIL) =>
% 101.76/17.04 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 101.76/17.04 (((setadjoinIR) =>
% 101.76/17.04 (((setadjoinE) =>
% 101.76/17.04 (((setadjoinOr) =>
% 101.76/17.04 (((setoftrueEq) =>
% 101.76/17.04 (((powersetI) =>
% 101.76/17.04 (((emptyinPowerset) =>
% 101.76/17.04 (((emptyInPowerset) =>
% 101.76/17.04 (((powersetE) =>
% 101.76/17.04 (((setunionI) =>
% 101.76/17.04 (((setunionE) =>
% 101.76/17.04 (((subPowSU) =>
% 101.76/17.04 (((exuE2) =>
% 101.76/17.04 (((nonemptyImpWitness) =>
% 101.76/17.04 (((uniqinunit) =>
% 101.76/17.04 (((notinsingleton) =>
% 101.76/17.04 (((eqinunit) =>
% 101.76/17.04 (((singletonsswitch) =>
% 101.76/17.04 (((upairsetE) =>
% 101.76/17.04 (((upairsetIL) =>
% 101.76/17.04 (((upairsetIR) =>
% 101.76/17.04 (((emptyE1) =>
% 101.76/17.04 (((vacuousDall) =>
% 101.76/17.04 (((quantDeMorgan1) =>
% 101.76/17.04 (((quantDeMorgan2) =>
% 101.76/17.04 (((quantDeMorgan3) =>
% 101.76/17.04 ((
% 101.76/17.04 (quantDeMorgan4) =>
% 101.76/17.04 ((
% 101.76/17.04 (prop2setI) =>
% 101.76/17.04 ((
% 101.76/17.04 (prop2set2propI) =>
% 101.76/17.04 ((
% 101.76/17.04 (notdexE) =>
% 101.76/17.04 ((
% 101.76/17.04 (notdallE) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuI3) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuI2) =>
% 101.76/17.04 ((
% 101.76/17.04 (inCongP) =>
% 101.76/17.04 ((
% 101.76/17.04 (in__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuE3u) =>
% 101.76/17.04 ((
% 101.76/17.04 (exu__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (setadjoin__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (powerset__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunion__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuEu) =>
% 101.76/17.04 ((
% 101.76/17.04 (descr__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (dsetconstr__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetI1) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (eqimpsubset1) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (emptysetsubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetE) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetE2) =>
% 101.76/17.04 ((
% 101.76/17.04 (notsubsetI) =>
% 101.76/17.04 ((
% 101.76/17.04 (notequalI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (notequalI2) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetRefl) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetTrans) =>
% 101.76/17.04 ((
% 101.76/17.04 (setadjoinSub) =>
% 101.76/17.04 ((
% 101.76/17.04 (setadjoinSub2) =>
% 101.76/17.04 ((
% 101.76/17.04 (subset2powerset) =>
% 101.76/17.04 ((
% 101.76/17.04 (setextsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetemptysetimpeq) =>
% 101.76/17.04 ((
% 101.76/17.04 (powersetI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (powersetE1) =>
% 101.76/17.04 ((
% 101.76/17.04 (inPowerset) =>
% 101.76/17.04 ((
% 101.76/17.04 (powersetsubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (sepInPowerset) =>
% 101.76/17.04 ((
% 101.76/17.04 (sepSubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionIL) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairset2IR) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionIR) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionEcases) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionE) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionLsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionRsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectI) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset5) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectEL) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectLsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset2) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset3) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectER) =>
% 101.76/17.04 ((
% 101.76/17.04 (disjointsetsI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectRsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset4) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset1) =>
% 101.76/17.04 ((
% 101.76/17.04 (bs114d) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusI) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusEL) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusER) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusSubset2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusERneg) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusELneg) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusILneg) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusIRneg) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusLsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusSubset1) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffE) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffI2) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffIneg1) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffIneg2) =>
% 101.76/17.04 ((
% 101.76/17.04 (secondinupair) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairIL) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairIR) =>
% 101.76/17.04 ((
% 101.76/17.04 (kpairiskpair) =>
% 101.76/17.04 ((
% 101.76/17.04 (kpairp) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletonsubset) =>
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% 101.76/17.04 (setukpairinjR12) =>
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% 101.76/17.04 (upairequniteq) =>
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% 101.76/17.04 (brelnall2) =>
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% 101.76/17.04 ((
% 101.76/17.04 (funcGraphProp1) =>
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% 101.76/17.04 (funcGraphProp3) =>
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% 101.76/17.04 (funcGraphProp4) =>
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% 101.76/17.04 (doubleComplementSub2) =>
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% 101.76/17.04 (demorgan2a1) =>
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 (image1I) =>
% 101.76/17.04 ((
% 101.76/17.04 (injFuncInInjFuncSet) =>
% 101.76/17.04 ((
% 101.76/17.04 (injFuncSetFuncIn) =>
% 101.76/17.04 ((
% 101.76/17.04 (injFuncSetFuncInj) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 (in @
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% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset3) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectER) =>
% 101.76/17.04 ((
% 101.76/17.04 (disjointsetsI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectRsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset4) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset1) =>
% 101.76/17.04 ((
% 101.76/17.04 (bs114d) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (setminusEL) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (setminusIRneg) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusLsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusSubset1) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffE) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffI2) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffIneg1) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffIneg2) =>
% 101.76/17.04 ((
% 101.76/17.04 (secondinupair) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (setukpairIR) =>
% 101.76/17.04 ((
% 101.76/17.04 (kpairiskpair) =>
% 101.76/17.04 ((
% 101.76/17.04 (kpairp) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletonsubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletoninpowerset) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletoninpowunion) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairset2E) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairsubunion) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairinpowunion) =>
% 101.76/17.04 ((
% 101.76/17.04 (ubforcartprodlem1) =>
% 101.76/17.04 ((
% 101.76/17.04 (ubforcartprodlem2) =>
% 101.76/17.04 ((
% 101.76/17.04 (ubforcartprodlem3) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodpairin) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodmempair1) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodmempair) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionE2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionsingleton1) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionsingleton2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionsingleton) =>
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% 101.76/17.04 (ex1I) =>
% 101.76/17.04 ((
% 101.76/17.04 (ex1I2) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletonsuniq) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjL1) =>
% 101.76/17.04 ((
% 101.76/17.04 (kfstsingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (theprop) =>
% 101.76/17.04 ((
% 101.76/17.04 (kfstpairEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodfstin) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjL2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjL) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR11) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR12) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR1) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairequniteq) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR) =>
% 101.76/17.04 ((
% 101.76/17.04 (ksndsingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (ksndpairEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (kpairsurjEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodsndin) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodpairmemEL) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodpairmemER) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodmempaircEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodfstpairEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodsndpairEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodpairsurjEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrI) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrSub) =>
% 101.76/17.04 ((
% 101.76/17.04 (setOfPairsIsBReln) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrERa) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrEL1) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrEL2) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrER) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcImageSingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (apProp) =>
% 101.76/17.04 ((
% 101.76/17.04 (app) =>
% 101.76/17.04 ((
% 101.76/17.04 (infuncsetfunc) =>
% 101.76/17.04 ((
% 101.76/17.04 (ap2p) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcinfuncset) =>
% 101.76/17.04 ((
% 101.76/17.04 (lamProp) =>
% 101.76/17.04 ((
% 101.76/17.04 (lamp) =>
% 101.76/17.04 ((
% 101.76/17.04 (lam2p) =>
% 101.76/17.04 ((
% 101.76/17.04 (brelnall1) =>
% 101.76/17.04 ((
% 101.76/17.04 (brelnall2) =>
% 101.76/17.04 ((
% 101.76/17.04 (ex1E2) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcGraphProp1) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcGraphProp3) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcGraphProp2) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcextLem) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcGraphProp4) =>
% 101.76/17.04 ((
% 101.76/17.04 (subbreln) =>
% 101.76/17.04 ((
% 101.76/17.04 (eqbreln) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcext) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcext2) =>
% 101.76/17.04 ((
% 101.76/17.04 (ap2apEq1) =>
% 101.76/17.04 ((
% 101.76/17.04 (ap2apEq2) =>
% 101.76/17.04 ((
% 101.76/17.04 (beta1) =>
% 101.76/17.04 ((
% 101.76/17.04 (eta1) =>
% 101.76/17.04 ((
% 101.76/17.04 (lam2lamEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (beta2) =>
% 101.76/17.04 ((
% 101.76/17.04 (eta2) =>
% 101.76/17.04 ((
% 101.76/17.04 (iffalseProp1) =>
% 101.76/17.04 ((
% 101.76/17.04 (iffalseProp2) =>
% 101.76/17.04 ((
% 101.76/17.04 (iftrueProp1) =>
% 101.76/17.04 ((
% 101.76/17.04 (iftrueProp2) =>
% 101.76/17.04 ((
% 101.76/17.04 (ifSingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (ifp) =>
% 101.76/17.04 ((
% 101.76/17.04 (theeq) =>
% 101.76/17.04 ((
% 101.76/17.04 (iftrue) =>
% 101.76/17.04 ((
% 101.76/17.04 (iffalse) =>
% 101.76/17.04 ((
% 101.76/17.04 (iftrueorfalse) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectT_lem) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionT_lem) =>
% 101.76/17.04 ((
% 101.76/17.04 (powersetT_lem) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusT_lem) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementT_lem) =>
% 101.76/17.04 ((
% 101.76/17.04 (setextT) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetTI) =>
% 101.76/17.04 ((
% 101.76/17.04 (powersetTI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (powersetTE1) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementTI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementTE1) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectTELcontra) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectTERcontra) =>
% 101.76/17.04 ((
% 101.76/17.04 (contrasubsetT) =>
% 101.76/17.04 ((
% 101.76/17.04 (contrasubsetT1) =>
% 101.76/17.04 ((
% 101.76/17.04 (contrasubsetT2) =>
% 101.76/17.04 ((
% 101.76/17.04 (contrasubsetT3) =>
% 101.76/17.04 ((
% 101.76/17.04 (doubleComplementI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (doubleComplementE1) =>
% 101.76/17.04 ((
% 101.76/17.04 (doubleComplementSub1) =>
% 101.76/17.04 ((
% 101.76/17.04 (doubleComplementSub2) =>
% 101.76/17.04 ((
% 101.76/17.04 (doubleComplementEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementTnotintersectT) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementImpComplementIntersect) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementSubsetComplementIntersect) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementInPowersetComplementIntersect) =>
% 101.76/17.04 ((
% 101.76/17.04 (contraSubsetComplement) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementTcontraSubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionTILcontra) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionTIRcontra) =>
% 101.76/17.04 ((
% 101.76/17.04 (inIntersectImpInUnion) =>
% 101.76/17.04 ((
% 101.76/17.04 (inIntersectImpInUnion2) =>
% 101.76/17.04 ((
% 101.76/17.04 (inIntersectImpInIntersectUnions) =>
% 101.76/17.04 ((
% 101.76/17.04 (intersectInPowersetIntersectUnions) =>
% 101.76/17.04 ((
% 101.76/17.04 (inComplementUnionImpNotIn1) =>
% 101.76/17.04 ((
% 101.76/17.04 (inComplementUnionImpInComplement1) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionTE) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionTEcontra) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan2a1) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementUnionInPowersetComplement) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan2a2) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan1a) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan1b) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan1) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan2a) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan2b2) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan2b) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan2) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz13rule0) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz13rule1) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz13rule2) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz13rule3) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz13rule4) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz1_1) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz1_2) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz1_3) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz1_4) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz1_5) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1all2) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1SetBreln1) =>
% 101.76/17.04 ((
% 101.76/17.04 (choice2fnsingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (setOfPairsIsBReln1) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1all1) =>
% 101.76/17.04 ((
% 101.76/17.04 (subbreln1) =>
% 101.76/17.04 ((
% 101.76/17.04 (eqbreln1) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1invprop) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1invI) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1invE) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1compprop) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1compI) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1compE) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1compEex) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1unionprop) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1unionIL) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1unionIR) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1unionI) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1unionE) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1unionEcases) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1unionCommutes) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz2Ex) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz2W) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz2A) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz2B) =>
% 101.76/17.04 ((
% 101.76/17.04 (image1Ex) =>
% 101.76/17.04 ((
% 101.76/17.04 (image1Ex1) =>
% 101.76/17.04 ((
% 101.76/17.04 (image1Equiv) =>
% 101.76/17.04 ((
% 101.76/17.04 (image1E) =>
% 101.76/17.04 ((
% 101.76/17.04 (image1I) =>
% 101.76/17.04 ((
% 101.76/17.04 (injFuncInInjFuncSet) =>
% 101.76/17.04 ((
% 101.76/17.04 (injFuncSetFuncIn) =>
% 101.76/17.04 ((
% 101.76/17.04 (injFuncSetFuncInj) =>
% 101.76/17.04 ((
% 101.76/17.04 (surjFuncSetFuncIn) =>
% 101.76/17.04 ((
% 101.76/17.04 (surjFuncSetFuncSurj) =>
% 101.76/17.04 ((
% 101.76/17.04 (leftInvIsSurj) =>
% 101.76/17.04 ((
% 101.76/17.04 (surjCantorThm) =>
% 101.76/17.04 ((
% 101.76/17.04 (foundation2) =>
% 101.76/17.04 ((
% 101.76/17.04 (notinself) =>
% 101.76/17.04 ((
% 101.76/17.04 (notinself2) =>
% 101.76/17.04 ((
% 101.76/17.04 (omegaSp) =>
% 101.76/17.04 ((
% 101.76/17.04 (omegaSclos) =>
% 101.76/17.04 ((
% 101.76/17.04 (peano0notS) =>
% 101.76/17.04 ((
% 101.76/17.04 (peanoSinj) =>
% 101.76/17.04 ((
% 101.76/17.04 (transitivesetOp1) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintTransitive) =>
% 101.76/17.04 ((
% 101.76/17.04 (transitivesetOp2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionTransitive) =>
% 101.76/17.04 ((
% 101.76/17.04 (ordinalMinLem1) =>
% 101.76/17.04 ((
% 101.76/17.04 (!!) @ (
% 101.76/17.04 ^[Y0 : $i]:
% 101.76/17.04 ((
% 101.76/17.04 (ordinal @
% 101.76/17.04 Y0) =>
% 101.76/17.04 ((
% 101.76/17.04 (!!) @ (
% 101.76/17.04 ^[Y1 : $i]:
% 101.76/17.04 ((
% 101.76/17.04 (!!) @ (
% 101.76/17.04 ^[Y2 : $i]:
% 101.76/17.04 ((
% 101.76/17.04 (in @
% 101.76/17.04 Y2 @
% 101.76/17.04 Y0) =>
% 101.76/17.04 ((
% 101.76/17.04 (in @
% 101.76/17.04 Y1 @
% 101.76/17.04 Y2) =>
% 101.76/17.04 (in @
% 101.76/17.04 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl244])).
% 101.76/17.04 thf(zip_derived_cl274, plain,
% 101.76/17.04 (~ (((nonemptyI1) =>
% 101.76/17.04 (((setadjoinIL) =>
% 101.76/17.04 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 101.76/17.04 (((setadjoinIR) =>
% 101.76/17.04 (((setadjoinE) =>
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% 101.76/17.04 (((emptyinPowerset) =>
% 101.76/17.04 (((emptyInPowerset) =>
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% 101.76/17.04 (((setunionE) =>
% 101.76/17.04 (((subPowSU) =>
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% 101.76/17.04 (((nonemptyImpWitness) =>
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% 101.76/17.04 (((notinsingleton) =>
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% 101.76/17.04 (((upairsetIR) =>
% 101.76/17.04 (((emptyE1) =>
% 101.76/17.04 (((vacuousDall) =>
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% 101.76/17.04 (((quantDeMorgan2) =>
% 101.76/17.04 (((quantDeMorgan3) =>
% 101.76/17.04 (((quantDeMorgan4) =>
% 101.76/17.04 (((prop2setI) =>
% 101.76/17.04 ((
% 101.76/17.04 (prop2set2propI) =>
% 101.76/17.04 ((
% 101.76/17.04 (notdexE) =>
% 101.76/17.04 ((
% 101.76/17.04 (notdallE) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuI3) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuI2) =>
% 101.76/17.04 ((
% 101.76/17.04 (inCongP) =>
% 101.76/17.04 ((
% 101.76/17.04 (in__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuE3u) =>
% 101.76/17.04 ((
% 101.76/17.04 (exu__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (setadjoin__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (powerset__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunion__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuEu) =>
% 101.76/17.04 ((
% 101.76/17.04 (descr__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (dsetconstr__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (eqimpsubset2) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (subsetE) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetE2) =>
% 101.76/17.04 ((
% 101.76/17.04 (notsubsetI) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 Y2) =>
% 101.76/17.04 (in @
% 101.76/17.04 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl274])).
% 101.76/17.04 thf(zip_derived_cl297, plain,
% 101.76/17.04 (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 101.76/17.04 (((setadjoinIR) =>
% 101.76/17.04 (((setadjoinE) =>
% 101.76/17.04 (((setadjoinOr) =>
% 101.76/17.04 (((setoftrueEq) =>
% 101.76/17.04 (((powersetI) =>
% 101.76/17.04 (((emptyinPowerset) =>
% 101.76/17.04 (((emptyInPowerset) =>
% 101.76/17.04 (((powersetE) =>
% 101.76/17.04 (((setunionI) =>
% 101.76/17.04 (((setunionE) =>
% 101.76/17.04 (((subPowSU) =>
% 101.76/17.04 (((exuE2) =>
% 101.76/17.04 (((nonemptyImpWitness) =>
% 101.76/17.04 (((uniqinunit) =>
% 101.76/17.04 (((notinsingleton) =>
% 101.76/17.04 (((eqinunit) =>
% 101.76/17.04 (((singletonsswitch) =>
% 101.76/17.04 (((upairsetE) =>
% 101.76/17.04 (((upairsetIL) =>
% 101.76/17.04 (((upairsetIR) =>
% 101.76/17.04 (((emptyE1) =>
% 101.76/17.04 (((vacuousDall) =>
% 101.76/17.04 (((quantDeMorgan1) =>
% 101.76/17.04 (((quantDeMorgan2) =>
% 101.76/17.04 (((quantDeMorgan3) =>
% 101.76/17.04 (((quantDeMorgan4) =>
% 101.76/17.04 (((prop2setI) =>
% 101.76/17.04 (((prop2set2propI) =>
% 101.76/17.04 (((notdexE) =>
% 101.76/17.04 ((
% 101.76/17.04 (notdallE) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuI3) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuI2) =>
% 101.76/17.04 ((
% 101.76/17.04 (inCongP) =>
% 101.76/17.04 ((
% 101.76/17.04 (in__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuE3u) =>
% 101.76/17.04 ((
% 101.76/17.04 (exu__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (setadjoin__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (powerset__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunion__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuEu) =>
% 101.76/17.04 ((
% 101.76/17.04 (descr__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (dsetconstr__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (eqimpsubset2) =>
% 101.76/17.04 ((
% 101.76/17.04 (eqimpsubset1) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetI2) =>
% 101.76/17.04 ((
% 101.76/17.04 (emptysetsubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetE) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetE2) =>
% 101.76/17.04 ((
% 101.76/17.04 (notsubsetI) =>
% 101.76/17.04 ((
% 101.76/17.04 (notequalI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (notequalI2) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetRefl) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetTrans) =>
% 101.76/17.04 ((
% 101.76/17.04 (setadjoinSub) =>
% 101.76/17.04 ((
% 101.76/17.04 (setadjoinSub2) =>
% 101.76/17.04 ((
% 101.76/17.04 (subset2powerset) =>
% 101.76/17.04 ((
% 101.76/17.04 (setextsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetemptysetimpeq) =>
% 101.76/17.04 ((
% 101.76/17.04 (powersetI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (powersetE1) =>
% 101.76/17.04 ((
% 101.76/17.04 (inPowerset) =>
% 101.76/17.04 ((
% 101.76/17.04 (powersetsubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (sepInPowerset) =>
% 101.76/17.04 ((
% 101.76/17.04 (sepSubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionIL) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairset2IR) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionIR) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionEcases) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionE) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionLsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionRsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectI) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset5) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectEL) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectLsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset2) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset3) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectER) =>
% 101.76/17.04 ((
% 101.76/17.04 (disjointsetsI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectRsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset4) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset1) =>
% 101.76/17.04 ((
% 101.76/17.04 (bs114d) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusI) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusEL) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusER) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusSubset2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusERneg) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusELneg) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusILneg) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusIRneg) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusLsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusSubset1) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffE) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffI2) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffIneg1) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffIneg2) =>
% 101.76/17.04 ((
% 101.76/17.04 (secondinupair) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairIL) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairIR) =>
% 101.76/17.04 ((
% 101.76/17.04 (kpairiskpair) =>
% 101.76/17.04 ((
% 101.76/17.04 (kpairp) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletonsubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletoninpowerset) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletoninpowunion) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairset2E) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairsubunion) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairinpowunion) =>
% 101.76/17.04 ((
% 101.76/17.04 (ubforcartprodlem1) =>
% 101.76/17.04 ((
% 101.76/17.04 (ubforcartprodlem2) =>
% 101.76/17.04 ((
% 101.76/17.04 (ubforcartprodlem3) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodpairin) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodmempair1) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodmempair) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionE2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionsingleton1) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionsingleton2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionsingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletonprop) =>
% 101.76/17.04 ((
% 101.76/17.04 (ex1E1) =>
% 101.76/17.04 ((
% 101.76/17.04 (ex1I) =>
% 101.76/17.04 ((
% 101.76/17.04 (ex1I2) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletonsuniq) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjL1) =>
% 101.76/17.04 ((
% 101.76/17.04 (kfstsingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (theprop) =>
% 101.76/17.04 ((
% 101.76/17.04 (kfstpairEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodfstin) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjL2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjL) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR11) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR12) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR1) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairequniteq) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR) =>
% 101.76/17.04 ((
% 101.76/17.04 (ksndsingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (ksndpairEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (kpairsurjEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodsndin) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodpairmemEL) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodpairmemER) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodmempaircEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodfstpairEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodsndpairEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodpairsurjEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrI) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrSub) =>
% 101.76/17.04 ((
% 101.76/17.04 (setOfPairsIsBReln) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrERa) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrEL1) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrEL2) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrER) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcImageSingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (apProp) =>
% 101.76/17.04 ((
% 101.76/17.04 (app) =>
% 101.76/17.04 ((
% 101.76/17.04 (infuncsetfunc) =>
% 101.76/17.04 ((
% 101.76/17.04 (ap2p) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcinfuncset) =>
% 101.76/17.04 ((
% 101.76/17.04 (lamProp) =>
% 101.76/17.04 ((
% 101.76/17.04 (lamp) =>
% 101.76/17.04 ((
% 101.76/17.04 (lam2p) =>
% 101.76/17.04 ((
% 101.76/17.04 (brelnall1) =>
% 101.76/17.04 ((
% 101.76/17.04 (brelnall2) =>
% 101.76/17.04 ((
% 101.76/17.04 (ex1E2) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcGraphProp1) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcGraphProp3) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcGraphProp2) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcextLem) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcGraphProp4) =>
% 101.76/17.04 ((
% 101.76/17.04 (subbreln) =>
% 101.76/17.04 ((
% 101.76/17.04 (eqbreln) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcext) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcext2) =>
% 101.76/17.04 ((
% 101.76/17.04 (ap2apEq1) =>
% 101.76/17.04 ((
% 101.76/17.04 (ap2apEq2) =>
% 101.76/17.04 ((
% 101.76/17.04 (beta1) =>
% 101.76/17.04 ((
% 101.76/17.04 (eta1) =>
% 101.76/17.04 ((
% 101.76/17.04 (lam2lamEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (beta2) =>
% 101.76/17.04 ((
% 101.76/17.04 (eta2) =>
% 101.76/17.04 ((
% 101.76/17.04 (iffalseProp1) =>
% 101.76/17.04 ((
% 101.76/17.04 (iffalseProp2) =>
% 101.76/17.04 ((
% 101.76/17.04 (iftrueProp1) =>
% 101.76/17.04 ((
% 101.76/17.04 (iftrueProp2) =>
% 101.76/17.04 ((
% 101.76/17.04 (ifSingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (ifp) =>
% 101.76/17.04 ((
% 101.76/17.04 (theeq) =>
% 101.76/17.04 ((
% 101.76/17.04 (iftrue) =>
% 101.76/17.04 ((
% 101.76/17.04 (iffalse) =>
% 101.76/17.04 ((
% 101.76/17.04 (iftrueorfalse) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectT_lem) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionT_lem) =>
% 101.76/17.04 ((
% 101.76/17.04 (powersetT_lem) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusT_lem) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementT_lem) =>
% 101.76/17.04 ((
% 101.76/17.04 (setextT) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetTI) =>
% 101.76/17.04 ((
% 101.76/17.04 (powersetTI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (powersetTE1) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementTI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementTE1) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectTELcontra) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectTERcontra) =>
% 101.76/17.04 ((
% 101.76/17.04 (contrasubsetT) =>
% 101.76/17.04 ((
% 101.76/17.04 (contrasubsetT1) =>
% 101.76/17.04 ((
% 101.76/17.04 (contrasubsetT2) =>
% 101.76/17.04 ((
% 101.76/17.04 (contrasubsetT3) =>
% 101.76/17.04 ((
% 101.76/17.04 (doubleComplementI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (doubleComplementE1) =>
% 101.76/17.04 ((
% 101.76/17.04 (doubleComplementSub1) =>
% 101.76/17.04 ((
% 101.76/17.04 (doubleComplementSub2) =>
% 101.76/17.04 ((
% 101.76/17.04 (doubleComplementEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementTnotintersectT) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementImpComplementIntersect) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementSubsetComplementIntersect) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementInPowersetComplementIntersect) =>
% 101.76/17.04 ((
% 101.76/17.04 (contraSubsetComplement) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementTcontraSubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionTILcontra) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionTIRcontra) =>
% 101.76/17.04 ((
% 101.76/17.04 (inIntersectImpInUnion) =>
% 101.76/17.04 ((
% 101.76/17.04 (inIntersectImpInUnion2) =>
% 101.76/17.04 ((
% 101.76/17.04 (inIntersectImpInIntersectUnions) =>
% 101.76/17.04 ((
% 101.76/17.04 (intersectInPowersetIntersectUnions) =>
% 101.76/17.04 ((
% 101.76/17.04 (inComplementUnionImpNotIn1) =>
% 101.76/17.04 ((
% 101.76/17.04 (inComplementUnionImpInComplement1) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionTE) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionTEcontra) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan2a1) =>
% 101.76/17.04 ((
% 101.76/17.04 (complementUnionInPowersetComplement) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan2a2) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan1a) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan1b) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan1) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan2a) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan2b2) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan2b) =>
% 101.76/17.04 ((
% 101.76/17.04 (demorgan2) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz13rule0) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz13rule1) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz13rule2) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz13rule3) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz13rule4) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz1_1) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz1_2) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz1_3) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz1_4) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz1_5) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1all2) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1SetBreln1) =>
% 101.76/17.04 ((
% 101.76/17.04 (choice2fnsingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (setOfPairsIsBReln1) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1all1) =>
% 101.76/17.04 ((
% 101.76/17.04 (subbreln1) =>
% 101.76/17.04 ((
% 101.76/17.04 (eqbreln1) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (breln1invI) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1invE) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (breln1compE) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1compEex) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (breln1unionI) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1unionE) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1unionEcases) =>
% 101.76/17.04 ((
% 101.76/17.04 (breln1unionCommutes) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz2Ex) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz2W) =>
% 101.76/17.04 ((
% 101.76/17.04 (woz2A) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (image1Ex1) =>
% 101.76/17.04 ((
% 101.76/17.04 (image1Equiv) =>
% 101.76/17.04 ((
% 101.76/17.04 (image1E) =>
% 101.76/17.04 ((
% 101.76/17.04 (image1I) =>
% 101.76/17.04 ((
% 101.76/17.04 (injFuncInInjFuncSet) =>
% 101.76/17.04 ((
% 101.76/17.04 (injFuncSetFuncIn) =>
% 101.76/17.04 ((
% 101.76/17.04 (injFuncSetFuncInj) =>
% 101.76/17.04 ((
% 101.76/17.04 (surjFuncSetFuncIn) =>
% 101.76/17.04 ((
% 101.76/17.04 (surjFuncSetFuncSurj) =>
% 101.76/17.04 ((
% 101.76/17.04 (leftInvIsSurj) =>
% 101.76/17.04 ((
% 101.76/17.04 (surjCantorThm) =>
% 101.76/17.04 ((
% 101.76/17.04 (foundation2) =>
% 101.76/17.04 ((
% 101.76/17.04 (notinself) =>
% 101.76/17.04 ((
% 101.76/17.04 (notinself2) =>
% 101.76/17.04 ((
% 101.76/17.04 (omegaSp) =>
% 101.76/17.04 ((
% 101.76/17.04 (omegaSclos) =>
% 101.76/17.04 ((
% 101.76/17.04 (peano0notS) =>
% 101.76/17.04 ((
% 101.76/17.04 (peanoSinj) =>
% 101.76/17.04 ((
% 101.76/17.04 (transitivesetOp1) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintTransitive) =>
% 101.76/17.04 ((
% 101.76/17.04 (transitivesetOp2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionTransitive) =>
% 101.76/17.04 ((
% 101.76/17.04 (ordinalMinLem1) =>
% 101.76/17.04 ((
% 101.76/17.04 (!!) @ (
% 101.76/17.04 ^[Y0 : $i]:
% 101.76/17.04 ((
% 101.76/17.04 (ordinal @
% 101.76/17.04 Y0) =>
% 101.76/17.04 ((
% 101.76/17.04 (!!) @ (
% 101.76/17.04 ^[Y1 : $i]:
% 101.76/17.04 ((
% 101.76/17.04 (!!) @ (
% 101.76/17.04 ^[Y2 : $i]:
% 101.76/17.04 ((
% 101.76/17.04 (in @
% 101.76/17.04 Y2 @
% 101.76/17.04 Y0) =>
% 101.76/17.04 ((
% 101.76/17.04 (in @
% 101.76/17.04 Y1 @
% 101.76/17.04 Y2) =>
% 101.76/17.04 (in @
% 101.76/17.04 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 101.76/17.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl285])).
% 101.76/17.04 thf(zip_derived_cl305, plain,
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% 101.76/17.04 (((setadjoinE) =>
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% 101.76/17.04 (((emptyInPowerset) =>
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% 101.76/17.04 (((setunionE) =>
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% 101.76/17.04 (((notinsingleton) =>
% 101.76/17.04 (((eqinunit) =>
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% 101.76/17.04 (((quantDeMorgan1) =>
% 101.76/17.04 (((quantDeMorgan2) =>
% 101.76/17.04 (((quantDeMorgan3) =>
% 101.76/17.04 (((quantDeMorgan4) =>
% 101.76/17.04 (((prop2setI) =>
% 101.76/17.04 (((prop2set2propI) =>
% 101.76/17.04 (((notdexE) =>
% 101.76/17.04 (((notdallE) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuI3) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuI2) =>
% 101.76/17.04 ((
% 101.76/17.04 (inCongP) =>
% 101.76/17.04 ((
% 101.76/17.04 (in__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuE3u) =>
% 101.76/17.04 ((
% 101.76/17.04 (exu__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (setadjoin__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (powerset__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunion__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (exuEu) =>
% 101.76/17.04 ((
% 101.76/17.04 (descr__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (dsetconstr__Cong) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (eqimpsubset2) =>
% 101.76/17.04 ((
% 101.76/17.04 (eqimpsubset1) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetI2) =>
% 101.76/17.04 ((
% 101.76/17.04 (emptysetsubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetE) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetE2) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (notequalI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (notequalI2) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetRefl) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetTrans) =>
% 101.76/17.04 ((
% 101.76/17.04 (setadjoinSub) =>
% 101.76/17.04 ((
% 101.76/17.04 (setadjoinSub2) =>
% 101.76/17.04 ((
% 101.76/17.04 (subset2powerset) =>
% 101.76/17.04 ((
% 101.76/17.04 (setextsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (subsetemptysetimpeq) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (powersetE1) =>
% 101.76/17.04 ((
% 101.76/17.04 (inPowerset) =>
% 101.76/17.04 ((
% 101.76/17.04 (powersetsubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (sepInPowerset) =>
% 101.76/17.04 ((
% 101.76/17.04 (sepSubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionIL) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairset2IR) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (binunionEcases) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionE) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionLsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionRsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectI) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset5) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectEL) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectLsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset2) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset3) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectER) =>
% 101.76/17.04 ((
% 101.76/17.04 (disjointsetsI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectRsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset4) =>
% 101.76/17.04 ((
% 101.76/17.04 (binintersectSubset1) =>
% 101.76/17.04 ((
% 101.76/17.04 (bs114d) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusI) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusEL) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusER) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusSubset2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusERneg) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusELneg) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusILneg) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusIRneg) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusLsub) =>
% 101.76/17.04 ((
% 101.76/17.04 (setminusSubset1) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffE) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffI1) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffI2) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffIneg1) =>
% 101.76/17.04 ((
% 101.76/17.04 (symdiffIneg2) =>
% 101.76/17.04 ((
% 101.76/17.04 (secondinupair) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairIL) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairIR) =>
% 101.76/17.04 ((
% 101.76/17.04 (kpairiskpair) =>
% 101.76/17.04 ((
% 101.76/17.04 (kpairp) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletonsubset) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletoninpowerset) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletoninpowunion) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairset2E) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairsubunion) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairinpowunion) =>
% 101.76/17.04 ((
% 101.76/17.04 (ubforcartprodlem1) =>
% 101.76/17.04 ((
% 101.76/17.04 (ubforcartprodlem2) =>
% 101.76/17.04 ((
% 101.76/17.04 (ubforcartprodlem3) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodpairin) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodmempair1) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodmempair) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionE2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionsingleton1) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionsingleton2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setunionsingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletonprop) =>
% 101.76/17.04 ((
% 101.76/17.04 (ex1E1) =>
% 101.76/17.04 ((
% 101.76/17.04 (ex1I) =>
% 101.76/17.04 ((
% 101.76/17.04 (ex1I2) =>
% 101.76/17.04 ((
% 101.76/17.04 (singletonsuniq) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjL1) =>
% 101.76/17.04 ((
% 101.76/17.04 (kfstsingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (theprop) =>
% 101.76/17.04 ((
% 101.76/17.04 (kfstpairEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodfstin) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjL2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjL) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR11) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR12) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR1) =>
% 101.76/17.04 ((
% 101.76/17.04 (upairequniteq) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR2) =>
% 101.76/17.04 ((
% 101.76/17.04 (setukpairinjR) =>
% 101.76/17.04 ((
% 101.76/17.04 (ksndsingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (ksndpairEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (kpairsurjEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodsndin) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodpairmemEL) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodpairmemER) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodmempaircEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodfstpairEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodsndpairEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (cartprodpairsurjEq) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrI) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrSub) =>
% 101.76/17.04 ((
% 101.76/17.04 (setOfPairsIsBReln) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrERa) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrEL1) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrEL2) =>
% 101.76/17.04 ((
% 101.76/17.04 (dpsetconstrER) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcImageSingleton) =>
% 101.76/17.04 ((
% 101.76/17.04 (apProp) =>
% 101.76/17.04 ((
% 101.76/17.04 (app) =>
% 101.76/17.04 ((
% 101.76/17.04 (infuncsetfunc) =>
% 101.76/17.04 ((
% 101.76/17.04 (ap2p) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcinfuncset) =>
% 101.76/17.04 ((
% 101.76/17.04 (lamProp) =>
% 101.76/17.04 ((
% 101.76/17.04 (lamp) =>
% 101.76/17.04 ((
% 101.76/17.04 (lam2p) =>
% 101.76/17.04 ((
% 101.76/17.04 (brelnall1) =>
% 101.76/17.04 ((
% 101.76/17.04 (brelnall2) =>
% 101.76/17.04 ((
% 101.76/17.04 (ex1E2) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcGraphProp1) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcGraphProp3) =>
% 101.76/17.04 ((
% 101.76/17.04 (funcGraphProp2) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (funcGraphProp4) =>
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% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (funcext2) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (eta1) =>
% 101.76/17.04 ((
% 101.76/17.04 (lam2lamEq) =>
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.04 ((
% 101.76/17.04 (inComplementUnionImpInComplement1) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionTE) =>
% 101.76/17.04 ((
% 101.76/17.04 (binunionTEcontra) =>
% 101.76/17.04 ((
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% 101.76/17.04 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 (breln1compEex) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionIL) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionIR) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionI) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionE) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionEcases) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionCommutes) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (woz2W) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (woz2B) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (image1Equiv) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1E) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1I) =>
% 101.76/17.05 ((
% 101.76/17.05 (injFuncInInjFuncSet) =>
% 101.76/17.05 ((
% 101.76/17.05 (injFuncSetFuncIn) =>
% 101.76/17.05 ((
% 101.76/17.05 (injFuncSetFuncInj) =>
% 101.76/17.05 ((
% 101.76/17.05 (surjFuncSetFuncIn) =>
% 101.76/17.05 ((
% 101.76/17.05 (surjFuncSetFuncSurj) =>
% 101.76/17.05 ((
% 101.76/17.05 (leftInvIsSurj) =>
% 101.76/17.05 ((
% 101.76/17.05 (surjCantorThm) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (omegaSclos) =>
% 101.76/17.05 ((
% 101.76/17.05 (peano0notS) =>
% 101.76/17.05 ((
% 101.76/17.05 (peanoSinj) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 (!!) @ (
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% 101.76/17.05 (in @
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (secondinupair) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairIL) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairIR) =>
% 101.76/17.05 ((
% 101.76/17.05 (kpairiskpair) =>
% 101.76/17.05 ((
% 101.76/17.05 (kpairp) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (ubforcartprodlem1) =>
% 101.76/17.05 ((
% 101.76/17.05 (ubforcartprodlem2) =>
% 101.76/17.05 ((
% 101.76/17.05 (ubforcartprodlem3) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodpairin) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodmempair1) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodmempair) =>
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% 101.76/17.05 (setunionE2) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (setunionsingleton2) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (breln1unionprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionIL) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (breln1unionE) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionEcases) =>
% 101.76/17.05 ((
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% 101.76/17.05 (woz2W) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (image1I) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (surjFuncSetFuncIn) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 (ubforcartprodlem2) =>
% 101.76/17.05 ((
% 101.76/17.05 (ubforcartprodlem3) =>
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% 101.76/17.05 (cartprodmempair) =>
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% 101.76/17.05 (inIntersectImpInUnion2) =>
% 101.76/17.05 ((
% 101.76/17.05 (inIntersectImpInIntersectUnions) =>
% 101.76/17.05 ((
% 101.76/17.05 (intersectInPowersetIntersectUnions) =>
% 101.76/17.05 ((
% 101.76/17.05 (inComplementUnionImpNotIn1) =>
% 101.76/17.05 ((
% 101.76/17.05 (inComplementUnionImpInComplement1) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionTE) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionTEcontra) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2a1) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementUnionInPowersetComplement) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2a2) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan1a) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan1b) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan1) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2a) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2b2) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2b) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz13rule0) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz13rule1) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz13rule2) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz13rule3) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz13rule4) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz1_1) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz1_2) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz1_3) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz1_4) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz1_5) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1all2) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1SetBreln1) =>
% 101.76/17.05 ((
% 101.76/17.05 (choice2fnsingleton) =>
% 101.76/17.05 ((
% 101.76/17.05 (setOfPairsIsBReln1) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1all1) =>
% 101.76/17.05 ((
% 101.76/17.05 (subbreln1) =>
% 101.76/17.05 ((
% 101.76/17.05 (eqbreln1) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1invprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1invI) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1invE) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1compprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1compI) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1compE) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1compEex) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionIL) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionIR) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionI) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionE) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionEcases) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionCommutes) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz2Ex) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz2W) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz2A) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz2B) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1Ex) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1Ex1) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1Equiv) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1E) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1I) =>
% 101.76/17.05 ((
% 101.76/17.05 (injFuncInInjFuncSet) =>
% 101.76/17.05 ((
% 101.76/17.05 (injFuncSetFuncIn) =>
% 101.76/17.05 ((
% 101.76/17.05 (injFuncSetFuncInj) =>
% 101.76/17.05 ((
% 101.76/17.05 (surjFuncSetFuncIn) =>
% 101.76/17.05 ((
% 101.76/17.05 (surjFuncSetFuncSurj) =>
% 101.76/17.05 ((
% 101.76/17.05 (leftInvIsSurj) =>
% 101.76/17.05 ((
% 101.76/17.05 (surjCantorThm) =>
% 101.76/17.05 ((
% 101.76/17.05 (foundation2) =>
% 101.76/17.05 ((
% 101.76/17.05 (notinself) =>
% 101.76/17.05 ((
% 101.76/17.05 (notinself2) =>
% 101.76/17.05 ((
% 101.76/17.05 (omegaSp) =>
% 101.76/17.05 ((
% 101.76/17.05 (omegaSclos) =>
% 101.76/17.05 ((
% 101.76/17.05 (peano0notS) =>
% 101.76/17.05 ((
% 101.76/17.05 (peanoSinj) =>
% 101.76/17.05 ((
% 101.76/17.05 (transitivesetOp1) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintTransitive) =>
% 101.76/17.05 ((
% 101.76/17.05 (transitivesetOp2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionTransitive) =>
% 101.76/17.05 ((
% 101.76/17.05 (ordinalMinLem1) =>
% 101.76/17.05 ((
% 101.76/17.05 (!!) @ (
% 101.76/17.05 ^[Y0 : $i]:
% 101.76/17.05 ((
% 101.76/17.05 (ordinal @
% 101.76/17.05 Y0) =>
% 101.76/17.05 ((
% 101.76/17.05 (!!) @ (
% 101.76/17.05 ^[Y1 : $i]:
% 101.76/17.05 ((
% 101.76/17.05 (!!) @ (
% 101.76/17.05 ^[Y2 : $i]:
% 101.76/17.05 ((
% 101.76/17.05 (in @
% 101.76/17.05 Y2 @
% 101.76/17.05 Y0) =>
% 101.76/17.05 ((
% 101.76/17.05 (in @
% 101.76/17.05 Y1 @
% 101.76/17.05 Y2) =>
% 101.76/17.05 (in @
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% 101.76/17.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl312])).
% 101.76/17.05 thf(zip_derived_cl325, plain,
% 101.76/17.05 (~ (((setoftrueEq) =>
% 101.76/17.05 (((powersetI) =>
% 101.76/17.05 (((emptyinPowerset) =>
% 101.76/17.05 (((emptyInPowerset) =>
% 101.76/17.05 (((powersetE) =>
% 101.76/17.05 (((setunionI) =>
% 101.76/17.05 (((setunionE) =>
% 101.76/17.05 (((subPowSU) =>
% 101.76/17.05 (((exuE2) =>
% 101.76/17.05 (((nonemptyImpWitness) =>
% 101.76/17.05 (((uniqinunit) =>
% 101.76/17.05 (((notinsingleton) =>
% 101.76/17.05 (((eqinunit) =>
% 101.76/17.05 (((singletonsswitch) =>
% 101.76/17.05 (((upairsetE) =>
% 101.76/17.05 (((upairsetIL) =>
% 101.76/17.05 (((upairsetIR) =>
% 101.76/17.05 (((emptyE1) =>
% 101.76/17.05 (((vacuousDall) =>
% 101.76/17.05 (((quantDeMorgan1) =>
% 101.76/17.05 (((quantDeMorgan2) =>
% 101.76/17.05 (((quantDeMorgan3) =>
% 101.76/17.05 (((quantDeMorgan4) =>
% 101.76/17.05 (((prop2setI) =>
% 101.76/17.05 (((prop2set2propI) =>
% 101.76/17.05 (((notdexE) =>
% 101.76/17.05 (((notdallE) =>
% 101.76/17.05 (((exuI1) =>
% 101.76/17.05 (((exuI3) =>
% 101.76/17.05 (((exuI2) =>
% 101.76/17.05 ((
% 101.76/17.05 (inCongP) =>
% 101.76/17.05 ((
% 101.76/17.05 (in__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (exuE3u) =>
% 101.76/17.05 ((
% 101.76/17.05 (exu__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (setadjoin__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (powerset__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunion__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (exuEu) =>
% 101.76/17.05 ((
% 101.76/17.05 (descr__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (dsetconstr__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (eqimpsubset2) =>
% 101.76/17.05 ((
% 101.76/17.05 (eqimpsubset1) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetI2) =>
% 101.76/17.05 ((
% 101.76/17.05 (emptysetsubset) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetE) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetE2) =>
% 101.76/17.05 ((
% 101.76/17.05 (notsubsetI) =>
% 101.76/17.05 ((
% 101.76/17.05 (notequalI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (notequalI2) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetRefl) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetTrans) =>
% 101.76/17.05 ((
% 101.76/17.05 (setadjoinSub) =>
% 101.76/17.05 ((
% 101.76/17.05 (setadjoinSub2) =>
% 101.76/17.05 ((
% 101.76/17.05 (subset2powerset) =>
% 101.76/17.05 ((
% 101.76/17.05 (setextsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetemptysetimpeq) =>
% 101.76/17.05 ((
% 101.76/17.05 (powersetI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (powersetE1) =>
% 101.76/17.05 ((
% 101.76/17.05 (inPowerset) =>
% 101.76/17.05 ((
% 101.76/17.05 (powersetsubset) =>
% 101.76/17.05 ((
% 101.76/17.05 (sepInPowerset) =>
% 101.76/17.05 ((
% 101.76/17.05 (sepSubset) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionIL) =>
% 101.76/17.05 ((
% 101.76/17.05 (upairset2IR) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionIR) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionEcases) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionE) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionLsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionRsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectI) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset5) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectEL) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectLsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset2) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset3) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectER) =>
% 101.76/17.05 ((
% 101.76/17.05 (disjointsetsI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectRsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset4) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset1) =>
% 101.76/17.05 ((
% 101.76/17.05 (bs114d) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusI) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusEL) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusER) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusSubset2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusERneg) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusELneg) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusILneg) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusIRneg) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusLsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusSubset1) =>
% 101.76/17.05 ((
% 101.76/17.05 (symdiffE) =>
% 101.76/17.05 ((
% 101.76/17.05 (symdiffI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (symdiffI2) =>
% 101.76/17.05 ((
% 101.76/17.05 (symdiffIneg1) =>
% 101.76/17.05 ((
% 101.76/17.05 (symdiffIneg2) =>
% 101.76/17.05 ((
% 101.76/17.05 (secondinupair) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairIL) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairIR) =>
% 101.76/17.05 ((
% 101.76/17.05 (kpairiskpair) =>
% 101.76/17.05 ((
% 101.76/17.05 (kpairp) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletonsubset) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletoninpowerset) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletoninpowunion) =>
% 101.76/17.05 ((
% 101.76/17.05 (upairset2E) =>
% 101.76/17.05 ((
% 101.76/17.05 (upairsubunion) =>
% 101.76/17.05 ((
% 101.76/17.05 (upairinpowunion) =>
% 101.76/17.05 ((
% 101.76/17.05 (ubforcartprodlem1) =>
% 101.76/17.05 ((
% 101.76/17.05 (ubforcartprodlem2) =>
% 101.76/17.05 ((
% 101.76/17.05 (ubforcartprodlem3) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodpairin) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodmempair1) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodmempair) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionE2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionsingleton1) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionsingleton2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionsingleton) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletonprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (ex1E1) =>
% 101.76/17.05 ((
% 101.76/17.05 (ex1I) =>
% 101.76/17.05 ((
% 101.76/17.05 (ex1I2) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletonsuniq) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjL1) =>
% 101.76/17.05 ((
% 101.76/17.05 (kfstsingleton) =>
% 101.76/17.05 ((
% 101.76/17.05 (theprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (kfstpairEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodfstin) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjL2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjL) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjR11) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjR12) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjR1) =>
% 101.76/17.05 ((
% 101.76/17.05 (upairequniteq) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjR2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjR) =>
% 101.76/17.05 ((
% 101.76/17.05 (ksndsingleton) =>
% 101.76/17.05 ((
% 101.76/17.05 (ksndpairEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (kpairsurjEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodsndin) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodpairmemEL) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodpairmemER) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodmempaircEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodfstpairEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodsndpairEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodpairsurjEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (dpsetconstrI) =>
% 101.76/17.05 ((
% 101.76/17.05 (dpsetconstrSub) =>
% 101.76/17.05 ((
% 101.76/17.05 (setOfPairsIsBReln) =>
% 101.76/17.05 ((
% 101.76/17.05 (dpsetconstrERa) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 (dpsetconstrER) =>
% 101.76/17.05 ((
% 101.76/17.05 (funcImageSingleton) =>
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% 101.76/17.05 ((
% 101.76/17.05 (app) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (ap2p) =>
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (contrasubsetT) =>
% 101.76/17.05 ((
% 101.76/17.05 (contrasubsetT1) =>
% 101.76/17.05 ((
% 101.76/17.05 (contrasubsetT2) =>
% 101.76/17.05 ((
% 101.76/17.05 (contrasubsetT3) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementE1) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementSub1) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementSub2) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementTnotintersectT) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementImpComplementIntersect) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementSubsetComplementIntersect) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementInPowersetComplementIntersect) =>
% 101.76/17.05 ((
% 101.76/17.05 (contraSubsetComplement) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementTcontraSubset) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionTILcontra) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionTIRcontra) =>
% 101.76/17.05 ((
% 101.76/17.05 (inIntersectImpInUnion) =>
% 101.76/17.05 ((
% 101.76/17.05 (inIntersectImpInUnion2) =>
% 101.76/17.05 ((
% 101.76/17.05 (inIntersectImpInIntersectUnions) =>
% 101.76/17.05 ((
% 101.76/17.05 (intersectInPowersetIntersectUnions) =>
% 101.76/17.05 ((
% 101.76/17.05 (inComplementUnionImpNotIn1) =>
% 101.76/17.05 ((
% 101.76/17.05 (inComplementUnionImpInComplement1) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionTE) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionTEcontra) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2a1) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementUnionInPowersetComplement) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2a2) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (demorgan1b) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan1) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2a) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2b2) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2b) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz13rule0) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz13rule1) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz13rule2) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz13rule3) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz13rule4) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (woz1_2) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz1_3) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz1_4) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz1_5) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1all2) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1SetBreln1) =>
% 101.76/17.05 ((
% 101.76/17.05 (choice2fnsingleton) =>
% 101.76/17.05 ((
% 101.76/17.05 (setOfPairsIsBReln1) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1all1) =>
% 101.76/17.05 ((
% 101.76/17.05 (subbreln1) =>
% 101.76/17.05 ((
% 101.76/17.05 (eqbreln1) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1invprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1invI) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1invE) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1compprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1compI) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1compE) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1compEex) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionIL) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionIR) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionI) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionE) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionEcases) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionCommutes) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz2Ex) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz2W) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz2A) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz2B) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1Ex) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1Ex1) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1Equiv) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1E) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1I) =>
% 101.76/17.05 ((
% 101.76/17.05 (injFuncInInjFuncSet) =>
% 101.76/17.05 ((
% 101.76/17.05 (injFuncSetFuncIn) =>
% 101.76/17.05 ((
% 101.76/17.05 (injFuncSetFuncInj) =>
% 101.76/17.05 ((
% 101.76/17.05 (surjFuncSetFuncIn) =>
% 101.76/17.05 ((
% 101.76/17.05 (surjFuncSetFuncSurj) =>
% 101.76/17.05 ((
% 101.76/17.05 (leftInvIsSurj) =>
% 101.76/17.05 ((
% 101.76/17.05 (surjCantorThm) =>
% 101.76/17.05 ((
% 101.76/17.05 (foundation2) =>
% 101.76/17.05 ((
% 101.76/17.05 (notinself) =>
% 101.76/17.05 ((
% 101.76/17.05 (notinself2) =>
% 101.76/17.05 ((
% 101.76/17.05 (omegaSp) =>
% 101.76/17.05 ((
% 101.76/17.05 (omegaSclos) =>
% 101.76/17.05 ((
% 101.76/17.05 (peano0notS) =>
% 101.76/17.05 ((
% 101.76/17.05 (peanoSinj) =>
% 101.76/17.05 ((
% 101.76/17.05 (transitivesetOp1) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintTransitive) =>
% 101.76/17.05 ((
% 101.76/17.05 (transitivesetOp2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionTransitive) =>
% 101.76/17.05 ((
% 101.76/17.05 (ordinalMinLem1) =>
% 101.76/17.05 ((
% 101.76/17.05 (!!) @ (
% 101.76/17.05 ^[Y0 : $i]:
% 101.76/17.05 ((
% 101.76/17.05 (ordinal @
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% 101.76/17.05 ((
% 101.76/17.05 (!!) @ (
% 101.76/17.05 ^[Y1 : $i]:
% 101.76/17.05 ((
% 101.76/17.05 (!!) @ (
% 101.76/17.05 ^[Y2 : $i]:
% 101.76/17.05 ((
% 101.76/17.05 (in @
% 101.76/17.05 Y2 @
% 101.76/17.05 Y0) =>
% 101.76/17.05 ((
% 101.76/17.05 (in @
% 101.76/17.05 Y1 @
% 101.76/17.05 Y2) =>
% 101.76/17.05 (in @
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% 101.76/17.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl318])).
% 101.76/17.05 thf(zip_derived_cl331, plain,
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% 101.76/17.05 (((emptyInPowerset) =>
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% 101.76/17.05 (((setunionE) =>
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% 101.76/17.05 (((notinsingleton) =>
% 101.76/17.05 (((eqinunit) =>
% 101.76/17.05 (((singletonsswitch) =>
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% 101.76/17.05 (((upairsetIL) =>
% 101.76/17.05 (((upairsetIR) =>
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% 101.76/17.05 (((quantDeMorgan1) =>
% 101.76/17.05 (((quantDeMorgan2) =>
% 101.76/17.05 (((quantDeMorgan3) =>
% 101.76/17.05 (((quantDeMorgan4) =>
% 101.76/17.05 (((prop2setI) =>
% 101.76/17.05 (((prop2set2propI) =>
% 101.76/17.05 (((notdexE) =>
% 101.76/17.05 (((notdallE) =>
% 101.76/17.05 (((exuI1) =>
% 101.76/17.05 (((exuI3) =>
% 101.76/17.05 (((exuI2) =>
% 101.76/17.05 (((inCongP) =>
% 101.76/17.05 ((
% 101.76/17.05 (in__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (exuE3u) =>
% 101.76/17.05 ((
% 101.76/17.05 (exu__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (setadjoin__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (powerset__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunion__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (exuEu) =>
% 101.76/17.05 ((
% 101.76/17.05 (descr__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (dsetconstr__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (eqimpsubset2) =>
% 101.76/17.05 ((
% 101.76/17.05 (eqimpsubset1) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetI2) =>
% 101.76/17.05 ((
% 101.76/17.05 (emptysetsubset) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetE) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetE2) =>
% 101.76/17.05 ((
% 101.76/17.05 (notsubsetI) =>
% 101.76/17.05 ((
% 101.76/17.05 (notequalI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (notequalI2) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetRefl) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetTrans) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (setadjoinSub2) =>
% 101.76/17.05 ((
% 101.76/17.05 (subset2powerset) =>
% 101.76/17.05 ((
% 101.76/17.05 (setextsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetemptysetimpeq) =>
% 101.76/17.05 ((
% 101.76/17.05 (powersetI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (powersetE1) =>
% 101.76/17.05 ((
% 101.76/17.05 (inPowerset) =>
% 101.76/17.05 ((
% 101.76/17.05 (powersetsubset) =>
% 101.76/17.05 ((
% 101.76/17.05 (sepInPowerset) =>
% 101.76/17.05 ((
% 101.76/17.05 (sepSubset) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionIL) =>
% 101.76/17.05 ((
% 101.76/17.05 (upairset2IR) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionIR) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionEcases) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionE) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionLsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionRsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectI) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset5) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectEL) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectLsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset2) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset3) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectER) =>
% 101.76/17.05 ((
% 101.76/17.05 (disjointsetsI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectRsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset4) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset1) =>
% 101.76/17.05 ((
% 101.76/17.05 (bs114d) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusI) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusEL) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusER) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusSubset2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusERneg) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusELneg) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusILneg) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusIRneg) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusLsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusSubset1) =>
% 101.76/17.05 ((
% 101.76/17.05 (symdiffE) =>
% 101.76/17.05 ((
% 101.76/17.05 (symdiffI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (symdiffI2) =>
% 101.76/17.05 ((
% 101.76/17.05 (symdiffIneg1) =>
% 101.76/17.05 ((
% 101.76/17.05 (symdiffIneg2) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (setukpairIL) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairIR) =>
% 101.76/17.05 ((
% 101.76/17.05 (kpairiskpair) =>
% 101.76/17.05 ((
% 101.76/17.05 (kpairp) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletonsubset) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletoninpowerset) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletoninpowunion) =>
% 101.76/17.05 ((
% 101.76/17.05 (upairset2E) =>
% 101.76/17.05 ((
% 101.76/17.05 (upairsubunion) =>
% 101.76/17.05 ((
% 101.76/17.05 (upairinpowunion) =>
% 101.76/17.05 ((
% 101.76/17.05 (ubforcartprodlem1) =>
% 101.76/17.05 ((
% 101.76/17.05 (ubforcartprodlem2) =>
% 101.76/17.05 ((
% 101.76/17.05 (ubforcartprodlem3) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodpairin) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodmempair1) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodmempair) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionE2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionsingleton1) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionsingleton2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionsingleton) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletonprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (ex1E1) =>
% 101.76/17.05 ((
% 101.76/17.05 (ex1I) =>
% 101.76/17.05 ((
% 101.76/17.05 (ex1I2) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletonsuniq) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjL1) =>
% 101.76/17.05 ((
% 101.76/17.05 (kfstsingleton) =>
% 101.76/17.05 ((
% 101.76/17.05 (theprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (kfstpairEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodfstin) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjL2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjL) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjR11) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjR12) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjR1) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (ksndpairEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (kpairsurjEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodsndin) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodpairmemEL) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodpairmemER) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodmempaircEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodfstpairEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodsndpairEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodpairsurjEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (dpsetconstrI) =>
% 101.76/17.05 ((
% 101.76/17.05 (dpsetconstrSub) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 (ifSingleton) =>
% 101.76/17.05 ((
% 101.76/17.05 (ifp) =>
% 101.76/17.05 ((
% 101.76/17.05 (theeq) =>
% 101.76/17.05 ((
% 101.76/17.05 (iftrue) =>
% 101.76/17.05 ((
% 101.76/17.05 (iffalse) =>
% 101.76/17.05 ((
% 101.76/17.05 (iftrueorfalse) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectT_lem) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionT_lem) =>
% 101.76/17.05 ((
% 101.76/17.05 (powersetT_lem) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusT_lem) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementT_lem) =>
% 101.76/17.05 ((
% 101.76/17.05 (setextT) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetTI) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (powersetTE1) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementTI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementTE1) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectTELcontra) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectTERcontra) =>
% 101.76/17.05 ((
% 101.76/17.05 (contrasubsetT) =>
% 101.76/17.05 ((
% 101.76/17.05 (contrasubsetT1) =>
% 101.76/17.05 ((
% 101.76/17.05 (contrasubsetT2) =>
% 101.76/17.05 ((
% 101.76/17.05 (contrasubsetT3) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementE1) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementSub1) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementSub2) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementTnotintersectT) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementImpComplementIntersect) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementSubsetComplementIntersect) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementInPowersetComplementIntersect) =>
% 101.76/17.05 ((
% 101.76/17.05 (contraSubsetComplement) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementTcontraSubset) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionTILcontra) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionTIRcontra) =>
% 101.76/17.05 ((
% 101.76/17.05 (inIntersectImpInUnion) =>
% 101.76/17.05 ((
% 101.76/17.05 (inIntersectImpInUnion2) =>
% 101.76/17.05 ((
% 101.76/17.05 (inIntersectImpInIntersectUnions) =>
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% 101.76/17.05 (intersectInPowersetIntersectUnions) =>
% 101.76/17.05 ((
% 101.76/17.05 (inComplementUnionImpNotIn1) =>
% 101.76/17.05 ((
% 101.76/17.05 (inComplementUnionImpInComplement1) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionTE) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionTEcontra) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2a1) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementUnionInPowersetComplement) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2a2) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (demorgan1b) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (demorgan2a) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2b2) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2b) =>
% 101.76/17.05 ((
% 101.76/17.05 (demorgan2) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz13rule0) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (woz13rule2) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz13rule3) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz13rule4) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz1_1) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz1_2) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz1_3) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz1_4) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz1_5) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1all2) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1SetBreln1) =>
% 101.76/17.05 ((
% 101.76/17.05 (choice2fnsingleton) =>
% 101.76/17.05 ((
% 101.76/17.05 (setOfPairsIsBReln1) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1all1) =>
% 101.76/17.05 ((
% 101.76/17.05 (subbreln1) =>
% 101.76/17.05 ((
% 101.76/17.05 (eqbreln1) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1invprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1invI) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1invE) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1compprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1compI) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1compE) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1compEex) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionIL) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionIR) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionI) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionE) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionEcases) =>
% 101.76/17.05 ((
% 101.76/17.05 (breln1unionCommutes) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz2Ex) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz2W) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz2A) =>
% 101.76/17.05 ((
% 101.76/17.05 (woz2B) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1Ex) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1Ex1) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1Equiv) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1E) =>
% 101.76/17.05 ((
% 101.76/17.05 (image1I) =>
% 101.76/17.05 ((
% 101.76/17.05 (injFuncInInjFuncSet) =>
% 101.76/17.05 ((
% 101.76/17.05 (injFuncSetFuncIn) =>
% 101.76/17.05 ((
% 101.76/17.05 (injFuncSetFuncInj) =>
% 101.76/17.05 ((
% 101.76/17.05 (surjFuncSetFuncIn) =>
% 101.76/17.05 ((
% 101.76/17.05 (surjFuncSetFuncSurj) =>
% 101.76/17.05 ((
% 101.76/17.05 (leftInvIsSurj) =>
% 101.76/17.05 ((
% 101.76/17.05 (surjCantorThm) =>
% 101.76/17.05 ((
% 101.76/17.05 (foundation2) =>
% 101.76/17.05 ((
% 101.76/17.05 (notinself) =>
% 101.76/17.05 ((
% 101.76/17.05 (notinself2) =>
% 101.76/17.05 ((
% 101.76/17.05 (omegaSp) =>
% 101.76/17.05 ((
% 101.76/17.05 (omegaSclos) =>
% 101.76/17.05 ((
% 101.76/17.05 (peano0notS) =>
% 101.76/17.05 ((
% 101.76/17.05 (peanoSinj) =>
% 101.76/17.05 ((
% 101.76/17.05 (transitivesetOp1) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintTransitive) =>
% 101.76/17.05 ((
% 101.76/17.05 (transitivesetOp2) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (ordinalMinLem1) =>
% 101.76/17.05 ((
% 101.76/17.05 (!!) @ (
% 101.76/17.05 ^[Y0 : $i]:
% 101.76/17.05 ((
% 101.76/17.05 (ordinal @
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% 101.76/17.05 ((
% 101.76/17.05 (!!) @ (
% 101.76/17.05 ^[Y1 : $i]:
% 101.76/17.05 ((
% 101.76/17.05 (!!) @ (
% 101.76/17.05 ^[Y2 : $i]:
% 101.76/17.05 ((
% 101.76/17.05 (in @
% 101.76/17.05 Y2 @
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% 101.76/17.05 ((
% 101.76/17.05 (in @
% 101.76/17.05 Y1 @
% 101.76/17.05 Y2) =>
% 101.76/17.05 (in @
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% 101.76/17.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])).
% 101.76/17.05 thf(zip_derived_cl337, plain,
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% 101.76/17.05 (((emptyInPowerset) =>
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% 101.76/17.05 (((setunionI) =>
% 101.76/17.05 (((setunionE) =>
% 101.76/17.05 (((subPowSU) =>
% 101.76/17.05 (((exuE2) =>
% 101.76/17.05 (((nonemptyImpWitness) =>
% 101.76/17.05 (((uniqinunit) =>
% 101.76/17.05 (((notinsingleton) =>
% 101.76/17.05 (((eqinunit) =>
% 101.76/17.05 (((singletonsswitch) =>
% 101.76/17.05 (((upairsetE) =>
% 101.76/17.05 (((upairsetIL) =>
% 101.76/17.05 (((upairsetIR) =>
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% 101.76/17.05 (((quantDeMorgan1) =>
% 101.76/17.05 (((quantDeMorgan2) =>
% 101.76/17.05 (((quantDeMorgan3) =>
% 101.76/17.05 (((quantDeMorgan4) =>
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% 101.76/17.05 (((prop2set2propI) =>
% 101.76/17.05 (((notdexE) =>
% 101.76/17.05 (((notdallE) =>
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% 101.76/17.05 ((
% 101.76/17.05 (exuE3u) =>
% 101.76/17.05 ((
% 101.76/17.05 (exu__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (setadjoin__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (powerset__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunion__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (exuEu) =>
% 101.76/17.05 ((
% 101.76/17.05 (descr__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (dsetconstr__Cong) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetI1) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (subsetE) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetE2) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (sepSubset) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionIL) =>
% 101.76/17.05 ((
% 101.76/17.05 (upairset2IR) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionIR) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionEcases) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionE) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionLsub) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset5) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectEL) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectLsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset2) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset3) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectER) =>
% 101.76/17.05 ((
% 101.76/17.05 (disjointsetsI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectRsub) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (binintersectSubset1) =>
% 101.76/17.05 ((
% 101.76/17.05 (bs114d) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusI) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusEL) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusER) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusSubset2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusERneg) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusELneg) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (setminusIRneg) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusLsub) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusSubset1) =>
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% 101.76/17.05 ((
% 101.76/17.05 (symdiffI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (symdiffI2) =>
% 101.76/17.05 ((
% 101.76/17.05 (symdiffIneg1) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (setukpairIR) =>
% 101.76/17.05 ((
% 101.76/17.05 (kpairiskpair) =>
% 101.76/17.05 ((
% 101.76/17.05 (kpairp) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletonsubset) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletoninpowerset) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletoninpowunion) =>
% 101.76/17.05 ((
% 101.76/17.05 (upairset2E) =>
% 101.76/17.05 ((
% 101.76/17.05 (upairsubunion) =>
% 101.76/17.05 ((
% 101.76/17.05 (upairinpowunion) =>
% 101.76/17.05 ((
% 101.76/17.05 (ubforcartprodlem1) =>
% 101.76/17.05 ((
% 101.76/17.05 (ubforcartprodlem2) =>
% 101.76/17.05 ((
% 101.76/17.05 (ubforcartprodlem3) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodpairin) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodmempair1) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodmempair) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionE2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionsingleton1) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionsingleton2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setunionsingleton) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletonprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (ex1E1) =>
% 101.76/17.05 ((
% 101.76/17.05 (ex1I) =>
% 101.76/17.05 ((
% 101.76/17.05 (ex1I2) =>
% 101.76/17.05 ((
% 101.76/17.05 (singletonsuniq) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjL1) =>
% 101.76/17.05 ((
% 101.76/17.05 (kfstsingleton) =>
% 101.76/17.05 ((
% 101.76/17.05 (theprop) =>
% 101.76/17.05 ((
% 101.76/17.05 (kfstpairEq) =>
% 101.76/17.05 ((
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% 101.76/17.05 (setukpairinjL2) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjL) =>
% 101.76/17.05 ((
% 101.76/17.05 (setukpairinjR11) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (ksndpairEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (kpairsurjEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodsndin) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodpairmemEL) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodpairmemER) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodmempaircEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodfstpairEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodsndpairEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (cartprodpairsurjEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (dpsetconstrI) =>
% 101.76/17.05 ((
% 101.76/17.05 (dpsetconstrSub) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 ((
% 101.76/17.05 (app) =>
% 101.76/17.05 ((
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% 101.76/17.05 ((
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% 101.76/17.05 (funcGraphProp3) =>
% 101.76/17.05 ((
% 101.76/17.05 (funcGraphProp2) =>
% 101.76/17.05 ((
% 101.76/17.05 (funcextLem) =>
% 101.76/17.05 ((
% 101.76/17.05 (funcGraphProp4) =>
% 101.76/17.05 ((
% 101.76/17.05 (subbreln) =>
% 101.76/17.05 ((
% 101.76/17.05 (eqbreln) =>
% 101.76/17.05 ((
% 101.76/17.05 (funcext) =>
% 101.76/17.05 ((
% 101.76/17.05 (funcext2) =>
% 101.76/17.05 ((
% 101.76/17.05 (ap2apEq1) =>
% 101.76/17.05 ((
% 101.76/17.05 (ap2apEq2) =>
% 101.76/17.05 ((
% 101.76/17.05 (beta1) =>
% 101.76/17.05 ((
% 101.76/17.05 (eta1) =>
% 101.76/17.05 ((
% 101.76/17.05 (lam2lamEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (beta2) =>
% 101.76/17.05 ((
% 101.76/17.05 (eta2) =>
% 101.76/17.05 ((
% 101.76/17.05 (iffalseProp1) =>
% 101.76/17.05 ((
% 101.76/17.05 (iffalseProp2) =>
% 101.76/17.05 ((
% 101.76/17.05 (iftrueProp1) =>
% 101.76/17.05 ((
% 101.76/17.05 (iftrueProp2) =>
% 101.76/17.05 ((
% 101.76/17.05 (ifSingleton) =>
% 101.76/17.05 ((
% 101.76/17.05 (ifp) =>
% 101.76/17.05 ((
% 101.76/17.05 (theeq) =>
% 101.76/17.05 ((
% 101.76/17.05 (iftrue) =>
% 101.76/17.05 ((
% 101.76/17.05 (iffalse) =>
% 101.76/17.05 ((
% 101.76/17.05 (iftrueorfalse) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectT_lem) =>
% 101.76/17.05 ((
% 101.76/17.05 (binunionT_lem) =>
% 101.76/17.05 ((
% 101.76/17.05 (powersetT_lem) =>
% 101.76/17.05 ((
% 101.76/17.05 (setminusT_lem) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementT_lem) =>
% 101.76/17.05 ((
% 101.76/17.05 (setextT) =>
% 101.76/17.05 ((
% 101.76/17.05 (subsetTI) =>
% 101.76/17.05 ((
% 101.76/17.05 (powersetTI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (powersetTE1) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementTI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementTE1) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectTELcontra) =>
% 101.76/17.05 ((
% 101.76/17.05 (binintersectTERcontra) =>
% 101.76/17.05 ((
% 101.76/17.05 (contrasubsetT) =>
% 101.76/17.05 ((
% 101.76/17.05 (contrasubsetT1) =>
% 101.76/17.05 ((
% 101.76/17.05 (contrasubsetT2) =>
% 101.76/17.05 ((
% 101.76/17.05 (contrasubsetT3) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementI1) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementE1) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementSub1) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementSub2) =>
% 101.76/17.05 ((
% 101.76/17.05 (doubleComplementEq) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementTnotintersectT) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementImpComplementIntersect) =>
% 101.76/17.05 ((
% 101.76/17.05 (complementSubsetComplementIntersect) =>
% 102.15/17.05 ((
% 102.15/17.05 (complementInPowersetComplementIntersect) =>
% 102.15/17.05 ((
% 102.15/17.05 (contraSubsetComplement) =>
% 102.15/17.05 ((
% 102.15/17.05 (complementTcontraSubset) =>
% 102.15/17.05 ((
% 102.15/17.05 (binunionTILcontra) =>
% 102.15/17.05 ((
% 102.15/17.05 (binunionTIRcontra) =>
% 102.15/17.05 ((
% 102.15/17.05 (inIntersectImpInUnion) =>
% 102.15/17.05 ((
% 102.15/17.05 (inIntersectImpInUnion2) =>
% 102.15/17.05 ((
% 102.15/17.05 (inIntersectImpInIntersectUnions) =>
% 102.15/17.05 ((
% 102.15/17.05 (intersectInPowersetIntersectUnions) =>
% 102.15/17.05 ((
% 102.15/17.05 (inComplementUnionImpNotIn1) =>
% 102.15/17.05 ((
% 102.15/17.05 (inComplementUnionImpInComplement1) =>
% 102.15/17.05 ((
% 102.15/17.05 (binunionTE) =>
% 102.15/17.05 ((
% 102.15/17.05 (binunionTEcontra) =>
% 102.15/17.05 ((
% 102.15/17.05 (demorgan2a1) =>
% 102.15/17.05 ((
% 102.15/17.05 (complementUnionInPowersetComplement) =>
% 102.15/17.05 ((
% 102.15/17.05 (demorgan2a2) =>
% 102.15/17.05 ((
% 102.15/17.05 (demorgan1a) =>
% 102.15/17.05 ((
% 102.15/17.05 (demorgan1b) =>
% 102.15/17.05 ((
% 102.15/17.05 (demorgan1) =>
% 102.15/17.05 ((
% 102.15/17.05 (demorgan2a) =>
% 102.15/17.05 ((
% 102.15/17.05 (demorgan2b2) =>
% 102.15/17.05 ((
% 102.15/17.05 (demorgan2b) =>
% 102.15/17.05 ((
% 102.15/17.05 (demorgan2) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz13rule0) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz13rule1) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz13rule2) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz13rule3) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz13rule4) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz1_1) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz1_2) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz1_3) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz1_4) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz1_5) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1all2) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1SetBreln1) =>
% 102.15/17.05 ((
% 102.15/17.05 (choice2fnsingleton) =>
% 102.15/17.05 ((
% 102.15/17.05 (setOfPairsIsBReln1) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1all1) =>
% 102.15/17.05 ((
% 102.15/17.05 (subbreln1) =>
% 102.15/17.05 ((
% 102.15/17.05 (eqbreln1) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1invprop) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1invI) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1invE) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1compprop) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1compI) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1compE) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1compEex) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1unionprop) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1unionIL) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1unionIR) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1unionI) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1unionE) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1unionEcases) =>
% 102.15/17.05 ((
% 102.15/17.05 (breln1unionCommutes) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz2Ex) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz2W) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz2A) =>
% 102.15/17.05 ((
% 102.15/17.05 (woz2B) =>
% 102.15/17.05 ((
% 102.15/17.05 (image1Ex) =>
% 102.15/17.05 ((
% 102.15/17.05 (image1Ex1) =>
% 102.15/17.05 ((
% 102.15/17.05 (image1Equiv) =>
% 102.15/17.05 ((
% 102.15/17.05 (image1E) =>
% 102.15/17.05 ((
% 102.15/17.05 (image1I) =>
% 102.15/17.05 ((
% 102.15/17.05 (injFuncInInjFuncSet) =>
% 102.15/17.05 ((
% 102.15/17.05 (injFuncSetFuncIn) =>
% 102.15/17.05 ((
% 102.15/17.05 (injFuncSetFuncInj) =>
% 102.15/17.05 ((
% 102.15/17.05 (surjFuncSetFuncIn) =>
% 102.15/17.05 ((
% 102.15/17.05 (surjFuncSetFuncSurj) =>
% 102.15/17.05 ((
% 102.15/17.05 (leftInvIsSurj) =>
% 102.15/17.05 ((
% 102.15/17.05 (surjCantorThm) =>
% 102.15/17.05 ((
% 102.15/17.05 (foundation2) =>
% 102.15/17.05 ((
% 102.15/17.05 (notinself) =>
% 102.15/17.05 ((
% 102.15/17.05 (notinself2) =>
% 102.15/17.05 ((
% 102.15/17.05 (omegaSp) =>
% 102.15/17.05 ((
% 102.15/17.05 (omegaSclos) =>
% 102.15/17.05 ((
% 102.15/17.05 (peano0notS) =>
% 102.15/17.05 ((
% 102.15/17.05 (peanoSinj) =>
% 102.15/17.05 ((
% 102.15/17.05 (transitivesetOp1) =>
% 102.15/17.05 ((
% 102.15/17.05 (binintTransitive) =>
% 102.15/17.05 ((
% 102.15/17.05 (transitivesetOp2) =>
% 102.15/17.05 ((
% 102.15/17.05 (setunionTransitive) =>
% 102.15/17.05 ((
% 102.15/17.05 (ordinalMinLem1) =>
% 102.15/17.05 ((
% 102.15/17.05 (!!) @ (
% 102.15/17.05 ^[Y0 : $i]:
% 102.15/17.05 ((
% 102.15/17.05 (ordinal @
% 102.15/17.05 Y0) =>
% 102.15/17.05 ((
% 102.15/17.05 (!!) @ (
% 102.15/17.05 ^[Y1 : $i]:
% 102.15/17.05 ((
% 102.15/17.05 (!!) @ (
% 102.15/17.05 ^[Y2 : $i]:
% 102.15/17.05 ((
% 102.15/17.05 (in @
% 102.15/17.05 Y2 @
% 102.15/17.05 Y0) =>
% 102.15/17.05 ((
% 102.15/17.05 (in @
% 102.15/17.05 Y1 @
% 102.15/17.05 Y2) =>
% 102.15/17.05 (in @
% 102.15/17.05 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.15/17.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl331])).
% 102.15/17.05 thf(zip_derived_cl343, plain,
% 102.15/17.05 (~ (((emptyInPowerset) =>
% 102.15/17.05 (((powersetE) =>
% 102.15/17.05 (((setunionI) =>
% 102.15/17.05 (((setunionE) =>
% 102.15/17.05 (((subPowSU) =>
% 102.15/17.05 (((exuE2) =>
% 102.15/17.05 (((nonemptyImpWitness) =>
% 102.15/17.05 (((uniqinunit) =>
% 102.15/17.05 (((notinsingleton) =>
% 102.15/17.05 (((eqinunit) =>
% 102.15/17.05 (((singletonsswitch) =>
% 102.15/17.05 (((upairsetE) =>
% 102.15/17.05 (((upairsetIL) =>
% 102.15/17.05 (((upairsetIR) =>
% 102.15/17.05 (((emptyE1) =>
% 102.15/17.05 (((vacuousDall) =>
% 102.15/17.05 (((quantDeMorgan1) =>
% 102.15/17.05 (((quantDeMorgan2) =>
% 102.15/17.05 (((quantDeMorgan3) =>
% 102.15/17.05 (((quantDeMorgan4) =>
% 102.15/17.05 (((prop2setI) =>
% 102.15/17.05 (((prop2set2propI) =>
% 102.15/17.05 (((notdexE) =>
% 102.15/17.05 (((notdallE) =>
% 102.15/17.05 (((exuI1) =>
% 102.15/17.05 (((exuI3) =>
% 102.15/17.05 (((exuI2) =>
% 102.15/17.05 (((inCongP) =>
% 102.15/17.05 (((in__Cong) =>
% 102.15/17.05 (((exuE3u) =>
% 102.15/17.05 ((
% 102.15/17.05 (exu__Cong) =>
% 102.15/17.05 ((
% 102.15/17.05 (setadjoin__Cong) =>
% 102.15/17.05 ((
% 102.15/17.05 (powerset__Cong) =>
% 102.15/17.05 ((
% 102.15/17.05 (setunion__Cong) =>
% 102.15/17.05 ((
% 102.15/17.05 (exuEu) =>
% 102.15/17.05 ((
% 102.15/17.05 (descr__Cong) =>
% 102.15/17.05 ((
% 102.15/17.05 (dsetconstr__Cong) =>
% 102.15/17.05 ((
% 102.15/17.05 (subsetI1) =>
% 102.15/17.05 ((
% 102.15/17.05 (eqimpsubset2) =>
% 102.15/17.05 ((
% 102.15/17.05 (eqimpsubset1) =>
% 102.15/17.05 ((
% 102.15/17.05 (subsetI2) =>
% 102.15/17.05 ((
% 102.15/17.05 (emptysetsubset) =>
% 102.15/17.05 ((
% 102.15/17.05 (subsetE) =>
% 102.15/17.05 ((
% 102.15/17.05 (subsetE2) =>
% 102.15/17.05 ((
% 102.15/17.05 (notsubsetI) =>
% 102.15/17.05 ((
% 102.15/17.05 (notequalI1) =>
% 102.15/17.05 ((
% 102.15/17.05 (notequalI2) =>
% 102.15/17.05 ((
% 102.15/17.05 (subsetRefl) =>
% 102.15/17.05 ((
% 102.15/17.05 (subsetTrans) =>
% 102.15/17.05 ((
% 102.15/17.05 (setadjoinSub) =>
% 102.15/17.05 ((
% 102.15/17.05 (setadjoinSub2) =>
% 102.15/17.05 ((
% 102.15/17.05 (subset2powerset) =>
% 102.15/17.05 ((
% 102.15/17.05 (setextsub) =>
% 102.15/17.05 ((
% 102.15/17.05 (subsetemptysetimpeq) =>
% 102.15/17.05 ((
% 102.15/17.05 (powersetI1) =>
% 102.15/17.05 ((
% 102.15/17.05 (powersetE1) =>
% 102.15/17.05 ((
% 102.15/17.05 (inPowerset) =>
% 102.15/17.05 ((
% 102.15/17.05 (powersetsubset) =>
% 102.15/17.05 ((
% 102.15/17.05 (sepInPowerset) =>
% 102.15/17.05 ((
% 102.15/17.05 (sepSubset) =>
% 102.15/17.05 ((
% 102.15/17.05 (binunionIL) =>
% 102.15/17.05 ((
% 102.15/17.05 (upairset2IR) =>
% 102.15/17.05 ((
% 102.15/17.05 (binunionIR) =>
% 102.15/17.05 ((
% 102.15/17.05 (binunionEcases) =>
% 102.15/17.05 ((
% 102.15/17.05 (binunionE) =>
% 102.15/17.05 ((
% 102.15/17.05 (binunionLsub) =>
% 102.15/17.05 ((
% 102.15/17.05 (binunionRsub) =>
% 102.15/17.05 ((
% 102.15/17.05 (binintersectI) =>
% 102.15/17.05 ((
% 102.15/17.05 (binintersectSubset5) =>
% 102.15/17.05 ((
% 102.15/17.05 (binintersectEL) =>
% 102.15/17.05 ((
% 102.15/17.05 (binintersectLsub) =>
% 102.15/17.05 ((
% 102.15/17.05 (binintersectSubset2) =>
% 102.15/17.05 ((
% 102.15/17.05 (binintersectSubset3) =>
% 102.15/17.05 ((
% 102.15/17.05 (binintersectER) =>
% 102.15/17.05 ((
% 102.15/17.05 (disjointsetsI1) =>
% 102.15/17.05 ((
% 102.15/17.05 (binintersectRsub) =>
% 102.15/17.05 ((
% 102.15/17.05 (binintersectSubset4) =>
% 102.15/17.05 ((
% 102.15/17.05 (binintersectSubset1) =>
% 102.15/17.05 ((
% 102.15/17.05 (bs114d) =>
% 102.15/17.05 ((
% 102.15/17.05 (setminusI) =>
% 102.15/17.05 ((
% 102.15/17.05 (setminusEL) =>
% 102.15/17.05 ((
% 102.15/17.05 (setminusER) =>
% 102.15/17.05 ((
% 102.15/17.05 (setminusSubset2) =>
% 102.15/17.05 ((
% 102.15/17.05 (setminusERneg) =>
% 102.15/17.05 ((
% 102.15/17.05 (setminusELneg) =>
% 102.15/17.05 ((
% 102.15/17.05 (setminusILneg) =>
% 102.15/17.05 ((
% 102.15/17.05 (setminusIRneg) =>
% 102.15/17.05 ((
% 102.15/17.05 (setminusLsub) =>
% 102.15/17.05 ((
% 102.15/17.05 (setminusSubset1) =>
% 102.15/17.05 ((
% 102.15/17.05 (symdiffE) =>
% 102.15/17.05 ((
% 102.15/17.05 (symdiffI1) =>
% 102.15/17.05 ((
% 102.15/17.05 (symdiffI2) =>
% 102.15/17.05 ((
% 102.15/17.05 (symdiffIneg1) =>
% 102.15/17.05 ((
% 102.15/17.05 (symdiffIneg2) =>
% 102.15/17.05 ((
% 102.15/17.05 (secondinupair) =>
% 102.15/17.05 ((
% 102.15/17.05 (setukpairIL) =>
% 102.15/17.05 ((
% 102.15/17.05 (setukpairIR) =>
% 102.15/17.05 ((
% 102.15/17.05 (kpairiskpair) =>
% 102.15/17.05 ((
% 102.15/17.05 (kpairp) =>
% 102.15/17.05 ((
% 102.15/17.05 (singletonsubset) =>
% 102.15/17.05 ((
% 102.15/17.05 (singletoninpowerset) =>
% 102.15/17.05 ((
% 102.15/17.05 (singletoninpowunion) =>
% 102.15/17.05 ((
% 102.15/17.05 (upairset2E) =>
% 102.15/17.05 ((
% 102.15/17.05 (upairsubunion) =>
% 102.15/17.05 ((
% 102.15/17.05 (upairinpowunion) =>
% 102.15/17.05 ((
% 102.15/17.05 (ubforcartprodlem1) =>
% 102.15/17.05 ((
% 102.15/17.05 (ubforcartprodlem2) =>
% 102.15/17.05 ((
% 102.15/17.05 (ubforcartprodlem3) =>
% 102.15/17.05 ((
% 102.15/17.05 (cartprodpairin) =>
% 102.15/17.05 ((
% 102.15/17.05 (cartprodmempair1) =>
% 102.15/17.05 ((
% 102.15/17.05 (cartprodmempair) =>
% 102.15/17.05 ((
% 102.15/17.05 (setunionE2) =>
% 102.15/17.05 ((
% 102.15/17.05 (setunionsingleton1) =>
% 102.15/17.05 ((
% 102.15/17.05 (setunionsingleton2) =>
% 102.15/17.05 ((
% 102.15/17.05 (setunionsingleton) =>
% 102.15/17.05 ((
% 102.15/17.05 (singletonprop) =>
% 102.15/17.05 ((
% 102.15/17.05 (ex1E1) =>
% 102.15/17.05 ((
% 102.15/17.05 (ex1I) =>
% 102.15/17.05 ((
% 102.15/17.05 (ex1I2) =>
% 102.15/17.05 ((
% 102.15/17.05 (singletonsuniq) =>
% 102.15/17.05 ((
% 102.15/17.05 (setukpairinjL1) =>
% 102.15/17.05 ((
% 102.15/17.05 (kfstsingleton) =>
% 102.15/17.05 ((
% 102.15/17.05 (theprop) =>
% 102.15/17.05 ((
% 102.15/17.05 (kfstpairEq) =>
% 102.15/17.05 ((
% 102.15/17.05 (cartprodfstin) =>
% 102.15/17.05 ((
% 102.15/17.05 (setukpairinjL2) =>
% 102.15/17.05 ((
% 102.15/17.05 (setukpairinjL) =>
% 102.15/17.05 ((
% 102.15/17.05 (setukpairinjR11) =>
% 102.15/17.05 ((
% 102.15/17.05 (setukpairinjR12) =>
% 102.15/17.05 ((
% 102.15/17.05 (setukpairinjR1) =>
% 102.15/17.05 ((
% 102.15/17.05 (upairequniteq) =>
% 102.15/17.05 ((
% 102.15/17.05 (setukpairinjR2) =>
% 102.15/17.05 ((
% 102.15/17.05 (setukpairinjR) =>
% 102.15/17.05 ((
% 102.15/17.05 (ksndsingleton) =>
% 102.15/17.05 ((
% 102.15/17.05 (ksndpairEq) =>
% 102.15/17.05 ((
% 102.15/17.05 (kpairsurjEq) =>
% 102.15/17.05 ((
% 102.15/17.05 (cartprodsndin) =>
% 102.15/17.05 ((
% 102.15/17.05 (cartprodpairmemEL) =>
% 102.15/17.05 ((
% 102.15/17.05 (cartprodpairmemER) =>
% 102.15/17.05 ((
% 102.15/17.05 (cartprodmempaircEq) =>
% 102.15/17.05 ((
% 102.15/17.05 (cartprodfstpairEq) =>
% 102.15/17.05 ((
% 102.15/17.05 (cartprodsndpairEq) =>
% 102.15/17.05 ((
% 102.15/17.05 (cartprodpairsurjEq) =>
% 102.15/17.05 ((
% 102.15/17.05 (dpsetconstrI) =>
% 102.15/17.05 ((
% 102.15/17.05 (dpsetconstrSub) =>
% 102.15/17.05 ((
% 102.15/17.05 (setOfPairsIsBReln) =>
% 102.15/17.05 ((
% 102.15/17.05 (dpsetconstrERa) =>
% 102.15/17.05 ((
% 102.15/17.05 (dpsetconstrEL1) =>
% 102.15/17.05 ((
% 102.15/17.05 (dpsetconstrEL2) =>
% 102.15/17.05 ((
% 102.15/17.05 (dpsetconstrER) =>
% 102.15/17.05 ((
% 102.15/17.05 (funcImageSingleton) =>
% 102.15/17.05 ((
% 102.15/17.05 (apProp) =>
% 102.15/17.05 ((
% 102.15/17.05 (app) =>
% 102.15/17.05 ((
% 102.15/17.05 (infuncsetfunc) =>
% 102.15/17.05 ((
% 102.15/17.05 (ap2p) =>
% 102.15/17.05 ((
% 102.15/17.05 (funcinfuncset) =>
% 102.15/17.05 ((
% 102.15/17.05 (lamProp) =>
% 102.15/17.05 ((
% 102.15/17.05 (lamp) =>
% 102.15/17.05 ((
% 102.15/17.05 (lam2p) =>
% 102.15/17.05 ((
% 102.15/17.05 (brelnall1) =>
% 102.15/17.05 ((
% 102.15/17.05 (brelnall2) =>
% 102.15/17.05 ((
% 102.15/17.05 (ex1E2) =>
% 102.15/17.05 ((
% 102.15/17.05 (funcGraphProp1) =>
% 102.15/17.05 ((
% 102.15/17.05 (funcGraphProp3) =>
% 102.15/17.05 ((
% 102.15/17.05 (funcGraphProp2) =>
% 102.15/17.05 ((
% 102.15/17.05 (funcextLem) =>
% 102.15/17.05 ((
% 102.15/17.05 (funcGraphProp4) =>
% 102.15/17.05 ((
% 102.15/17.05 (subbreln) =>
% 102.15/17.05 ((
% 102.15/17.05 (eqbreln) =>
% 102.15/17.05 ((
% 102.15/17.05 (funcext) =>
% 102.15/17.05 ((
% 102.15/17.05 (funcext2) =>
% 102.15/17.05 ((
% 102.15/17.05 (ap2apEq1) =>
% 102.15/17.05 ((
% 102.15/17.05 (ap2apEq2) =>
% 102.15/17.05 ((
% 102.15/17.05 (beta1) =>
% 102.15/17.05 ((
% 102.15/17.05 (eta1) =>
% 102.15/17.05 ((
% 102.15/17.05 (lam2lamEq) =>
% 102.15/17.05 ((
% 102.15/17.05 (beta2) =>
% 102.15/17.05 ((
% 102.15/17.05 (eta2) =>
% 102.15/17.05 ((
% 102.15/17.05 (iffalseProp1) =>
% 102.15/17.05 ((
% 102.15/17.05 (iffalseProp2) =>
% 102.15/17.05 ((
% 102.15/17.05 (iftrueProp1) =>
% 102.15/17.05 ((
% 102.15/17.05 (iftrueProp2) =>
% 102.15/17.05 ((
% 102.15/17.05 (ifSingleton) =>
% 102.15/17.05 ((
% 102.15/17.05 (ifp) =>
% 102.15/17.05 ((
% 102.15/17.05 (theeq) =>
% 102.15/17.05 ((
% 102.15/17.05 (iftrue) =>
% 102.15/17.05 ((
% 102.15/17.05 (iffalse) =>
% 102.15/17.05 ((
% 102.15/17.05 (iftrueorfalse) =>
% 102.15/17.05 ((
% 102.15/17.05 (binintersectT_lem) =>
% 102.15/17.05 ((
% 102.15/17.05 (binunionT_lem) =>
% 102.15/17.05 ((
% 102.15/17.05 (powersetT_lem) =>
% 102.15/17.05 ((
% 102.15/17.05 (setminusT_lem) =>
% 102.15/17.05 ((
% 102.15/17.05 (complementT_lem) =>
% 102.15/17.05 ((
% 102.15/17.05 (setextT) =>
% 102.15/17.05 ((
% 102.15/17.05 (subsetTI) =>
% 102.15/17.05 ((
% 102.15/17.05 (powersetTI1) =>
% 102.15/17.05 ((
% 102.15/17.05 (powersetTE1) =>
% 102.15/17.05 ((
% 102.15/17.05 (complementTI1) =>
% 102.15/17.05 ((
% 102.15/17.05 (complementTE1) =>
% 102.15/17.05 ((
% 102.15/17.06 (binintersectTELcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectTERcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT1) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT2) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT3) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub2) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTnotintersectT) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementImpComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementSubsetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementInPowersetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (contraSubsetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTcontraSubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTILcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTIRcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion2) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (intersectInPowersetIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpNotIn1) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpInComplement1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTE) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTEcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementUnionInPowersetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a2) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1a) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1b) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2b2) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2b) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule0) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule1) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule3) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule4) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_1) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_3) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_4) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_5) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1all2) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1SetBreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (choice2fnsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (setOfPairsIsBReln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1all1) =>
% 102.15/17.06 ((
% 102.15/17.06 (subbreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqbreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compEex) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionEcases) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionCommutes) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2Ex) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2W) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2A) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2B) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Ex) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Ex1) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Equiv) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1E) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1I) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncInInjFuncSet) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncSetFuncIn) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncSetFuncInj) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjFuncSetFuncIn) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjFuncSetFuncSurj) =>
% 102.15/17.06 ((
% 102.15/17.06 (leftInvIsSurj) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjCantorThm) =>
% 102.15/17.06 ((
% 102.15/17.06 (foundation2) =>
% 102.15/17.06 ((
% 102.15/17.06 (notinself) =>
% 102.15/17.06 ((
% 102.15/17.06 (notinself2) =>
% 102.15/17.06 ((
% 102.15/17.06 (omegaSp) =>
% 102.15/17.06 ((
% 102.15/17.06 (omegaSclos) =>
% 102.15/17.06 ((
% 102.15/17.06 (peano0notS) =>
% 102.15/17.06 ((
% 102.15/17.06 (peanoSinj) =>
% 102.15/17.06 ((
% 102.15/17.06 (transitivesetOp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintTransitive) =>
% 102.15/17.06 ((
% 102.15/17.06 (transitivesetOp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionTransitive) =>
% 102.15/17.06 ((
% 102.15/17.06 (ordinalMinLem1) =>
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y0 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (ordinal @
% 102.15/17.06 Y0) =>
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y1 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y2 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (in @
% 102.15/17.06 Y2 @
% 102.15/17.06 Y0) =>
% 102.15/17.06 ((
% 102.15/17.06 (in @
% 102.15/17.06 Y1 @
% 102.15/17.06 Y2) =>
% 102.15/17.06 (in @
% 102.15/17.06 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.15/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
% 102.15/17.06 thf(zip_derived_cl350, plain,
% 102.15/17.06 (~ (((powersetE) =>
% 102.15/17.06 (((setunionI) =>
% 102.15/17.06 (((setunionE) =>
% 102.15/17.06 (((subPowSU) =>
% 102.15/17.06 (((exuE2) =>
% 102.15/17.06 (((nonemptyImpWitness) =>
% 102.15/17.06 (((uniqinunit) =>
% 102.15/17.06 (((notinsingleton) =>
% 102.15/17.06 (((eqinunit) =>
% 102.15/17.06 (((singletonsswitch) =>
% 102.15/17.06 (((upairsetE) =>
% 102.15/17.06 (((upairsetIL) =>
% 102.15/17.06 (((upairsetIR) =>
% 102.15/17.06 (((emptyE1) =>
% 102.15/17.06 (((vacuousDall) =>
% 102.15/17.06 (((quantDeMorgan1) =>
% 102.15/17.06 (((quantDeMorgan2) =>
% 102.15/17.06 (((quantDeMorgan3) =>
% 102.15/17.06 (((quantDeMorgan4) =>
% 102.15/17.06 (((prop2setI) =>
% 102.15/17.06 (((prop2set2propI) =>
% 102.15/17.06 (((notdexE) =>
% 102.15/17.06 (((notdallE) =>
% 102.15/17.06 (((exuI1) =>
% 102.15/17.06 (((exuI3) =>
% 102.15/17.06 (((exuI2) =>
% 102.15/17.06 (((inCongP) =>
% 102.15/17.06 (((in__Cong) =>
% 102.15/17.06 (((exuE3u) =>
% 102.15/17.06 (((exu__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (setadjoin__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (powerset__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunion__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (exuEu) =>
% 102.15/17.06 ((
% 102.15/17.06 (descr__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (dsetconstr__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqimpsubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqimpsubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (emptysetsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetE) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetE2) =>
% 102.15/17.06 ((
% 102.15/17.06 (notsubsetI) =>
% 102.15/17.06 ((
% 102.15/17.06 (notequalI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (notequalI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetRefl) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetTrans) =>
% 102.15/17.06 ((
% 102.15/17.06 (setadjoinSub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setadjoinSub2) =>
% 102.15/17.06 ((
% 102.15/17.06 (subset2powerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (setextsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetemptysetimpeq) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (inPowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (sepInPowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (sepSubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairset2IR) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionEcases) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionE) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionRsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectI) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset5) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset3) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectER) =>
% 102.15/17.06 ((
% 102.15/17.06 (disjointsetsI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectRsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset4) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (bs114d) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusI) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusER) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusSubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusERneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusELneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusILneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusIRneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusSubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffE) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffIneg1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffIneg2) =>
% 102.15/17.06 ((
% 102.15/17.06 (secondinupair) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairiskpair) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairp) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletoninpowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletoninpowunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairset2E) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairsubunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairinpowunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem3) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairin) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempair1) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempair) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionE2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton1) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1E1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1I) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1I2) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonsuniq) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL1) =>
% 102.15/17.06 ((
% 102.15/17.06 (kfstsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (theprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (kfstpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodfstin) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR11) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR12) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR1) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairequniteq) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR) =>
% 102.15/17.06 ((
% 102.15/17.06 (ksndsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (ksndpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairsurjEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodsndin) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairmemEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairmemER) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempaircEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodfstpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodsndpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairsurjEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrI) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrSub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setOfPairsIsBReln) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrERa) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrEL1) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrEL2) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrER) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcImageSingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (apProp) =>
% 102.15/17.06 ((
% 102.15/17.06 (app) =>
% 102.15/17.06 ((
% 102.15/17.06 (infuncsetfunc) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2p) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcinfuncset) =>
% 102.15/17.06 ((
% 102.15/17.06 (lamProp) =>
% 102.15/17.06 ((
% 102.15/17.06 (lamp) =>
% 102.15/17.06 ((
% 102.15/17.06 (lam2p) =>
% 102.15/17.06 ((
% 102.15/17.06 (brelnall1) =>
% 102.15/17.06 ((
% 102.15/17.06 (brelnall2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1E2) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp3) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcextLem) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp4) =>
% 102.15/17.06 ((
% 102.15/17.06 (subbreln) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqbreln) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcext) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcext2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2apEq1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2apEq2) =>
% 102.15/17.06 ((
% 102.15/17.06 (beta1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eta1) =>
% 102.15/17.06 ((
% 102.15/17.06 (lam2lamEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (beta2) =>
% 102.15/17.06 ((
% 102.15/17.06 (eta2) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalseProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalseProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ifSingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (ifp) =>
% 102.15/17.06 ((
% 102.15/17.06 (theeq) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrue) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalse) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueorfalse) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (setextT) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetTI) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetTI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetTE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectTELcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectTERcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT1) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT2) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT3) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub2) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTnotintersectT) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementImpComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementSubsetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementInPowersetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (contraSubsetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTcontraSubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTILcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTIRcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion2) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (intersectInPowersetIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpNotIn1) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpInComplement1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTE) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTEcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementUnionInPowersetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a2) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1a) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1b) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2b2) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2b) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule0) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule1) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule3) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule4) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_1) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_3) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_4) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_5) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1all2) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1SetBreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (choice2fnsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (setOfPairsIsBReln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1all1) =>
% 102.15/17.06 ((
% 102.15/17.06 (subbreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqbreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compEex) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionEcases) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionCommutes) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2Ex) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2W) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2A) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2B) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Ex) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Ex1) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Equiv) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1E) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1I) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncInInjFuncSet) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncSetFuncIn) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncSetFuncInj) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjFuncSetFuncIn) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjFuncSetFuncSurj) =>
% 102.15/17.06 ((
% 102.15/17.06 (leftInvIsSurj) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjCantorThm) =>
% 102.15/17.06 ((
% 102.15/17.06 (foundation2) =>
% 102.15/17.06 ((
% 102.15/17.06 (notinself) =>
% 102.15/17.06 ((
% 102.15/17.06 (notinself2) =>
% 102.15/17.06 ((
% 102.15/17.06 (omegaSp) =>
% 102.15/17.06 ((
% 102.15/17.06 (omegaSclos) =>
% 102.15/17.06 ((
% 102.15/17.06 (peano0notS) =>
% 102.15/17.06 ((
% 102.15/17.06 (peanoSinj) =>
% 102.15/17.06 ((
% 102.15/17.06 (transitivesetOp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintTransitive) =>
% 102.15/17.06 ((
% 102.15/17.06 (transitivesetOp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionTransitive) =>
% 102.15/17.06 ((
% 102.15/17.06 (ordinalMinLem1) =>
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y0 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (ordinal @
% 102.15/17.06 Y0) =>
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y1 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y2 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (in @
% 102.15/17.06 Y2 @
% 102.15/17.06 Y0) =>
% 102.15/17.06 ((
% 102.15/17.06 (in @
% 102.15/17.06 Y1 @
% 102.15/17.06 Y2) =>
% 102.15/17.06 (in @
% 102.15/17.06 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.15/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl343])).
% 102.15/17.06 thf(zip_derived_cl357, plain,
% 102.15/17.06 (~ (((setunionI) =>
% 102.15/17.06 (((setunionE) =>
% 102.15/17.06 (((subPowSU) =>
% 102.15/17.06 (((exuE2) =>
% 102.15/17.06 (((nonemptyImpWitness) =>
% 102.15/17.06 (((uniqinunit) =>
% 102.15/17.06 (((notinsingleton) =>
% 102.15/17.06 (((eqinunit) =>
% 102.15/17.06 (((singletonsswitch) =>
% 102.15/17.06 (((upairsetE) =>
% 102.15/17.06 (((upairsetIL) =>
% 102.15/17.06 (((upairsetIR) =>
% 102.15/17.06 (((emptyE1) =>
% 102.15/17.06 (((vacuousDall) =>
% 102.15/17.06 (((quantDeMorgan1) =>
% 102.15/17.06 (((quantDeMorgan2) =>
% 102.15/17.06 (((quantDeMorgan3) =>
% 102.15/17.06 (((quantDeMorgan4) =>
% 102.15/17.06 (((prop2setI) =>
% 102.15/17.06 (((prop2set2propI) =>
% 102.15/17.06 (((notdexE) =>
% 102.15/17.06 (((notdallE) =>
% 102.15/17.06 (((exuI1) =>
% 102.15/17.06 (((exuI3) =>
% 102.15/17.06 (((exuI2) =>
% 102.15/17.06 (((inCongP) =>
% 102.15/17.06 (((in__Cong) =>
% 102.15/17.06 (((exuE3u) =>
% 102.15/17.06 (((exu__Cong) =>
% 102.15/17.06 (((setadjoin__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (powerset__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunion__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (exuEu) =>
% 102.15/17.06 ((
% 102.15/17.06 (descr__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (dsetconstr__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqimpsubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqimpsubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (emptysetsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetE) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetE2) =>
% 102.15/17.06 ((
% 102.15/17.06 (notsubsetI) =>
% 102.15/17.06 ((
% 102.15/17.06 (notequalI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (notequalI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetRefl) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetTrans) =>
% 102.15/17.06 ((
% 102.15/17.06 (setadjoinSub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setadjoinSub2) =>
% 102.15/17.06 ((
% 102.15/17.06 (subset2powerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (setextsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetemptysetimpeq) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (inPowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (sepInPowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (sepSubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairset2IR) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionEcases) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionE) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionRsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectI) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset5) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset3) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectER) =>
% 102.15/17.06 ((
% 102.15/17.06 (disjointsetsI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectRsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset4) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (bs114d) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusI) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusER) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusSubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusERneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusELneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusILneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusIRneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusSubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffE) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffIneg1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffIneg2) =>
% 102.15/17.06 ((
% 102.15/17.06 (secondinupair) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairiskpair) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairp) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletoninpowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletoninpowunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairset2E) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairsubunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairinpowunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem3) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairin) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempair1) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempair) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionE2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton1) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1E1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1I) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1I2) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonsuniq) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL1) =>
% 102.15/17.06 ((
% 102.15/17.06 (kfstsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (theprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (kfstpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodfstin) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR11) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR12) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR1) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairequniteq) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR) =>
% 102.15/17.06 ((
% 102.15/17.06 (ksndsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (ksndpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairsurjEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodsndin) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairmemEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairmemER) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempaircEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodfstpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodsndpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairsurjEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrI) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrSub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setOfPairsIsBReln) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrERa) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrEL1) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrEL2) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrER) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcImageSingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (apProp) =>
% 102.15/17.06 ((
% 102.15/17.06 (app) =>
% 102.15/17.06 ((
% 102.15/17.06 (infuncsetfunc) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2p) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcinfuncset) =>
% 102.15/17.06 ((
% 102.15/17.06 (lamProp) =>
% 102.15/17.06 ((
% 102.15/17.06 (lamp) =>
% 102.15/17.06 ((
% 102.15/17.06 (lam2p) =>
% 102.15/17.06 ((
% 102.15/17.06 (brelnall1) =>
% 102.15/17.06 ((
% 102.15/17.06 (brelnall2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1E2) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp3) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcextLem) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp4) =>
% 102.15/17.06 ((
% 102.15/17.06 (subbreln) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqbreln) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcext) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcext2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2apEq1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2apEq2) =>
% 102.15/17.06 ((
% 102.15/17.06 (beta1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eta1) =>
% 102.15/17.06 ((
% 102.15/17.06 (lam2lamEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (beta2) =>
% 102.15/17.06 ((
% 102.15/17.06 (eta2) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalseProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalseProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ifSingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (ifp) =>
% 102.15/17.06 ((
% 102.15/17.06 (theeq) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrue) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalse) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueorfalse) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (setextT) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetTI) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetTI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetTE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectTELcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectTERcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT1) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT2) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT3) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub2) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTnotintersectT) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementImpComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementSubsetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementInPowersetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (contraSubsetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTcontraSubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTILcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTIRcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion2) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (intersectInPowersetIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpNotIn1) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpInComplement1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTE) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTEcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementUnionInPowersetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a2) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1a) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1b) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2b2) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2b) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule0) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule1) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule3) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule4) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_1) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_3) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_4) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_5) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1all2) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1SetBreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (choice2fnsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (setOfPairsIsBReln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1all1) =>
% 102.15/17.06 ((
% 102.15/17.06 (subbreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqbreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compEex) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionEcases) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionCommutes) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2Ex) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2W) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2A) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2B) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Ex) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Ex1) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Equiv) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1E) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1I) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncInInjFuncSet) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncSetFuncIn) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncSetFuncInj) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjFuncSetFuncIn) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjFuncSetFuncSurj) =>
% 102.15/17.06 ((
% 102.15/17.06 (leftInvIsSurj) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjCantorThm) =>
% 102.15/17.06 ((
% 102.15/17.06 (foundation2) =>
% 102.15/17.06 ((
% 102.15/17.06 (notinself) =>
% 102.15/17.06 ((
% 102.15/17.06 (notinself2) =>
% 102.15/17.06 ((
% 102.15/17.06 (omegaSp) =>
% 102.15/17.06 ((
% 102.15/17.06 (omegaSclos) =>
% 102.15/17.06 ((
% 102.15/17.06 (peano0notS) =>
% 102.15/17.06 ((
% 102.15/17.06 (peanoSinj) =>
% 102.15/17.06 ((
% 102.15/17.06 (transitivesetOp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintTransitive) =>
% 102.15/17.06 ((
% 102.15/17.06 (transitivesetOp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionTransitive) =>
% 102.15/17.06 ((
% 102.15/17.06 (ordinalMinLem1) =>
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y0 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (ordinal @
% 102.15/17.06 Y0) =>
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y1 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y2 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (in @
% 102.15/17.06 Y2 @
% 102.15/17.06 Y0) =>
% 102.15/17.06 ((
% 102.15/17.06 (in @
% 102.15/17.06 Y1 @
% 102.15/17.06 Y2) =>
% 102.15/17.06 (in @
% 102.15/17.06 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.15/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl350])).
% 102.15/17.06 thf(zip_derived_cl364, plain,
% 102.15/17.06 (~ (((setunionE) =>
% 102.15/17.06 (((subPowSU) =>
% 102.15/17.06 (((exuE2) =>
% 102.15/17.06 (((nonemptyImpWitness) =>
% 102.15/17.06 (((uniqinunit) =>
% 102.15/17.06 (((notinsingleton) =>
% 102.15/17.06 (((eqinunit) =>
% 102.15/17.06 (((singletonsswitch) =>
% 102.15/17.06 (((upairsetE) =>
% 102.15/17.06 (((upairsetIL) =>
% 102.15/17.06 (((upairsetIR) =>
% 102.15/17.06 (((emptyE1) =>
% 102.15/17.06 (((vacuousDall) =>
% 102.15/17.06 (((quantDeMorgan1) =>
% 102.15/17.06 (((quantDeMorgan2) =>
% 102.15/17.06 (((quantDeMorgan3) =>
% 102.15/17.06 (((quantDeMorgan4) =>
% 102.15/17.06 (((prop2setI) =>
% 102.15/17.06 (((prop2set2propI) =>
% 102.15/17.06 (((notdexE) =>
% 102.15/17.06 (((notdallE) =>
% 102.15/17.06 (((exuI1) =>
% 102.15/17.06 (((exuI3) =>
% 102.15/17.06 (((exuI2) =>
% 102.15/17.06 (((inCongP) =>
% 102.15/17.06 (((in__Cong) =>
% 102.15/17.06 (((exuE3u) =>
% 102.15/17.06 (((exu__Cong) =>
% 102.15/17.06 (((setadjoin__Cong) =>
% 102.15/17.06 (((powerset__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunion__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (exuEu) =>
% 102.15/17.06 ((
% 102.15/17.06 (descr__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (dsetconstr__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqimpsubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqimpsubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (emptysetsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetE) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetE2) =>
% 102.15/17.06 ((
% 102.15/17.06 (notsubsetI) =>
% 102.15/17.06 ((
% 102.15/17.06 (notequalI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (notequalI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetRefl) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetTrans) =>
% 102.15/17.06 ((
% 102.15/17.06 (setadjoinSub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setadjoinSub2) =>
% 102.15/17.06 ((
% 102.15/17.06 (subset2powerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (setextsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetemptysetimpeq) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (inPowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (sepInPowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (sepSubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairset2IR) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionEcases) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionE) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionRsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectI) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset5) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset3) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectER) =>
% 102.15/17.06 ((
% 102.15/17.06 (disjointsetsI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectRsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset4) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (bs114d) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusI) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusER) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusSubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusERneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusELneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusILneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusIRneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusSubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffE) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffIneg1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffIneg2) =>
% 102.15/17.06 ((
% 102.15/17.06 (secondinupair) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairiskpair) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairp) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletoninpowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletoninpowunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairset2E) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairsubunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairinpowunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem3) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairin) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempair1) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempair) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionE2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton1) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1E1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1I) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1I2) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonsuniq) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL1) =>
% 102.15/17.06 ((
% 102.15/17.06 (kfstsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (theprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (kfstpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodfstin) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR11) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR12) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR1) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairequniteq) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR) =>
% 102.15/17.06 ((
% 102.15/17.06 (ksndsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (ksndpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairsurjEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodsndin) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairmemEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairmemER) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempaircEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodfstpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodsndpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairsurjEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrI) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrSub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setOfPairsIsBReln) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrERa) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrEL1) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrEL2) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrER) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcImageSingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (apProp) =>
% 102.15/17.06 ((
% 102.15/17.06 (app) =>
% 102.15/17.06 ((
% 102.15/17.06 (infuncsetfunc) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2p) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcinfuncset) =>
% 102.15/17.06 ((
% 102.15/17.06 (lamProp) =>
% 102.15/17.06 ((
% 102.15/17.06 (lamp) =>
% 102.15/17.06 ((
% 102.15/17.06 (lam2p) =>
% 102.15/17.06 ((
% 102.15/17.06 (brelnall1) =>
% 102.15/17.06 ((
% 102.15/17.06 (brelnall2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1E2) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp3) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcextLem) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp4) =>
% 102.15/17.06 ((
% 102.15/17.06 (subbreln) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqbreln) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcext) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcext2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2apEq1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2apEq2) =>
% 102.15/17.06 ((
% 102.15/17.06 (beta1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eta1) =>
% 102.15/17.06 ((
% 102.15/17.06 (lam2lamEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (beta2) =>
% 102.15/17.06 ((
% 102.15/17.06 (eta2) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalseProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalseProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ifSingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (ifp) =>
% 102.15/17.06 ((
% 102.15/17.06 (theeq) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrue) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalse) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueorfalse) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (setextT) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetTI) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetTI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetTE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectTELcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectTERcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT1) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT2) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT3) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub2) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTnotintersectT) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementImpComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementSubsetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementInPowersetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (contraSubsetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTcontraSubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTILcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTIRcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion2) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (intersectInPowersetIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpNotIn1) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpInComplement1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTE) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTEcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementUnionInPowersetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a2) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1a) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1b) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2b2) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2b) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule0) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule1) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule3) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule4) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_1) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_3) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_4) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_5) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1all2) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1SetBreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (choice2fnsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (setOfPairsIsBReln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1all1) =>
% 102.15/17.06 ((
% 102.15/17.06 (subbreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqbreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compEex) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionEcases) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionCommutes) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2Ex) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2W) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2A) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2B) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Ex) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Ex1) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Equiv) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1E) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1I) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncInInjFuncSet) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncSetFuncIn) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncSetFuncInj) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjFuncSetFuncIn) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjFuncSetFuncSurj) =>
% 102.15/17.06 ((
% 102.15/17.06 (leftInvIsSurj) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjCantorThm) =>
% 102.15/17.06 ((
% 102.15/17.06 (foundation2) =>
% 102.15/17.06 ((
% 102.15/17.06 (notinself) =>
% 102.15/17.06 ((
% 102.15/17.06 (notinself2) =>
% 102.15/17.06 ((
% 102.15/17.06 (omegaSp) =>
% 102.15/17.06 ((
% 102.15/17.06 (omegaSclos) =>
% 102.15/17.06 ((
% 102.15/17.06 (peano0notS) =>
% 102.15/17.06 ((
% 102.15/17.06 (peanoSinj) =>
% 102.15/17.06 ((
% 102.15/17.06 (transitivesetOp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintTransitive) =>
% 102.15/17.06 ((
% 102.15/17.06 (transitivesetOp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionTransitive) =>
% 102.15/17.06 ((
% 102.15/17.06 (ordinalMinLem1) =>
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y0 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (ordinal @
% 102.15/17.06 Y0) =>
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y1 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y2 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (in @
% 102.15/17.06 Y2 @
% 102.15/17.06 Y0) =>
% 102.15/17.06 ((
% 102.15/17.06 (in @
% 102.15/17.06 Y1 @
% 102.15/17.06 Y2) =>
% 102.15/17.06 (in @
% 102.15/17.06 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.15/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl357])).
% 102.15/17.06 thf(zip_derived_cl372, plain,
% 102.15/17.06 (~ (((subPowSU) =>
% 102.15/17.06 (((exuE2) =>
% 102.15/17.06 (((nonemptyImpWitness) =>
% 102.15/17.06 (((uniqinunit) =>
% 102.15/17.06 (((notinsingleton) =>
% 102.15/17.06 (((eqinunit) =>
% 102.15/17.06 (((singletonsswitch) =>
% 102.15/17.06 (((upairsetE) =>
% 102.15/17.06 (((upairsetIL) =>
% 102.15/17.06 (((upairsetIR) =>
% 102.15/17.06 (((emptyE1) =>
% 102.15/17.06 (((vacuousDall) =>
% 102.15/17.06 (((quantDeMorgan1) =>
% 102.15/17.06 (((quantDeMorgan2) =>
% 102.15/17.06 (((quantDeMorgan3) =>
% 102.15/17.06 (((quantDeMorgan4) =>
% 102.15/17.06 (((prop2setI) =>
% 102.15/17.06 (((prop2set2propI) =>
% 102.15/17.06 (((notdexE) =>
% 102.15/17.06 (((notdallE) =>
% 102.15/17.06 (((exuI1) =>
% 102.15/17.06 (((exuI3) =>
% 102.15/17.06 (((exuI2) =>
% 102.15/17.06 (((inCongP) =>
% 102.15/17.06 (((in__Cong) =>
% 102.15/17.06 (((exuE3u) =>
% 102.15/17.06 (((exu__Cong) =>
% 102.15/17.06 (((setadjoin__Cong) =>
% 102.15/17.06 (((powerset__Cong) =>
% 102.15/17.06 (((setunion__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (exuEu) =>
% 102.15/17.06 ((
% 102.15/17.06 (descr__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (dsetconstr__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqimpsubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqimpsubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (emptysetsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetE) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetE2) =>
% 102.15/17.06 ((
% 102.15/17.06 (notsubsetI) =>
% 102.15/17.06 ((
% 102.15/17.06 (notequalI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (notequalI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetRefl) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetTrans) =>
% 102.15/17.06 ((
% 102.15/17.06 (setadjoinSub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setadjoinSub2) =>
% 102.15/17.06 ((
% 102.15/17.06 (subset2powerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (setextsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetemptysetimpeq) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (inPowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (sepInPowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (sepSubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairset2IR) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionEcases) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionE) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionRsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectI) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset5) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset3) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectER) =>
% 102.15/17.06 ((
% 102.15/17.06 (disjointsetsI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectRsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset4) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (bs114d) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusI) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusER) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusSubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusERneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusELneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusILneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusIRneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusSubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffE) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffIneg1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffIneg2) =>
% 102.15/17.06 ((
% 102.15/17.06 (secondinupair) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairiskpair) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairp) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletoninpowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletoninpowunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairset2E) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairsubunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairinpowunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem3) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairin) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempair1) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempair) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionE2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton1) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1E1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1I) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1I2) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonsuniq) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL1) =>
% 102.15/17.06 ((
% 102.15/17.06 (kfstsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (theprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (kfstpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodfstin) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR11) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR12) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR1) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairequniteq) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR) =>
% 102.15/17.06 ((
% 102.15/17.06 (ksndsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (ksndpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairsurjEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodsndin) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairmemEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairmemER) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempaircEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodfstpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodsndpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairsurjEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrI) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrSub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setOfPairsIsBReln) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrERa) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrEL1) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrEL2) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrER) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcImageSingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (apProp) =>
% 102.15/17.06 ((
% 102.15/17.06 (app) =>
% 102.15/17.06 ((
% 102.15/17.06 (infuncsetfunc) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2p) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcinfuncset) =>
% 102.15/17.06 ((
% 102.15/17.06 (lamProp) =>
% 102.15/17.06 ((
% 102.15/17.06 (lamp) =>
% 102.15/17.06 ((
% 102.15/17.06 (lam2p) =>
% 102.15/17.06 ((
% 102.15/17.06 (brelnall1) =>
% 102.15/17.06 ((
% 102.15/17.06 (brelnall2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1E2) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp3) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcextLem) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp4) =>
% 102.15/17.06 ((
% 102.15/17.06 (subbreln) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqbreln) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcext) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcext2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2apEq1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2apEq2) =>
% 102.15/17.06 ((
% 102.15/17.06 (beta1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eta1) =>
% 102.15/17.06 ((
% 102.15/17.06 (lam2lamEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (beta2) =>
% 102.15/17.06 ((
% 102.15/17.06 (eta2) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalseProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalseProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ifSingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (ifp) =>
% 102.15/17.06 ((
% 102.15/17.06 (theeq) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrue) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalse) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueorfalse) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (setextT) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetTI) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetTI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetTE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectTELcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectTERcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT1) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT2) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT3) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub2) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTnotintersectT) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementImpComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementSubsetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementInPowersetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (contraSubsetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTcontraSubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTILcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTIRcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion2) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (intersectInPowersetIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpNotIn1) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpInComplement1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTE) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTEcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementUnionInPowersetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a2) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1a) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1b) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2b2) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2b) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule0) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule1) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule3) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule4) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_1) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_3) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_4) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_5) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1all2) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1SetBreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (choice2fnsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (setOfPairsIsBReln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1all1) =>
% 102.15/17.06 ((
% 102.15/17.06 (subbreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqbreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compEex) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionEcases) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionCommutes) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2Ex) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2W) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2A) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2B) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Ex) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Ex1) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Equiv) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1E) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1I) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncInInjFuncSet) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncSetFuncIn) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncSetFuncInj) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjFuncSetFuncIn) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjFuncSetFuncSurj) =>
% 102.15/17.06 ((
% 102.15/17.06 (leftInvIsSurj) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjCantorThm) =>
% 102.15/17.06 ((
% 102.15/17.06 (foundation2) =>
% 102.15/17.06 ((
% 102.15/17.06 (notinself) =>
% 102.15/17.06 ((
% 102.15/17.06 (notinself2) =>
% 102.15/17.06 ((
% 102.15/17.06 (omegaSp) =>
% 102.15/17.06 ((
% 102.15/17.06 (omegaSclos) =>
% 102.15/17.06 ((
% 102.15/17.06 (peano0notS) =>
% 102.15/17.06 ((
% 102.15/17.06 (peanoSinj) =>
% 102.15/17.06 ((
% 102.15/17.06 (transitivesetOp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintTransitive) =>
% 102.15/17.06 ((
% 102.15/17.06 (transitivesetOp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionTransitive) =>
% 102.15/17.06 ((
% 102.15/17.06 (ordinalMinLem1) =>
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y0 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (ordinal @
% 102.15/17.06 Y0) =>
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y1 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y2 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (in @
% 102.15/17.06 Y2 @
% 102.15/17.06 Y0) =>
% 102.15/17.06 ((
% 102.15/17.06 (in @
% 102.15/17.06 Y1 @
% 102.15/17.06 Y2) =>
% 102.15/17.06 (in @
% 102.15/17.06 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.15/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl364])).
% 102.15/17.06 thf(zip_derived_cl382, plain,
% 102.15/17.06 (~ (((exuE2) =>
% 102.15/17.06 (((nonemptyImpWitness) =>
% 102.15/17.06 (((uniqinunit) =>
% 102.15/17.06 (((notinsingleton) =>
% 102.15/17.06 (((eqinunit) =>
% 102.15/17.06 (((singletonsswitch) =>
% 102.15/17.06 (((upairsetE) =>
% 102.15/17.06 (((upairsetIL) =>
% 102.15/17.06 (((upairsetIR) =>
% 102.15/17.06 (((emptyE1) =>
% 102.15/17.06 (((vacuousDall) =>
% 102.15/17.06 (((quantDeMorgan1) =>
% 102.15/17.06 (((quantDeMorgan2) =>
% 102.15/17.06 (((quantDeMorgan3) =>
% 102.15/17.06 (((quantDeMorgan4) =>
% 102.15/17.06 (((prop2setI) =>
% 102.15/17.06 (((prop2set2propI) =>
% 102.15/17.06 (((notdexE) =>
% 102.15/17.06 (((notdallE) =>
% 102.15/17.06 (((exuI1) =>
% 102.15/17.06 (((exuI3) =>
% 102.15/17.06 (((exuI2) =>
% 102.15/17.06 (((inCongP) =>
% 102.15/17.06 (((in__Cong) =>
% 102.15/17.06 (((exuE3u) =>
% 102.15/17.06 (((exu__Cong) =>
% 102.15/17.06 (((setadjoin__Cong) =>
% 102.15/17.06 (((powerset__Cong) =>
% 102.15/17.06 (((setunion__Cong) =>
% 102.15/17.06 (((exuEu) =>
% 102.15/17.06 ((
% 102.15/17.06 (descr__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (dsetconstr__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqimpsubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqimpsubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (emptysetsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetE) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetE2) =>
% 102.15/17.06 ((
% 102.15/17.06 (notsubsetI) =>
% 102.15/17.06 ((
% 102.15/17.06 (notequalI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (notequalI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetRefl) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetTrans) =>
% 102.15/17.06 ((
% 102.15/17.06 (setadjoinSub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setadjoinSub2) =>
% 102.15/17.06 ((
% 102.15/17.06 (subset2powerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (setextsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetemptysetimpeq) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (inPowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (sepInPowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (sepSubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairset2IR) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionEcases) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionE) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionRsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectI) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset5) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset3) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectER) =>
% 102.15/17.06 ((
% 102.15/17.06 (disjointsetsI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectRsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset4) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (bs114d) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusI) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusER) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusSubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusERneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusELneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusILneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusIRneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusSubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffE) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffIneg1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffIneg2) =>
% 102.15/17.06 ((
% 102.15/17.06 (secondinupair) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairiskpair) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairp) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletoninpowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletoninpowunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairset2E) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairsubunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairinpowunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem3) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairin) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempair1) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempair) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionE2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton1) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1E1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1I) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1I2) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonsuniq) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL1) =>
% 102.15/17.06 ((
% 102.15/17.06 (kfstsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (theprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (kfstpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodfstin) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR11) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR12) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR1) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairequniteq) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR) =>
% 102.15/17.06 ((
% 102.15/17.06 (ksndsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (ksndpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairsurjEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodsndin) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairmemEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairmemER) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempaircEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodfstpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodsndpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairsurjEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrI) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrSub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setOfPairsIsBReln) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrERa) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrEL1) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrEL2) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrER) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcImageSingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (apProp) =>
% 102.15/17.06 ((
% 102.15/17.06 (app) =>
% 102.15/17.06 ((
% 102.15/17.06 (infuncsetfunc) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2p) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcinfuncset) =>
% 102.15/17.06 ((
% 102.15/17.06 (lamProp) =>
% 102.15/17.06 ((
% 102.15/17.06 (lamp) =>
% 102.15/17.06 ((
% 102.15/17.06 (lam2p) =>
% 102.15/17.06 ((
% 102.15/17.06 (brelnall1) =>
% 102.15/17.06 ((
% 102.15/17.06 (brelnall2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1E2) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp3) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcextLem) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp4) =>
% 102.15/17.06 ((
% 102.15/17.06 (subbreln) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqbreln) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcext) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcext2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2apEq1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2apEq2) =>
% 102.15/17.06 ((
% 102.15/17.06 (beta1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eta1) =>
% 102.15/17.06 ((
% 102.15/17.06 (lam2lamEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (beta2) =>
% 102.15/17.06 ((
% 102.15/17.06 (eta2) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalseProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalseProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ifSingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (ifp) =>
% 102.15/17.06 ((
% 102.15/17.06 (theeq) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrue) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalse) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueorfalse) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (setextT) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetTI) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetTI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetTE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectTELcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectTERcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT1) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT2) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT3) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub2) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTnotintersectT) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementImpComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementSubsetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementInPowersetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (contraSubsetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTcontraSubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTILcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTIRcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion2) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (intersectInPowersetIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpNotIn1) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpInComplement1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTE) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTEcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementUnionInPowersetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a2) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1a) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1b) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2b2) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2b) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule0) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule1) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule3) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz13rule4) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_1) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_2) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_3) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_4) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz1_5) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1all2) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1SetBreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (choice2fnsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (setOfPairsIsBReln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1all1) =>
% 102.15/17.06 ((
% 102.15/17.06 (subbreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqbreln1) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1invE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1compEex) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionI) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionE) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionEcases) =>
% 102.15/17.06 ((
% 102.15/17.06 (breln1unionCommutes) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2Ex) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2W) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2A) =>
% 102.15/17.06 ((
% 102.15/17.06 (woz2B) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Ex) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Ex1) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1Equiv) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1E) =>
% 102.15/17.06 ((
% 102.15/17.06 (image1I) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncInInjFuncSet) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncSetFuncIn) =>
% 102.15/17.06 ((
% 102.15/17.06 (injFuncSetFuncInj) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjFuncSetFuncIn) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjFuncSetFuncSurj) =>
% 102.15/17.06 ((
% 102.15/17.06 (leftInvIsSurj) =>
% 102.15/17.06 ((
% 102.15/17.06 (surjCantorThm) =>
% 102.15/17.06 ((
% 102.15/17.06 (foundation2) =>
% 102.15/17.06 ((
% 102.15/17.06 (notinself) =>
% 102.15/17.06 ((
% 102.15/17.06 (notinself2) =>
% 102.15/17.06 ((
% 102.15/17.06 (omegaSp) =>
% 102.15/17.06 ((
% 102.15/17.06 (omegaSclos) =>
% 102.15/17.06 ((
% 102.15/17.06 (peano0notS) =>
% 102.15/17.06 ((
% 102.15/17.06 (peanoSinj) =>
% 102.15/17.06 ((
% 102.15/17.06 (transitivesetOp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintTransitive) =>
% 102.15/17.06 ((
% 102.15/17.06 (transitivesetOp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionTransitive) =>
% 102.15/17.06 ((
% 102.15/17.06 (ordinalMinLem1) =>
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y0 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (ordinal @
% 102.15/17.06 Y0) =>
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y1 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (!!) @ (
% 102.15/17.06 ^[Y2 : $i]:
% 102.15/17.06 ((
% 102.15/17.06 (in @
% 102.15/17.06 Y2 @
% 102.15/17.06 Y0) =>
% 102.15/17.06 ((
% 102.15/17.06 (in @
% 102.15/17.06 Y1 @
% 102.15/17.06 Y2) =>
% 102.15/17.06 (in @
% 102.15/17.06 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.15/17.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl372])).
% 102.15/17.06 thf(zip_derived_cl390, plain,
% 102.15/17.06 (~ (((nonemptyImpWitness) =>
% 102.15/17.06 (((uniqinunit) =>
% 102.15/17.06 (((notinsingleton) =>
% 102.15/17.06 (((eqinunit) =>
% 102.15/17.06 (((singletonsswitch) =>
% 102.15/17.06 (((upairsetE) =>
% 102.15/17.06 (((upairsetIL) =>
% 102.15/17.06 (((upairsetIR) =>
% 102.15/17.06 (((emptyE1) =>
% 102.15/17.06 (((vacuousDall) =>
% 102.15/17.06 (((quantDeMorgan1) =>
% 102.15/17.06 (((quantDeMorgan2) =>
% 102.15/17.06 (((quantDeMorgan3) =>
% 102.15/17.06 (((quantDeMorgan4) =>
% 102.15/17.06 (((prop2setI) =>
% 102.15/17.06 (((prop2set2propI) =>
% 102.15/17.06 (((notdexE) =>
% 102.15/17.06 (((notdallE) =>
% 102.15/17.06 (((exuI1) =>
% 102.15/17.06 (((exuI3) =>
% 102.15/17.06 (((exuI2) =>
% 102.15/17.06 (((inCongP) =>
% 102.15/17.06 (((in__Cong) =>
% 102.15/17.06 (((exuE3u) =>
% 102.15/17.06 (((exu__Cong) =>
% 102.15/17.06 (((setadjoin__Cong) =>
% 102.15/17.06 (((powerset__Cong) =>
% 102.15/17.06 (((setunion__Cong) =>
% 102.15/17.06 (((exuEu) =>
% 102.15/17.06 (((descr__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (dsetconstr__Cong) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqimpsubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqimpsubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (emptysetsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetE) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetE2) =>
% 102.15/17.06 ((
% 102.15/17.06 (notsubsetI) =>
% 102.15/17.06 ((
% 102.15/17.06 (notequalI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (notequalI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetRefl) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetTrans) =>
% 102.15/17.06 ((
% 102.15/17.06 (setadjoinSub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setadjoinSub2) =>
% 102.15/17.06 ((
% 102.15/17.06 (subset2powerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (setextsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetemptysetimpeq) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (inPowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (sepInPowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (sepSubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairset2IR) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionEcases) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionE) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionRsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectI) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset5) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset3) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectER) =>
% 102.15/17.06 ((
% 102.15/17.06 (disjointsetsI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectRsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset4) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectSubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (bs114d) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusI) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusER) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusSubset2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusERneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusELneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusILneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusIRneg) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusLsub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusSubset1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffE) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffI2) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffIneg1) =>
% 102.15/17.06 ((
% 102.15/17.06 (symdiffIneg2) =>
% 102.15/17.06 ((
% 102.15/17.06 (secondinupair) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairIL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairIR) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairiskpair) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairp) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonsubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletoninpowerset) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletoninpowunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairset2E) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairsubunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairinpowunion) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ubforcartprodlem3) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairin) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempair1) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempair) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionE2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton1) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setunionsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1E1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1I) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1I2) =>
% 102.15/17.06 ((
% 102.15/17.06 (singletonsuniq) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL1) =>
% 102.15/17.06 ((
% 102.15/17.06 (kfstsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (theprop) =>
% 102.15/17.06 ((
% 102.15/17.06 (kfstpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodfstin) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjL) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR11) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR12) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR1) =>
% 102.15/17.06 ((
% 102.15/17.06 (upairequniteq) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR2) =>
% 102.15/17.06 ((
% 102.15/17.06 (setukpairinjR) =>
% 102.15/17.06 ((
% 102.15/17.06 (ksndsingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (ksndpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (kpairsurjEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodsndin) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairmemEL) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairmemER) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodmempaircEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodfstpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodsndpairEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (cartprodpairsurjEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrI) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrSub) =>
% 102.15/17.06 ((
% 102.15/17.06 (setOfPairsIsBReln) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrERa) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrEL1) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrEL2) =>
% 102.15/17.06 ((
% 102.15/17.06 (dpsetconstrER) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcImageSingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (apProp) =>
% 102.15/17.06 ((
% 102.15/17.06 (app) =>
% 102.15/17.06 ((
% 102.15/17.06 (infuncsetfunc) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2p) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcinfuncset) =>
% 102.15/17.06 ((
% 102.15/17.06 (lamProp) =>
% 102.15/17.06 ((
% 102.15/17.06 (lamp) =>
% 102.15/17.06 ((
% 102.15/17.06 (lam2p) =>
% 102.15/17.06 ((
% 102.15/17.06 (brelnall1) =>
% 102.15/17.06 ((
% 102.15/17.06 (brelnall2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ex1E2) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp3) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcextLem) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcGraphProp4) =>
% 102.15/17.06 ((
% 102.15/17.06 (subbreln) =>
% 102.15/17.06 ((
% 102.15/17.06 (eqbreln) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcext) =>
% 102.15/17.06 ((
% 102.15/17.06 (funcext2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2apEq1) =>
% 102.15/17.06 ((
% 102.15/17.06 (ap2apEq2) =>
% 102.15/17.06 ((
% 102.15/17.06 (beta1) =>
% 102.15/17.06 ((
% 102.15/17.06 (eta1) =>
% 102.15/17.06 ((
% 102.15/17.06 (lam2lamEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (beta2) =>
% 102.15/17.06 ((
% 102.15/17.06 (eta2) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalseProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalseProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueProp1) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueProp2) =>
% 102.15/17.06 ((
% 102.15/17.06 (ifSingleton) =>
% 102.15/17.06 ((
% 102.15/17.06 (ifp) =>
% 102.15/17.06 ((
% 102.15/17.06 (theeq) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrue) =>
% 102.15/17.06 ((
% 102.15/17.06 (iffalse) =>
% 102.15/17.06 ((
% 102.15/17.06 (iftrueorfalse) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (setminusT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementT_lem) =>
% 102.15/17.06 ((
% 102.15/17.06 (setextT) =>
% 102.15/17.06 ((
% 102.15/17.06 (subsetTI) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetTI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (powersetTE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectTELcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binintersectTERcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT1) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT2) =>
% 102.15/17.06 ((
% 102.15/17.06 (contrasubsetT3) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementI1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementE1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub1) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementSub2) =>
% 102.15/17.06 ((
% 102.15/17.06 (doubleComplementEq) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTnotintersectT) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementImpComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementSubsetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementInPowersetComplementIntersect) =>
% 102.15/17.06 ((
% 102.15/17.06 (contraSubsetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementTcontraSubset) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTILcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTIRcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInUnion2) =>
% 102.15/17.06 ((
% 102.15/17.06 (inIntersectImpInIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (intersectInPowersetIntersectUnions) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpNotIn1) =>
% 102.15/17.06 ((
% 102.15/17.06 (inComplementUnionImpInComplement1) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTE) =>
% 102.15/17.06 ((
% 102.15/17.06 (binunionTEcontra) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a1) =>
% 102.15/17.06 ((
% 102.15/17.06 (complementUnionInPowersetComplement) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan2a2) =>
% 102.15/17.06 ((
% 102.15/17.06 (demorgan1a) =>
% 102.15/17.06 ((
% 102.15/17.07 (demorgan1b) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan1) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2a) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2b2) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2b) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule0) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule1) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule2) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule3) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule4) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_1) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_2) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_3) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_4) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_5) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1all2) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1SetBreln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (choice2fnsingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (setOfPairsIsBReln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1all1) =>
% 102.15/17.07 ((
% 102.15/17.07 (subbreln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (eqbreln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1invprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1invI) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1invE) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compI) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compE) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compEex) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionIL) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionIR) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionI) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionE) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionEcases) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionCommutes) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2Ex) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2W) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2A) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2B) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1Ex) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1Ex1) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1Equiv) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1E) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1I) =>
% 102.15/17.07 ((
% 102.15/17.07 (injFuncInInjFuncSet) =>
% 102.15/17.07 ((
% 102.15/17.07 (injFuncSetFuncIn) =>
% 102.15/17.07 ((
% 102.15/17.07 (injFuncSetFuncInj) =>
% 102.15/17.07 ((
% 102.15/17.07 (surjFuncSetFuncIn) =>
% 102.15/17.07 ((
% 102.15/17.07 (surjFuncSetFuncSurj) =>
% 102.15/17.07 ((
% 102.15/17.07 (leftInvIsSurj) =>
% 102.15/17.07 ((
% 102.15/17.07 (surjCantorThm) =>
% 102.15/17.07 ((
% 102.15/17.07 (foundation2) =>
% 102.15/17.07 ((
% 102.15/17.07 (notinself) =>
% 102.15/17.07 ((
% 102.15/17.07 (notinself2) =>
% 102.15/17.07 ((
% 102.15/17.07 (omegaSp) =>
% 102.15/17.07 ((
% 102.15/17.07 (omegaSclos) =>
% 102.15/17.07 ((
% 102.15/17.07 (peano0notS) =>
% 102.15/17.07 ((
% 102.15/17.07 (peanoSinj) =>
% 102.15/17.07 ((
% 102.15/17.07 (transitivesetOp1) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintTransitive) =>
% 102.15/17.07 ((
% 102.15/17.07 (transitivesetOp2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionTransitive) =>
% 102.15/17.07 ((
% 102.15/17.07 (ordinalMinLem1) =>
% 102.15/17.07 ((
% 102.15/17.07 (!!) @ (
% 102.15/17.07 ^[Y0 : $i]:
% 102.15/17.07 ((
% 102.15/17.07 (ordinal @
% 102.15/17.07 Y0) =>
% 102.15/17.07 ((
% 102.15/17.07 (!!) @ (
% 102.15/17.07 ^[Y1 : $i]:
% 102.15/17.07 ((
% 102.15/17.07 (!!) @ (
% 102.15/17.07 ^[Y2 : $i]:
% 102.15/17.07 ((
% 102.15/17.07 (in @
% 102.15/17.07 Y2 @
% 102.15/17.07 Y0) =>
% 102.15/17.07 ((
% 102.15/17.07 (in @
% 102.15/17.07 Y1 @
% 102.15/17.07 Y2) =>
% 102.15/17.07 (in @
% 102.15/17.07 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl382])).
% 102.15/17.07 thf(zip_derived_cl397, plain,
% 102.15/17.07 (~ (((uniqinunit) =>
% 102.15/17.07 (((notinsingleton) =>
% 102.15/17.07 (((eqinunit) =>
% 102.15/17.07 (((singletonsswitch) =>
% 102.15/17.07 (((upairsetE) =>
% 102.15/17.07 (((upairsetIL) =>
% 102.15/17.07 (((upairsetIR) =>
% 102.15/17.07 (((emptyE1) =>
% 102.15/17.07 (((vacuousDall) =>
% 102.15/17.07 (((quantDeMorgan1) =>
% 102.15/17.07 (((quantDeMorgan2) =>
% 102.15/17.07 (((quantDeMorgan3) =>
% 102.15/17.07 (((quantDeMorgan4) =>
% 102.15/17.07 (((prop2setI) =>
% 102.15/17.07 (((prop2set2propI) =>
% 102.15/17.07 (((notdexE) =>
% 102.15/17.07 (((notdallE) =>
% 102.15/17.07 (((exuI1) =>
% 102.15/17.07 (((exuI3) =>
% 102.15/17.07 (((exuI2) =>
% 102.15/17.07 (((inCongP) =>
% 102.15/17.07 (((in__Cong) =>
% 102.15/17.07 (((exuE3u) =>
% 102.15/17.07 (((exu__Cong) =>
% 102.15/17.07 (((setadjoin__Cong) =>
% 102.15/17.07 (((powerset__Cong) =>
% 102.15/17.07 (((setunion__Cong) =>
% 102.15/17.07 (((exuEu) =>
% 102.15/17.07 (((descr__Cong) =>
% 102.15/17.07 (((dsetconstr__Cong) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (eqimpsubset2) =>
% 102.15/17.07 ((
% 102.15/17.07 (eqimpsubset1) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetI2) =>
% 102.15/17.07 ((
% 102.15/17.07 (emptysetsubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetE) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetE2) =>
% 102.15/17.07 ((
% 102.15/17.07 (notsubsetI) =>
% 102.15/17.07 ((
% 102.15/17.07 (notequalI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (notequalI2) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetRefl) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetTrans) =>
% 102.15/17.07 ((
% 102.15/17.07 (setadjoinSub) =>
% 102.15/17.07 ((
% 102.15/17.07 (setadjoinSub2) =>
% 102.15/17.07 ((
% 102.15/17.07 (subset2powerset) =>
% 102.15/17.07 ((
% 102.15/17.07 (setextsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetemptysetimpeq) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetE1) =>
% 102.15/17.07 ((
% 102.15/17.07 (inPowerset) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetsubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (sepInPowerset) =>
% 102.15/17.07 ((
% 102.15/17.07 (sepSubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionIL) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairset2IR) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionIR) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionEcases) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionE) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionLsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionRsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectI) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset5) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectEL) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectLsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset2) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset3) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectER) =>
% 102.15/17.07 ((
% 102.15/17.07 (disjointsetsI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectRsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset4) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset1) =>
% 102.15/17.07 ((
% 102.15/17.07 (bs114d) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusI) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusEL) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusER) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusSubset2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusERneg) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusELneg) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusILneg) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusIRneg) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusLsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusSubset1) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffE) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffI2) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffIneg1) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffIneg2) =>
% 102.15/17.07 ((
% 102.15/17.07 (secondinupair) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairIL) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairIR) =>
% 102.15/17.07 ((
% 102.15/17.07 (kpairiskpair) =>
% 102.15/17.07 ((
% 102.15/17.07 (kpairp) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletonsubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletoninpowerset) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletoninpowunion) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairset2E) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairsubunion) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairinpowunion) =>
% 102.15/17.07 ((
% 102.15/17.07 (ubforcartprodlem1) =>
% 102.15/17.07 ((
% 102.15/17.07 (ubforcartprodlem2) =>
% 102.15/17.07 ((
% 102.15/17.07 (ubforcartprodlem3) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodpairin) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodmempair1) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodmempair) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionE2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionsingleton1) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionsingleton2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionsingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletonprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (ex1E1) =>
% 102.15/17.07 ((
% 102.15/17.07 (ex1I) =>
% 102.15/17.07 ((
% 102.15/17.07 (ex1I2) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletonsuniq) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjL1) =>
% 102.15/17.07 ((
% 102.15/17.07 (kfstsingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (theprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (kfstpairEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodfstin) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjL2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjL) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR11) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR12) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR1) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairequniteq) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR) =>
% 102.15/17.07 ((
% 102.15/17.07 (ksndsingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (ksndpairEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (kpairsurjEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodsndin) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodpairmemEL) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodpairmemER) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodmempaircEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodfstpairEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodsndpairEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodpairsurjEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrI) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrSub) =>
% 102.15/17.07 ((
% 102.15/17.07 (setOfPairsIsBReln) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrERa) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrEL1) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrEL2) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrER) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcImageSingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (apProp) =>
% 102.15/17.07 ((
% 102.15/17.07 (app) =>
% 102.15/17.07 ((
% 102.15/17.07 (infuncsetfunc) =>
% 102.15/17.07 ((
% 102.15/17.07 (ap2p) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcinfuncset) =>
% 102.15/17.07 ((
% 102.15/17.07 (lamProp) =>
% 102.15/17.07 ((
% 102.15/17.07 (lamp) =>
% 102.15/17.07 ((
% 102.15/17.07 (lam2p) =>
% 102.15/17.07 ((
% 102.15/17.07 (brelnall1) =>
% 102.15/17.07 ((
% 102.15/17.07 (brelnall2) =>
% 102.15/17.07 ((
% 102.15/17.07 (ex1E2) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcGraphProp1) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcGraphProp3) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcGraphProp2) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcextLem) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcGraphProp4) =>
% 102.15/17.07 ((
% 102.15/17.07 (subbreln) =>
% 102.15/17.07 ((
% 102.15/17.07 (eqbreln) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcext) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcext2) =>
% 102.15/17.07 ((
% 102.15/17.07 (ap2apEq1) =>
% 102.15/17.07 ((
% 102.15/17.07 (ap2apEq2) =>
% 102.15/17.07 ((
% 102.15/17.07 (beta1) =>
% 102.15/17.07 ((
% 102.15/17.07 (eta1) =>
% 102.15/17.07 ((
% 102.15/17.07 (lam2lamEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (beta2) =>
% 102.15/17.07 ((
% 102.15/17.07 (eta2) =>
% 102.15/17.07 ((
% 102.15/17.07 (iffalseProp1) =>
% 102.15/17.07 ((
% 102.15/17.07 (iffalseProp2) =>
% 102.15/17.07 ((
% 102.15/17.07 (iftrueProp1) =>
% 102.15/17.07 ((
% 102.15/17.07 (iftrueProp2) =>
% 102.15/17.07 ((
% 102.15/17.07 (ifSingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (ifp) =>
% 102.15/17.07 ((
% 102.15/17.07 (theeq) =>
% 102.15/17.07 ((
% 102.15/17.07 (iftrue) =>
% 102.15/17.07 ((
% 102.15/17.07 (iffalse) =>
% 102.15/17.07 ((
% 102.15/17.07 (iftrueorfalse) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (setextT) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetTI) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetTI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetTE1) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementTI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementTE1) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectTELcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectTERcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (contrasubsetT) =>
% 102.15/17.07 ((
% 102.15/17.07 (contrasubsetT1) =>
% 102.15/17.07 ((
% 102.15/17.07 (contrasubsetT2) =>
% 102.15/17.07 ((
% 102.15/17.07 (contrasubsetT3) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementE1) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementSub1) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementSub2) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementTnotintersectT) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementImpComplementIntersect) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementSubsetComplementIntersect) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementInPowersetComplementIntersect) =>
% 102.15/17.07 ((
% 102.15/17.07 (contraSubsetComplement) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementTcontraSubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionTILcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionTIRcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (inIntersectImpInUnion) =>
% 102.15/17.07 ((
% 102.15/17.07 (inIntersectImpInUnion2) =>
% 102.15/17.07 ((
% 102.15/17.07 (inIntersectImpInIntersectUnions) =>
% 102.15/17.07 ((
% 102.15/17.07 (intersectInPowersetIntersectUnions) =>
% 102.15/17.07 ((
% 102.15/17.07 (inComplementUnionImpNotIn1) =>
% 102.15/17.07 ((
% 102.15/17.07 (inComplementUnionImpInComplement1) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionTE) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionTEcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2a1) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementUnionInPowersetComplement) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2a2) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan1a) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan1b) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan1) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2a) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2b2) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2b) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule0) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule1) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule2) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule3) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule4) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_1) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_2) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_3) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_4) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_5) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1all2) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1SetBreln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (choice2fnsingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (setOfPairsIsBReln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1all1) =>
% 102.15/17.07 ((
% 102.15/17.07 (subbreln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (eqbreln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1invprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1invI) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1invE) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compI) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compE) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compEex) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionIL) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionIR) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionI) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionE) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionEcases) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionCommutes) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2Ex) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2W) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2A) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2B) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1Ex) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1Ex1) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1Equiv) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1E) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1I) =>
% 102.15/17.07 ((
% 102.15/17.07 (injFuncInInjFuncSet) =>
% 102.15/17.07 ((
% 102.15/17.07 (injFuncSetFuncIn) =>
% 102.15/17.07 ((
% 102.15/17.07 (injFuncSetFuncInj) =>
% 102.15/17.07 ((
% 102.15/17.07 (surjFuncSetFuncIn) =>
% 102.15/17.07 ((
% 102.15/17.07 (surjFuncSetFuncSurj) =>
% 102.15/17.07 ((
% 102.15/17.07 (leftInvIsSurj) =>
% 102.15/17.07 ((
% 102.15/17.07 (surjCantorThm) =>
% 102.15/17.07 ((
% 102.15/17.07 (foundation2) =>
% 102.15/17.07 ((
% 102.15/17.07 (notinself) =>
% 102.15/17.07 ((
% 102.15/17.07 (notinself2) =>
% 102.15/17.07 ((
% 102.15/17.07 (omegaSp) =>
% 102.15/17.07 ((
% 102.15/17.07 (omegaSclos) =>
% 102.15/17.07 ((
% 102.15/17.07 (peano0notS) =>
% 102.15/17.07 ((
% 102.15/17.07 (peanoSinj) =>
% 102.15/17.07 ((
% 102.15/17.07 (transitivesetOp1) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintTransitive) =>
% 102.15/17.07 ((
% 102.15/17.07 (transitivesetOp2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionTransitive) =>
% 102.15/17.07 ((
% 102.15/17.07 (ordinalMinLem1) =>
% 102.15/17.07 ((
% 102.15/17.07 (!!) @ (
% 102.15/17.07 ^[Y0 : $i]:
% 102.15/17.07 ((
% 102.15/17.07 (ordinal @
% 102.15/17.07 Y0) =>
% 102.15/17.07 ((
% 102.15/17.07 (!!) @ (
% 102.15/17.07 ^[Y1 : $i]:
% 102.15/17.07 ((
% 102.15/17.07 (!!) @ (
% 102.15/17.07 ^[Y2 : $i]:
% 102.15/17.07 ((
% 102.15/17.07 (in @
% 102.15/17.07 Y2 @
% 102.15/17.07 Y0) =>
% 102.15/17.07 ((
% 102.15/17.07 (in @
% 102.15/17.07 Y1 @
% 102.15/17.07 Y2) =>
% 102.15/17.07 (in @
% 102.15/17.07 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl390])).
% 102.15/17.07 thf(zip_derived_cl406, plain,
% 102.15/17.07 (~ (((notinsingleton) =>
% 102.15/17.07 (((eqinunit) =>
% 102.15/17.07 (((singletonsswitch) =>
% 102.15/17.07 (((upairsetE) =>
% 102.15/17.07 (((upairsetIL) =>
% 102.15/17.07 (((upairsetIR) =>
% 102.15/17.07 (((emptyE1) =>
% 102.15/17.07 (((vacuousDall) =>
% 102.15/17.07 (((quantDeMorgan1) =>
% 102.15/17.07 (((quantDeMorgan2) =>
% 102.15/17.07 (((quantDeMorgan3) =>
% 102.15/17.07 (((quantDeMorgan4) =>
% 102.15/17.07 (((prop2setI) =>
% 102.15/17.07 (((prop2set2propI) =>
% 102.15/17.07 (((notdexE) =>
% 102.15/17.07 (((notdallE) =>
% 102.15/17.07 (((exuI1) =>
% 102.15/17.07 (((exuI3) =>
% 102.15/17.07 (((exuI2) =>
% 102.15/17.07 (((inCongP) =>
% 102.15/17.07 (((in__Cong) =>
% 102.15/17.07 (((exuE3u) =>
% 102.15/17.07 (((exu__Cong) =>
% 102.15/17.07 (((setadjoin__Cong) =>
% 102.15/17.07 (((powerset__Cong) =>
% 102.15/17.07 (((setunion__Cong) =>
% 102.15/17.07 (((exuEu) =>
% 102.15/17.07 (((descr__Cong) =>
% 102.15/17.07 (((dsetconstr__Cong) =>
% 102.15/17.07 (((subsetI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (eqimpsubset2) =>
% 102.15/17.07 ((
% 102.15/17.07 (eqimpsubset1) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetI2) =>
% 102.15/17.07 ((
% 102.15/17.07 (emptysetsubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetE) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetE2) =>
% 102.15/17.07 ((
% 102.15/17.07 (notsubsetI) =>
% 102.15/17.07 ((
% 102.15/17.07 (notequalI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (notequalI2) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetRefl) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetTrans) =>
% 102.15/17.07 ((
% 102.15/17.07 (setadjoinSub) =>
% 102.15/17.07 ((
% 102.15/17.07 (setadjoinSub2) =>
% 102.15/17.07 ((
% 102.15/17.07 (subset2powerset) =>
% 102.15/17.07 ((
% 102.15/17.07 (setextsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetemptysetimpeq) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetE1) =>
% 102.15/17.07 ((
% 102.15/17.07 (inPowerset) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetsubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (sepInPowerset) =>
% 102.15/17.07 ((
% 102.15/17.07 (sepSubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionIL) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairset2IR) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionIR) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionEcases) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionE) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionLsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionRsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectI) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset5) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectEL) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectLsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset2) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset3) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectER) =>
% 102.15/17.07 ((
% 102.15/17.07 (disjointsetsI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectRsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset4) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset1) =>
% 102.15/17.07 ((
% 102.15/17.07 (bs114d) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusI) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusEL) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusER) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusSubset2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusERneg) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusELneg) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusILneg) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusIRneg) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusLsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusSubset1) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffE) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffI2) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffIneg1) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffIneg2) =>
% 102.15/17.07 ((
% 102.15/17.07 (secondinupair) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairIL) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairIR) =>
% 102.15/17.07 ((
% 102.15/17.07 (kpairiskpair) =>
% 102.15/17.07 ((
% 102.15/17.07 (kpairp) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletonsubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletoninpowerset) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletoninpowunion) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairset2E) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairsubunion) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairinpowunion) =>
% 102.15/17.07 ((
% 102.15/17.07 (ubforcartprodlem1) =>
% 102.15/17.07 ((
% 102.15/17.07 (ubforcartprodlem2) =>
% 102.15/17.07 ((
% 102.15/17.07 (ubforcartprodlem3) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodpairin) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodmempair1) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodmempair) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionE2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionsingleton1) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionsingleton2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionsingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletonprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (ex1E1) =>
% 102.15/17.07 ((
% 102.15/17.07 (ex1I) =>
% 102.15/17.07 ((
% 102.15/17.07 (ex1I2) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletonsuniq) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjL1) =>
% 102.15/17.07 ((
% 102.15/17.07 (kfstsingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (theprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (kfstpairEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodfstin) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjL2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjL) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR11) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR12) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR1) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairequniteq) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR) =>
% 102.15/17.07 ((
% 102.15/17.07 (ksndsingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (ksndpairEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (kpairsurjEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodsndin) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodpairmemEL) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodpairmemER) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodmempaircEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodfstpairEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodsndpairEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodpairsurjEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrI) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrSub) =>
% 102.15/17.07 ((
% 102.15/17.07 (setOfPairsIsBReln) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrERa) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrEL1) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrEL2) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrER) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcImageSingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (apProp) =>
% 102.15/17.07 ((
% 102.15/17.07 (app) =>
% 102.15/17.07 ((
% 102.15/17.07 (infuncsetfunc) =>
% 102.15/17.07 ((
% 102.15/17.07 (ap2p) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcinfuncset) =>
% 102.15/17.07 ((
% 102.15/17.07 (lamProp) =>
% 102.15/17.07 ((
% 102.15/17.07 (lamp) =>
% 102.15/17.07 ((
% 102.15/17.07 (lam2p) =>
% 102.15/17.07 ((
% 102.15/17.07 (brelnall1) =>
% 102.15/17.07 ((
% 102.15/17.07 (brelnall2) =>
% 102.15/17.07 ((
% 102.15/17.07 (ex1E2) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcGraphProp1) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcGraphProp3) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcGraphProp2) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcextLem) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcGraphProp4) =>
% 102.15/17.07 ((
% 102.15/17.07 (subbreln) =>
% 102.15/17.07 ((
% 102.15/17.07 (eqbreln) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcext) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcext2) =>
% 102.15/17.07 ((
% 102.15/17.07 (ap2apEq1) =>
% 102.15/17.07 ((
% 102.15/17.07 (ap2apEq2) =>
% 102.15/17.07 ((
% 102.15/17.07 (beta1) =>
% 102.15/17.07 ((
% 102.15/17.07 (eta1) =>
% 102.15/17.07 ((
% 102.15/17.07 (lam2lamEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (beta2) =>
% 102.15/17.07 ((
% 102.15/17.07 (eta2) =>
% 102.15/17.07 ((
% 102.15/17.07 (iffalseProp1) =>
% 102.15/17.07 ((
% 102.15/17.07 (iffalseProp2) =>
% 102.15/17.07 ((
% 102.15/17.07 (iftrueProp1) =>
% 102.15/17.07 ((
% 102.15/17.07 (iftrueProp2) =>
% 102.15/17.07 ((
% 102.15/17.07 (ifSingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (ifp) =>
% 102.15/17.07 ((
% 102.15/17.07 (theeq) =>
% 102.15/17.07 ((
% 102.15/17.07 (iftrue) =>
% 102.15/17.07 ((
% 102.15/17.07 (iffalse) =>
% 102.15/17.07 ((
% 102.15/17.07 (iftrueorfalse) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (setextT) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetTI) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetTI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetTE1) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementTI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementTE1) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectTELcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectTERcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (contrasubsetT) =>
% 102.15/17.07 ((
% 102.15/17.07 (contrasubsetT1) =>
% 102.15/17.07 ((
% 102.15/17.07 (contrasubsetT2) =>
% 102.15/17.07 ((
% 102.15/17.07 (contrasubsetT3) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementE1) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementSub1) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementSub2) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementTnotintersectT) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementImpComplementIntersect) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementSubsetComplementIntersect) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementInPowersetComplementIntersect) =>
% 102.15/17.07 ((
% 102.15/17.07 (contraSubsetComplement) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementTcontraSubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionTILcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionTIRcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (inIntersectImpInUnion) =>
% 102.15/17.07 ((
% 102.15/17.07 (inIntersectImpInUnion2) =>
% 102.15/17.07 ((
% 102.15/17.07 (inIntersectImpInIntersectUnions) =>
% 102.15/17.07 ((
% 102.15/17.07 (intersectInPowersetIntersectUnions) =>
% 102.15/17.07 ((
% 102.15/17.07 (inComplementUnionImpNotIn1) =>
% 102.15/17.07 ((
% 102.15/17.07 (inComplementUnionImpInComplement1) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionTE) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionTEcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2a1) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementUnionInPowersetComplement) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2a2) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan1a) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan1b) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan1) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2a) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2b2) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2b) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule0) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule1) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule2) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule3) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule4) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_1) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_2) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_3) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_4) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_5) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1all2) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1SetBreln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (choice2fnsingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (setOfPairsIsBReln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1all1) =>
% 102.15/17.07 ((
% 102.15/17.07 (subbreln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (eqbreln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1invprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1invI) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1invE) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compI) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compE) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compEex) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionIL) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionIR) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionI) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionE) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionEcases) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionCommutes) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2Ex) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2W) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2A) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2B) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1Ex) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1Ex1) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1Equiv) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1E) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1I) =>
% 102.15/17.07 ((
% 102.15/17.07 (injFuncInInjFuncSet) =>
% 102.15/17.07 ((
% 102.15/17.07 (injFuncSetFuncIn) =>
% 102.15/17.07 ((
% 102.15/17.07 (injFuncSetFuncInj) =>
% 102.15/17.07 ((
% 102.15/17.07 (surjFuncSetFuncIn) =>
% 102.15/17.07 ((
% 102.15/17.07 (surjFuncSetFuncSurj) =>
% 102.15/17.07 ((
% 102.15/17.07 (leftInvIsSurj) =>
% 102.15/17.07 ((
% 102.15/17.07 (surjCantorThm) =>
% 102.15/17.07 ((
% 102.15/17.07 (foundation2) =>
% 102.15/17.07 ((
% 102.15/17.07 (notinself) =>
% 102.15/17.07 ((
% 102.15/17.07 (notinself2) =>
% 102.15/17.07 ((
% 102.15/17.07 (omegaSp) =>
% 102.15/17.07 ((
% 102.15/17.07 (omegaSclos) =>
% 102.15/17.07 ((
% 102.15/17.07 (peano0notS) =>
% 102.15/17.07 ((
% 102.15/17.07 (peanoSinj) =>
% 102.15/17.07 ((
% 102.15/17.07 (transitivesetOp1) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintTransitive) =>
% 102.15/17.07 ((
% 102.15/17.07 (transitivesetOp2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionTransitive) =>
% 102.15/17.07 ((
% 102.15/17.07 (ordinalMinLem1) =>
% 102.15/17.07 ((
% 102.15/17.07 (!!) @ (
% 102.15/17.07 ^[Y0 : $i]:
% 102.15/17.07 ((
% 102.15/17.07 (ordinal @
% 102.15/17.07 Y0) =>
% 102.15/17.07 ((
% 102.15/17.07 (!!) @ (
% 102.15/17.07 ^[Y1 : $i]:
% 102.15/17.07 ((
% 102.15/17.07 (!!) @ (
% 102.15/17.07 ^[Y2 : $i]:
% 102.15/17.07 ((
% 102.15/17.07 (in @
% 102.15/17.07 Y2 @
% 102.15/17.07 Y0) =>
% 102.15/17.07 ((
% 102.15/17.07 (in @
% 102.15/17.07 Y1 @
% 102.15/17.07 Y2) =>
% 102.15/17.07 (in @
% 102.15/17.07 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl397])).
% 102.15/17.07 thf(zip_derived_cl413, plain,
% 102.15/17.07 (~ (((eqinunit) =>
% 102.15/17.07 (((singletonsswitch) =>
% 102.15/17.07 (((upairsetE) =>
% 102.15/17.07 (((upairsetIL) =>
% 102.15/17.07 (((upairsetIR) =>
% 102.15/17.07 (((emptyE1) =>
% 102.15/17.07 (((vacuousDall) =>
% 102.15/17.07 (((quantDeMorgan1) =>
% 102.15/17.07 (((quantDeMorgan2) =>
% 102.15/17.07 (((quantDeMorgan3) =>
% 102.15/17.07 (((quantDeMorgan4) =>
% 102.15/17.07 (((prop2setI) =>
% 102.15/17.07 (((prop2set2propI) =>
% 102.15/17.07 (((notdexE) =>
% 102.15/17.07 (((notdallE) =>
% 102.15/17.07 (((exuI1) =>
% 102.15/17.07 (((exuI3) =>
% 102.15/17.07 (((exuI2) =>
% 102.15/17.07 (((inCongP) =>
% 102.15/17.07 (((in__Cong) =>
% 102.15/17.07 (((exuE3u) =>
% 102.15/17.07 (((exu__Cong) =>
% 102.15/17.07 (((setadjoin__Cong) =>
% 102.15/17.07 (((powerset__Cong) =>
% 102.15/17.07 (((setunion__Cong) =>
% 102.15/17.07 (((exuEu) =>
% 102.15/17.07 (((descr__Cong) =>
% 102.15/17.07 (((dsetconstr__Cong) =>
% 102.15/17.07 (((subsetI1) =>
% 102.15/17.07 (((eqimpsubset2) =>
% 102.15/17.07 ((
% 102.15/17.07 (eqimpsubset1) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetI2) =>
% 102.15/17.07 ((
% 102.15/17.07 (emptysetsubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetE) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetE2) =>
% 102.15/17.07 ((
% 102.15/17.07 (notsubsetI) =>
% 102.15/17.07 ((
% 102.15/17.07 (notequalI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (notequalI2) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetRefl) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetTrans) =>
% 102.15/17.07 ((
% 102.15/17.07 (setadjoinSub) =>
% 102.15/17.07 ((
% 102.15/17.07 (setadjoinSub2) =>
% 102.15/17.07 ((
% 102.15/17.07 (subset2powerset) =>
% 102.15/17.07 ((
% 102.15/17.07 (setextsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetemptysetimpeq) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetE1) =>
% 102.15/17.07 ((
% 102.15/17.07 (inPowerset) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetsubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (sepInPowerset) =>
% 102.15/17.07 ((
% 102.15/17.07 (sepSubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionIL) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairset2IR) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionIR) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionEcases) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionE) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionLsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionRsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectI) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset5) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectEL) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectLsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset2) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset3) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectER) =>
% 102.15/17.07 ((
% 102.15/17.07 (disjointsetsI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectRsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset4) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectSubset1) =>
% 102.15/17.07 ((
% 102.15/17.07 (bs114d) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusI) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusEL) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusER) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusSubset2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusERneg) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusELneg) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusILneg) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusIRneg) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusLsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusSubset1) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffE) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffI2) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffIneg1) =>
% 102.15/17.07 ((
% 102.15/17.07 (symdiffIneg2) =>
% 102.15/17.07 ((
% 102.15/17.07 (secondinupair) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairIL) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairIR) =>
% 102.15/17.07 ((
% 102.15/17.07 (kpairiskpair) =>
% 102.15/17.07 ((
% 102.15/17.07 (kpairp) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletonsubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletoninpowerset) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletoninpowunion) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairset2E) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairsubunion) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairinpowunion) =>
% 102.15/17.07 ((
% 102.15/17.07 (ubforcartprodlem1) =>
% 102.15/17.07 ((
% 102.15/17.07 (ubforcartprodlem2) =>
% 102.15/17.07 ((
% 102.15/17.07 (ubforcartprodlem3) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodpairin) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodmempair1) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodmempair) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionE2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionsingleton1) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionsingleton2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionsingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletonprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (ex1E1) =>
% 102.15/17.07 ((
% 102.15/17.07 (ex1I) =>
% 102.15/17.07 ((
% 102.15/17.07 (ex1I2) =>
% 102.15/17.07 ((
% 102.15/17.07 (singletonsuniq) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjL1) =>
% 102.15/17.07 ((
% 102.15/17.07 (kfstsingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (theprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (kfstpairEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodfstin) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjL2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjL) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR11) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR12) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR1) =>
% 102.15/17.07 ((
% 102.15/17.07 (upairequniteq) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setukpairinjR) =>
% 102.15/17.07 ((
% 102.15/17.07 (ksndsingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (ksndpairEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (kpairsurjEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodsndin) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodpairmemEL) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodpairmemER) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodmempaircEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodfstpairEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodsndpairEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (cartprodpairsurjEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrI) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrSub) =>
% 102.15/17.07 ((
% 102.15/17.07 (setOfPairsIsBReln) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrERa) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrEL1) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrEL2) =>
% 102.15/17.07 ((
% 102.15/17.07 (dpsetconstrER) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcImageSingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (apProp) =>
% 102.15/17.07 ((
% 102.15/17.07 (app) =>
% 102.15/17.07 ((
% 102.15/17.07 (infuncsetfunc) =>
% 102.15/17.07 ((
% 102.15/17.07 (ap2p) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcinfuncset) =>
% 102.15/17.07 ((
% 102.15/17.07 (lamProp) =>
% 102.15/17.07 ((
% 102.15/17.07 (lamp) =>
% 102.15/17.07 ((
% 102.15/17.07 (lam2p) =>
% 102.15/17.07 ((
% 102.15/17.07 (brelnall1) =>
% 102.15/17.07 ((
% 102.15/17.07 (brelnall2) =>
% 102.15/17.07 ((
% 102.15/17.07 (ex1E2) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcGraphProp1) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcGraphProp3) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcGraphProp2) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcextLem) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcGraphProp4) =>
% 102.15/17.07 ((
% 102.15/17.07 (subbreln) =>
% 102.15/17.07 ((
% 102.15/17.07 (eqbreln) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcext) =>
% 102.15/17.07 ((
% 102.15/17.07 (funcext2) =>
% 102.15/17.07 ((
% 102.15/17.07 (ap2apEq1) =>
% 102.15/17.07 ((
% 102.15/17.07 (ap2apEq2) =>
% 102.15/17.07 ((
% 102.15/17.07 (beta1) =>
% 102.15/17.07 ((
% 102.15/17.07 (eta1) =>
% 102.15/17.07 ((
% 102.15/17.07 (lam2lamEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (beta2) =>
% 102.15/17.07 ((
% 102.15/17.07 (eta2) =>
% 102.15/17.07 ((
% 102.15/17.07 (iffalseProp1) =>
% 102.15/17.07 ((
% 102.15/17.07 (iffalseProp2) =>
% 102.15/17.07 ((
% 102.15/17.07 (iftrueProp1) =>
% 102.15/17.07 ((
% 102.15/17.07 (iftrueProp2) =>
% 102.15/17.07 ((
% 102.15/17.07 (ifSingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (ifp) =>
% 102.15/17.07 ((
% 102.15/17.07 (theeq) =>
% 102.15/17.07 ((
% 102.15/17.07 (iftrue) =>
% 102.15/17.07 ((
% 102.15/17.07 (iffalse) =>
% 102.15/17.07 ((
% 102.15/17.07 (iftrueorfalse) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (setminusT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementT_lem) =>
% 102.15/17.07 ((
% 102.15/17.07 (setextT) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetTI) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetTI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetTE1) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementTI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementTE1) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectTELcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintersectTERcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (contrasubsetT) =>
% 102.15/17.07 ((
% 102.15/17.07 (contrasubsetT1) =>
% 102.15/17.07 ((
% 102.15/17.07 (contrasubsetT2) =>
% 102.15/17.07 ((
% 102.15/17.07 (contrasubsetT3) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementE1) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementSub1) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementSub2) =>
% 102.15/17.07 ((
% 102.15/17.07 (doubleComplementEq) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementTnotintersectT) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementImpComplementIntersect) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementSubsetComplementIntersect) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementInPowersetComplementIntersect) =>
% 102.15/17.07 ((
% 102.15/17.07 (contraSubsetComplement) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementTcontraSubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionTILcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionTIRcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (inIntersectImpInUnion) =>
% 102.15/17.07 ((
% 102.15/17.07 (inIntersectImpInUnion2) =>
% 102.15/17.07 ((
% 102.15/17.07 (inIntersectImpInIntersectUnions) =>
% 102.15/17.07 ((
% 102.15/17.07 (intersectInPowersetIntersectUnions) =>
% 102.15/17.07 ((
% 102.15/17.07 (inComplementUnionImpNotIn1) =>
% 102.15/17.07 ((
% 102.15/17.07 (inComplementUnionImpInComplement1) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionTE) =>
% 102.15/17.07 ((
% 102.15/17.07 (binunionTEcontra) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2a1) =>
% 102.15/17.07 ((
% 102.15/17.07 (complementUnionInPowersetComplement) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2a2) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan1a) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan1b) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan1) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2a) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2b2) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2b) =>
% 102.15/17.07 ((
% 102.15/17.07 (demorgan2) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule0) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule1) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule2) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule3) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz13rule4) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_1) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_2) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_3) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_4) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz1_5) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1all2) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1SetBreln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (choice2fnsingleton) =>
% 102.15/17.07 ((
% 102.15/17.07 (setOfPairsIsBReln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1all1) =>
% 102.15/17.07 ((
% 102.15/17.07 (subbreln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (eqbreln1) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1invprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1invI) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1invE) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compI) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compE) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1compEex) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionprop) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionIL) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionIR) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionI) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionE) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionEcases) =>
% 102.15/17.07 ((
% 102.15/17.07 (breln1unionCommutes) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2Ex) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2W) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2A) =>
% 102.15/17.07 ((
% 102.15/17.07 (woz2B) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1Ex) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1Ex1) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1Equiv) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1E) =>
% 102.15/17.07 ((
% 102.15/17.07 (image1I) =>
% 102.15/17.07 ((
% 102.15/17.07 (injFuncInInjFuncSet) =>
% 102.15/17.07 ((
% 102.15/17.07 (injFuncSetFuncIn) =>
% 102.15/17.07 ((
% 102.15/17.07 (injFuncSetFuncInj) =>
% 102.15/17.07 ((
% 102.15/17.07 (surjFuncSetFuncIn) =>
% 102.15/17.07 ((
% 102.15/17.07 (surjFuncSetFuncSurj) =>
% 102.15/17.07 ((
% 102.15/17.07 (leftInvIsSurj) =>
% 102.15/17.07 ((
% 102.15/17.07 (surjCantorThm) =>
% 102.15/17.07 ((
% 102.15/17.07 (foundation2) =>
% 102.15/17.07 ((
% 102.15/17.07 (notinself) =>
% 102.15/17.07 ((
% 102.15/17.07 (notinself2) =>
% 102.15/17.07 ((
% 102.15/17.07 (omegaSp) =>
% 102.15/17.07 ((
% 102.15/17.07 (omegaSclos) =>
% 102.15/17.07 ((
% 102.15/17.07 (peano0notS) =>
% 102.15/17.07 ((
% 102.15/17.07 (peanoSinj) =>
% 102.15/17.07 ((
% 102.15/17.07 (transitivesetOp1) =>
% 102.15/17.07 ((
% 102.15/17.07 (binintTransitive) =>
% 102.15/17.07 ((
% 102.15/17.07 (transitivesetOp2) =>
% 102.15/17.07 ((
% 102.15/17.07 (setunionTransitive) =>
% 102.15/17.07 ((
% 102.15/17.07 (ordinalMinLem1) =>
% 102.15/17.07 ((
% 102.15/17.07 (!!) @ (
% 102.15/17.07 ^[Y0 : $i]:
% 102.15/17.07 ((
% 102.15/17.07 (ordinal @
% 102.15/17.07 Y0) =>
% 102.15/17.07 ((
% 102.15/17.07 (!!) @ (
% 102.15/17.07 ^[Y1 : $i]:
% 102.15/17.07 ((
% 102.15/17.07 (!!) @ (
% 102.15/17.07 ^[Y2 : $i]:
% 102.15/17.07 ((
% 102.15/17.07 (in @
% 102.15/17.07 Y2 @
% 102.15/17.07 Y0) =>
% 102.15/17.07 ((
% 102.15/17.07 (in @
% 102.15/17.07 Y1 @
% 102.15/17.07 Y2) =>
% 102.15/17.07 (in @
% 102.15/17.07 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.15/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl406])).
% 102.15/17.07 thf(zip_derived_cl420, plain,
% 102.15/17.07 (~ (((singletonsswitch) =>
% 102.15/17.07 (((upairsetE) =>
% 102.15/17.07 (((upairsetIL) =>
% 102.15/17.07 (((upairsetIR) =>
% 102.15/17.07 (((emptyE1) =>
% 102.15/17.07 (((vacuousDall) =>
% 102.15/17.07 (((quantDeMorgan1) =>
% 102.15/17.07 (((quantDeMorgan2) =>
% 102.15/17.07 (((quantDeMorgan3) =>
% 102.15/17.07 (((quantDeMorgan4) =>
% 102.15/17.07 (((prop2setI) =>
% 102.15/17.07 (((prop2set2propI) =>
% 102.15/17.07 (((notdexE) =>
% 102.15/17.07 (((notdallE) =>
% 102.15/17.07 (((exuI1) =>
% 102.15/17.07 (((exuI3) =>
% 102.15/17.07 (((exuI2) =>
% 102.15/17.07 (((inCongP) =>
% 102.15/17.07 (((in__Cong) =>
% 102.15/17.07 (((exuE3u) =>
% 102.15/17.07 (((exu__Cong) =>
% 102.15/17.07 (((setadjoin__Cong) =>
% 102.15/17.07 (((powerset__Cong) =>
% 102.15/17.07 (((setunion__Cong) =>
% 102.15/17.07 (((exuEu) =>
% 102.15/17.07 (((descr__Cong) =>
% 102.15/17.07 (((dsetconstr__Cong) =>
% 102.15/17.07 (((subsetI1) =>
% 102.15/17.07 (((eqimpsubset2) =>
% 102.15/17.07 (((eqimpsubset1) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetI2) =>
% 102.15/17.07 ((
% 102.15/17.07 (emptysetsubset) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetE) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetE2) =>
% 102.15/17.07 ((
% 102.15/17.07 (notsubsetI) =>
% 102.15/17.07 ((
% 102.15/17.07 (notequalI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (notequalI2) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetRefl) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetTrans) =>
% 102.15/17.07 ((
% 102.15/17.07 (setadjoinSub) =>
% 102.15/17.07 ((
% 102.15/17.07 (setadjoinSub2) =>
% 102.15/17.07 ((
% 102.15/17.07 (subset2powerset) =>
% 102.15/17.07 ((
% 102.15/17.07 (setextsub) =>
% 102.15/17.07 ((
% 102.15/17.07 (subsetemptysetimpeq) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetI1) =>
% 102.15/17.07 ((
% 102.15/17.07 (powersetE1) =>
% 102.25/17.07 ((
% 102.25/17.07 (inPowerset) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetsubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (sepInPowerset) =>
% 102.25/17.07 ((
% 102.25/17.07 (sepSubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionIL) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairset2IR) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionIR) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionEcases) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionE) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionLsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionRsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectI) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset5) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectEL) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectLsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset2) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset3) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectER) =>
% 102.25/17.07 ((
% 102.25/17.07 (disjointsetsI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectRsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset4) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset1) =>
% 102.25/17.07 ((
% 102.25/17.07 (bs114d) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusI) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusEL) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusER) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusSubset2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusERneg) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusELneg) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusILneg) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusIRneg) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusLsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusSubset1) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffE) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffI2) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffIneg1) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffIneg2) =>
% 102.25/17.07 ((
% 102.25/17.07 (secondinupair) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairIL) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairIR) =>
% 102.25/17.07 ((
% 102.25/17.07 (kpairiskpair) =>
% 102.25/17.07 ((
% 102.25/17.07 (kpairp) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletonsubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletoninpowerset) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletoninpowunion) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairset2E) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairsubunion) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairinpowunion) =>
% 102.25/17.07 ((
% 102.25/17.07 (ubforcartprodlem1) =>
% 102.25/17.07 ((
% 102.25/17.07 (ubforcartprodlem2) =>
% 102.25/17.07 ((
% 102.25/17.07 (ubforcartprodlem3) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodpairin) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodmempair1) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodmempair) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionE2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionsingleton1) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionsingleton2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionsingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletonprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (ex1E1) =>
% 102.25/17.07 ((
% 102.25/17.07 (ex1I) =>
% 102.25/17.07 ((
% 102.25/17.07 (ex1I2) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletonsuniq) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjL1) =>
% 102.25/17.07 ((
% 102.25/17.07 (kfstsingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (theprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (kfstpairEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodfstin) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjL2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjL) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR11) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR12) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR1) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairequniteq) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR) =>
% 102.25/17.07 ((
% 102.25/17.07 (ksndsingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (ksndpairEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (kpairsurjEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodsndin) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodpairmemEL) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodpairmemER) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodmempaircEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodfstpairEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodsndpairEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodpairsurjEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrI) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrSub) =>
% 102.25/17.07 ((
% 102.25/17.07 (setOfPairsIsBReln) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrERa) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrEL1) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrEL2) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrER) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcImageSingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (apProp) =>
% 102.25/17.07 ((
% 102.25/17.07 (app) =>
% 102.25/17.07 ((
% 102.25/17.07 (infuncsetfunc) =>
% 102.25/17.07 ((
% 102.25/17.07 (ap2p) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcinfuncset) =>
% 102.25/17.07 ((
% 102.25/17.07 (lamProp) =>
% 102.25/17.07 ((
% 102.25/17.07 (lamp) =>
% 102.25/17.07 ((
% 102.25/17.07 (lam2p) =>
% 102.25/17.07 ((
% 102.25/17.07 (brelnall1) =>
% 102.25/17.07 ((
% 102.25/17.07 (brelnall2) =>
% 102.25/17.07 ((
% 102.25/17.07 (ex1E2) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcGraphProp1) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcGraphProp3) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcGraphProp2) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcextLem) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcGraphProp4) =>
% 102.25/17.07 ((
% 102.25/17.07 (subbreln) =>
% 102.25/17.07 ((
% 102.25/17.07 (eqbreln) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcext) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcext2) =>
% 102.25/17.07 ((
% 102.25/17.07 (ap2apEq1) =>
% 102.25/17.07 ((
% 102.25/17.07 (ap2apEq2) =>
% 102.25/17.07 ((
% 102.25/17.07 (beta1) =>
% 102.25/17.07 ((
% 102.25/17.07 (eta1) =>
% 102.25/17.07 ((
% 102.25/17.07 (lam2lamEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (beta2) =>
% 102.25/17.07 ((
% 102.25/17.07 (eta2) =>
% 102.25/17.07 ((
% 102.25/17.07 (iffalseProp1) =>
% 102.25/17.07 ((
% 102.25/17.07 (iffalseProp2) =>
% 102.25/17.07 ((
% 102.25/17.07 (iftrueProp1) =>
% 102.25/17.07 ((
% 102.25/17.07 (iftrueProp2) =>
% 102.25/17.07 ((
% 102.25/17.07 (ifSingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (ifp) =>
% 102.25/17.07 ((
% 102.25/17.07 (theeq) =>
% 102.25/17.07 ((
% 102.25/17.07 (iftrue) =>
% 102.25/17.07 ((
% 102.25/17.07 (iffalse) =>
% 102.25/17.07 ((
% 102.25/17.07 (iftrueorfalse) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (setextT) =>
% 102.25/17.07 ((
% 102.25/17.07 (subsetTI) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetTI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetTE1) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementTI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementTE1) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectTELcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectTERcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (contrasubsetT) =>
% 102.25/17.07 ((
% 102.25/17.07 (contrasubsetT1) =>
% 102.25/17.07 ((
% 102.25/17.07 (contrasubsetT2) =>
% 102.25/17.07 ((
% 102.25/17.07 (contrasubsetT3) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementE1) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementSub1) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementSub2) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementTnotintersectT) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementImpComplementIntersect) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementSubsetComplementIntersect) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementInPowersetComplementIntersect) =>
% 102.25/17.07 ((
% 102.25/17.07 (contraSubsetComplement) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementTcontraSubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionTILcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionTIRcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (inIntersectImpInUnion) =>
% 102.25/17.07 ((
% 102.25/17.07 (inIntersectImpInUnion2) =>
% 102.25/17.07 ((
% 102.25/17.07 (inIntersectImpInIntersectUnions) =>
% 102.25/17.07 ((
% 102.25/17.07 (intersectInPowersetIntersectUnions) =>
% 102.25/17.07 ((
% 102.25/17.07 (inComplementUnionImpNotIn1) =>
% 102.25/17.07 ((
% 102.25/17.07 (inComplementUnionImpInComplement1) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionTE) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionTEcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2a1) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementUnionInPowersetComplement) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2a2) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan1a) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan1b) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan1) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2a) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2b2) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2b) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule0) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule1) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule2) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule3) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule4) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_1) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_2) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_3) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_4) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_5) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1all2) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1SetBreln1) =>
% 102.25/17.07 ((
% 102.25/17.07 (choice2fnsingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (setOfPairsIsBReln1) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1all1) =>
% 102.25/17.07 ((
% 102.25/17.07 (subbreln1) =>
% 102.25/17.07 ((
% 102.25/17.07 (eqbreln1) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1invprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1invI) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1invE) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1compprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1compI) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1compE) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1compEex) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionIL) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionIR) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionI) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionE) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionEcases) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionCommutes) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz2Ex) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz2W) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz2A) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz2B) =>
% 102.25/17.07 ((
% 102.25/17.07 (image1Ex) =>
% 102.25/17.07 ((
% 102.25/17.07 (image1Ex1) =>
% 102.25/17.07 ((
% 102.25/17.07 (image1Equiv) =>
% 102.25/17.07 ((
% 102.25/17.07 (image1E) =>
% 102.25/17.07 ((
% 102.25/17.07 (image1I) =>
% 102.25/17.07 ((
% 102.25/17.07 (injFuncInInjFuncSet) =>
% 102.25/17.07 ((
% 102.25/17.07 (injFuncSetFuncIn) =>
% 102.25/17.07 ((
% 102.25/17.07 (injFuncSetFuncInj) =>
% 102.25/17.07 ((
% 102.25/17.07 (surjFuncSetFuncIn) =>
% 102.25/17.07 ((
% 102.25/17.07 (surjFuncSetFuncSurj) =>
% 102.25/17.07 ((
% 102.25/17.07 (leftInvIsSurj) =>
% 102.25/17.07 ((
% 102.25/17.07 (surjCantorThm) =>
% 102.25/17.07 ((
% 102.25/17.07 (foundation2) =>
% 102.25/17.07 ((
% 102.25/17.07 (notinself) =>
% 102.25/17.07 ((
% 102.25/17.07 (notinself2) =>
% 102.25/17.07 ((
% 102.25/17.07 (omegaSp) =>
% 102.25/17.07 ((
% 102.25/17.07 (omegaSclos) =>
% 102.25/17.07 ((
% 102.25/17.07 (peano0notS) =>
% 102.25/17.07 ((
% 102.25/17.07 (peanoSinj) =>
% 102.25/17.07 ((
% 102.25/17.07 (transitivesetOp1) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintTransitive) =>
% 102.25/17.07 ((
% 102.25/17.07 (transitivesetOp2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionTransitive) =>
% 102.25/17.07 ((
% 102.25/17.07 (ordinalMinLem1) =>
% 102.25/17.07 ((
% 102.25/17.07 (!!) @ (
% 102.25/17.07 ^[Y0 : $i]:
% 102.25/17.07 ((
% 102.25/17.07 (ordinal @
% 102.25/17.07 Y0) =>
% 102.25/17.07 ((
% 102.25/17.07 (!!) @ (
% 102.25/17.07 ^[Y1 : $i]:
% 102.25/17.07 ((
% 102.25/17.07 (!!) @ (
% 102.25/17.07 ^[Y2 : $i]:
% 102.25/17.07 ((
% 102.25/17.07 (in @
% 102.25/17.07 Y2 @
% 102.25/17.07 Y0) =>
% 102.25/17.07 ((
% 102.25/17.07 (in @
% 102.25/17.07 Y1 @
% 102.25/17.07 Y2) =>
% 102.25/17.07 (in @
% 102.25/17.07 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl413])).
% 102.25/17.07 thf(zip_derived_cl428, plain,
% 102.25/17.07 (~ (((upairsetE) =>
% 102.25/17.07 (((upairsetIL) =>
% 102.25/17.07 (((upairsetIR) =>
% 102.25/17.07 (((emptyE1) =>
% 102.25/17.07 (((vacuousDall) =>
% 102.25/17.07 (((quantDeMorgan1) =>
% 102.25/17.07 (((quantDeMorgan2) =>
% 102.25/17.07 (((quantDeMorgan3) =>
% 102.25/17.07 (((quantDeMorgan4) =>
% 102.25/17.07 (((prop2setI) =>
% 102.25/17.07 (((prop2set2propI) =>
% 102.25/17.07 (((notdexE) =>
% 102.25/17.07 (((notdallE) =>
% 102.25/17.07 (((exuI1) =>
% 102.25/17.07 (((exuI3) =>
% 102.25/17.07 (((exuI2) =>
% 102.25/17.07 (((inCongP) =>
% 102.25/17.07 (((in__Cong) =>
% 102.25/17.07 (((exuE3u) =>
% 102.25/17.07 (((exu__Cong) =>
% 102.25/17.07 (((setadjoin__Cong) =>
% 102.25/17.07 (((powerset__Cong) =>
% 102.25/17.07 (((setunion__Cong) =>
% 102.25/17.07 (((exuEu) =>
% 102.25/17.07 (((descr__Cong) =>
% 102.25/17.07 (((dsetconstr__Cong) =>
% 102.25/17.07 (((subsetI1) =>
% 102.25/17.07 (((eqimpsubset2) =>
% 102.25/17.07 (((eqimpsubset1) =>
% 102.25/17.07 (((subsetI2) =>
% 102.25/17.07 ((
% 102.25/17.07 (emptysetsubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (subsetE) =>
% 102.25/17.07 ((
% 102.25/17.07 (subsetE2) =>
% 102.25/17.07 ((
% 102.25/17.07 (notsubsetI) =>
% 102.25/17.07 ((
% 102.25/17.07 (notequalI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (notequalI2) =>
% 102.25/17.07 ((
% 102.25/17.07 (subsetRefl) =>
% 102.25/17.07 ((
% 102.25/17.07 (subsetTrans) =>
% 102.25/17.07 ((
% 102.25/17.07 (setadjoinSub) =>
% 102.25/17.07 ((
% 102.25/17.07 (setadjoinSub2) =>
% 102.25/17.07 ((
% 102.25/17.07 (subset2powerset) =>
% 102.25/17.07 ((
% 102.25/17.07 (setextsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (subsetemptysetimpeq) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetE1) =>
% 102.25/17.07 ((
% 102.25/17.07 (inPowerset) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetsubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (sepInPowerset) =>
% 102.25/17.07 ((
% 102.25/17.07 (sepSubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionIL) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairset2IR) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionIR) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionEcases) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionE) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionLsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionRsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectI) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset5) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectEL) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectLsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset2) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset3) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectER) =>
% 102.25/17.07 ((
% 102.25/17.07 (disjointsetsI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectRsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset4) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset1) =>
% 102.25/17.07 ((
% 102.25/17.07 (bs114d) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusI) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusEL) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusER) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusSubset2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusERneg) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusELneg) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusILneg) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusIRneg) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusLsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusSubset1) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffE) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffI2) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffIneg1) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffIneg2) =>
% 102.25/17.07 ((
% 102.25/17.07 (secondinupair) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairIL) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairIR) =>
% 102.25/17.07 ((
% 102.25/17.07 (kpairiskpair) =>
% 102.25/17.07 ((
% 102.25/17.07 (kpairp) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletonsubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletoninpowerset) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletoninpowunion) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairset2E) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairsubunion) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairinpowunion) =>
% 102.25/17.07 ((
% 102.25/17.07 (ubforcartprodlem1) =>
% 102.25/17.07 ((
% 102.25/17.07 (ubforcartprodlem2) =>
% 102.25/17.07 ((
% 102.25/17.07 (ubforcartprodlem3) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodpairin) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodmempair1) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodmempair) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionE2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionsingleton1) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionsingleton2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionsingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletonprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (ex1E1) =>
% 102.25/17.07 ((
% 102.25/17.07 (ex1I) =>
% 102.25/17.07 ((
% 102.25/17.07 (ex1I2) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletonsuniq) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjL1) =>
% 102.25/17.07 ((
% 102.25/17.07 (kfstsingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (theprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (kfstpairEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodfstin) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjL2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjL) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR11) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR12) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR1) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairequniteq) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR) =>
% 102.25/17.07 ((
% 102.25/17.07 (ksndsingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (ksndpairEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (kpairsurjEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodsndin) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodpairmemEL) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodpairmemER) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodmempaircEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodfstpairEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodsndpairEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodpairsurjEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrI) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrSub) =>
% 102.25/17.07 ((
% 102.25/17.07 (setOfPairsIsBReln) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrERa) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrEL1) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrEL2) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrER) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcImageSingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (apProp) =>
% 102.25/17.07 ((
% 102.25/17.07 (app) =>
% 102.25/17.07 ((
% 102.25/17.07 (infuncsetfunc) =>
% 102.25/17.07 ((
% 102.25/17.07 (ap2p) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcinfuncset) =>
% 102.25/17.07 ((
% 102.25/17.07 (lamProp) =>
% 102.25/17.07 ((
% 102.25/17.07 (lamp) =>
% 102.25/17.07 ((
% 102.25/17.07 (lam2p) =>
% 102.25/17.07 ((
% 102.25/17.07 (brelnall1) =>
% 102.25/17.07 ((
% 102.25/17.07 (brelnall2) =>
% 102.25/17.07 ((
% 102.25/17.07 (ex1E2) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcGraphProp1) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcGraphProp3) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcGraphProp2) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcextLem) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcGraphProp4) =>
% 102.25/17.07 ((
% 102.25/17.07 (subbreln) =>
% 102.25/17.07 ((
% 102.25/17.07 (eqbreln) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcext) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcext2) =>
% 102.25/17.07 ((
% 102.25/17.07 (ap2apEq1) =>
% 102.25/17.07 ((
% 102.25/17.07 (ap2apEq2) =>
% 102.25/17.07 ((
% 102.25/17.07 (beta1) =>
% 102.25/17.07 ((
% 102.25/17.07 (eta1) =>
% 102.25/17.07 ((
% 102.25/17.07 (lam2lamEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (beta2) =>
% 102.25/17.07 ((
% 102.25/17.07 (eta2) =>
% 102.25/17.07 ((
% 102.25/17.07 (iffalseProp1) =>
% 102.25/17.07 ((
% 102.25/17.07 (iffalseProp2) =>
% 102.25/17.07 ((
% 102.25/17.07 (iftrueProp1) =>
% 102.25/17.07 ((
% 102.25/17.07 (iftrueProp2) =>
% 102.25/17.07 ((
% 102.25/17.07 (ifSingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (ifp) =>
% 102.25/17.07 ((
% 102.25/17.07 (theeq) =>
% 102.25/17.07 ((
% 102.25/17.07 (iftrue) =>
% 102.25/17.07 ((
% 102.25/17.07 (iffalse) =>
% 102.25/17.07 ((
% 102.25/17.07 (iftrueorfalse) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (setextT) =>
% 102.25/17.07 ((
% 102.25/17.07 (subsetTI) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetTI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetTE1) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementTI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementTE1) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectTELcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectTERcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (contrasubsetT) =>
% 102.25/17.07 ((
% 102.25/17.07 (contrasubsetT1) =>
% 102.25/17.07 ((
% 102.25/17.07 (contrasubsetT2) =>
% 102.25/17.07 ((
% 102.25/17.07 (contrasubsetT3) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementE1) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementSub1) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementSub2) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementTnotintersectT) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementImpComplementIntersect) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementSubsetComplementIntersect) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementInPowersetComplementIntersect) =>
% 102.25/17.07 ((
% 102.25/17.07 (contraSubsetComplement) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementTcontraSubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionTILcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionTIRcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (inIntersectImpInUnion) =>
% 102.25/17.07 ((
% 102.25/17.07 (inIntersectImpInUnion2) =>
% 102.25/17.07 ((
% 102.25/17.07 (inIntersectImpInIntersectUnions) =>
% 102.25/17.07 ((
% 102.25/17.07 (intersectInPowersetIntersectUnions) =>
% 102.25/17.07 ((
% 102.25/17.07 (inComplementUnionImpNotIn1) =>
% 102.25/17.07 ((
% 102.25/17.07 (inComplementUnionImpInComplement1) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionTE) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionTEcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2a1) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementUnionInPowersetComplement) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2a2) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan1a) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan1b) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan1) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2a) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2b2) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2b) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule0) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule1) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule2) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule3) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule4) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_1) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_2) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_3) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_4) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_5) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1all2) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1SetBreln1) =>
% 102.25/17.07 ((
% 102.25/17.07 (choice2fnsingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (setOfPairsIsBReln1) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1all1) =>
% 102.25/17.07 ((
% 102.25/17.07 (subbreln1) =>
% 102.25/17.07 ((
% 102.25/17.07 (eqbreln1) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1invprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1invI) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1invE) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1compprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1compI) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1compE) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1compEex) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionIL) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionIR) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionI) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionE) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionEcases) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionCommutes) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz2Ex) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz2W) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz2A) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz2B) =>
% 102.25/17.07 ((
% 102.25/17.07 (image1Ex) =>
% 102.25/17.07 ((
% 102.25/17.07 (image1Ex1) =>
% 102.25/17.07 ((
% 102.25/17.07 (image1Equiv) =>
% 102.25/17.07 ((
% 102.25/17.07 (image1E) =>
% 102.25/17.07 ((
% 102.25/17.07 (image1I) =>
% 102.25/17.07 ((
% 102.25/17.07 (injFuncInInjFuncSet) =>
% 102.25/17.07 ((
% 102.25/17.07 (injFuncSetFuncIn) =>
% 102.25/17.07 ((
% 102.25/17.07 (injFuncSetFuncInj) =>
% 102.25/17.07 ((
% 102.25/17.07 (surjFuncSetFuncIn) =>
% 102.25/17.07 ((
% 102.25/17.07 (surjFuncSetFuncSurj) =>
% 102.25/17.07 ((
% 102.25/17.07 (leftInvIsSurj) =>
% 102.25/17.07 ((
% 102.25/17.07 (surjCantorThm) =>
% 102.25/17.07 ((
% 102.25/17.07 (foundation2) =>
% 102.25/17.07 ((
% 102.25/17.07 (notinself) =>
% 102.25/17.07 ((
% 102.25/17.07 (notinself2) =>
% 102.25/17.07 ((
% 102.25/17.07 (omegaSp) =>
% 102.25/17.07 ((
% 102.25/17.07 (omegaSclos) =>
% 102.25/17.07 ((
% 102.25/17.07 (peano0notS) =>
% 102.25/17.07 ((
% 102.25/17.07 (peanoSinj) =>
% 102.25/17.07 ((
% 102.25/17.07 (transitivesetOp1) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintTransitive) =>
% 102.25/17.07 ((
% 102.25/17.07 (transitivesetOp2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionTransitive) =>
% 102.25/17.07 ((
% 102.25/17.07 (ordinalMinLem1) =>
% 102.25/17.07 ((
% 102.25/17.07 (!!) @ (
% 102.25/17.07 ^[Y0 : $i]:
% 102.25/17.07 ((
% 102.25/17.07 (ordinal @
% 102.25/17.07 Y0) =>
% 102.25/17.07 ((
% 102.25/17.07 (!!) @ (
% 102.25/17.07 ^[Y1 : $i]:
% 102.25/17.07 ((
% 102.25/17.07 (!!) @ (
% 102.25/17.07 ^[Y2 : $i]:
% 102.25/17.07 ((
% 102.25/17.07 (in @
% 102.25/17.07 Y2 @
% 102.25/17.07 Y0) =>
% 102.25/17.07 ((
% 102.25/17.07 (in @
% 102.25/17.07 Y1 @
% 102.25/17.07 Y2) =>
% 102.25/17.07 (in @
% 102.25/17.07 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl420])).
% 102.25/17.07 thf(zip_derived_cl439, plain,
% 102.25/17.07 (~ (((upairsetIL) =>
% 102.25/17.07 (((upairsetIR) =>
% 102.25/17.07 (((emptyE1) =>
% 102.25/17.07 (((vacuousDall) =>
% 102.25/17.07 (((quantDeMorgan1) =>
% 102.25/17.07 (((quantDeMorgan2) =>
% 102.25/17.07 (((quantDeMorgan3) =>
% 102.25/17.07 (((quantDeMorgan4) =>
% 102.25/17.07 (((prop2setI) =>
% 102.25/17.07 (((prop2set2propI) =>
% 102.25/17.07 (((notdexE) =>
% 102.25/17.07 (((notdallE) =>
% 102.25/17.07 (((exuI1) =>
% 102.25/17.07 (((exuI3) =>
% 102.25/17.07 (((exuI2) =>
% 102.25/17.07 (((inCongP) =>
% 102.25/17.07 (((in__Cong) =>
% 102.25/17.07 (((exuE3u) =>
% 102.25/17.07 (((exu__Cong) =>
% 102.25/17.07 (((setadjoin__Cong) =>
% 102.25/17.07 (((powerset__Cong) =>
% 102.25/17.07 (((setunion__Cong) =>
% 102.25/17.07 (((exuEu) =>
% 102.25/17.07 (((descr__Cong) =>
% 102.25/17.07 (((dsetconstr__Cong) =>
% 102.25/17.07 (((subsetI1) =>
% 102.25/17.07 (((eqimpsubset2) =>
% 102.25/17.07 (((eqimpsubset1) =>
% 102.25/17.07 (((subsetI2) =>
% 102.25/17.07 (((emptysetsubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (subsetE) =>
% 102.25/17.07 ((
% 102.25/17.07 (subsetE2) =>
% 102.25/17.07 ((
% 102.25/17.07 (notsubsetI) =>
% 102.25/17.07 ((
% 102.25/17.07 (notequalI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (notequalI2) =>
% 102.25/17.07 ((
% 102.25/17.07 (subsetRefl) =>
% 102.25/17.07 ((
% 102.25/17.07 (subsetTrans) =>
% 102.25/17.07 ((
% 102.25/17.07 (setadjoinSub) =>
% 102.25/17.07 ((
% 102.25/17.07 (setadjoinSub2) =>
% 102.25/17.07 ((
% 102.25/17.07 (subset2powerset) =>
% 102.25/17.07 ((
% 102.25/17.07 (setextsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (subsetemptysetimpeq) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetE1) =>
% 102.25/17.07 ((
% 102.25/17.07 (inPowerset) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetsubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (sepInPowerset) =>
% 102.25/17.07 ((
% 102.25/17.07 (sepSubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionIL) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairset2IR) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionIR) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionEcases) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionE) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionLsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionRsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectI) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset5) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectEL) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectLsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset2) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset3) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectER) =>
% 102.25/17.07 ((
% 102.25/17.07 (disjointsetsI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectRsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset4) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectSubset1) =>
% 102.25/17.07 ((
% 102.25/17.07 (bs114d) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusI) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusEL) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusER) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusSubset2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusERneg) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusELneg) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusILneg) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusIRneg) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusLsub) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusSubset1) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffE) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffI2) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffIneg1) =>
% 102.25/17.07 ((
% 102.25/17.07 (symdiffIneg2) =>
% 102.25/17.07 ((
% 102.25/17.07 (secondinupair) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairIL) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairIR) =>
% 102.25/17.07 ((
% 102.25/17.07 (kpairiskpair) =>
% 102.25/17.07 ((
% 102.25/17.07 (kpairp) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletonsubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletoninpowerset) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletoninpowunion) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairset2E) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairsubunion) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairinpowunion) =>
% 102.25/17.07 ((
% 102.25/17.07 (ubforcartprodlem1) =>
% 102.25/17.07 ((
% 102.25/17.07 (ubforcartprodlem2) =>
% 102.25/17.07 ((
% 102.25/17.07 (ubforcartprodlem3) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodpairin) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodmempair1) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodmempair) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionE2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionsingleton1) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionsingleton2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setunionsingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletonprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (ex1E1) =>
% 102.25/17.07 ((
% 102.25/17.07 (ex1I) =>
% 102.25/17.07 ((
% 102.25/17.07 (ex1I2) =>
% 102.25/17.07 ((
% 102.25/17.07 (singletonsuniq) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjL1) =>
% 102.25/17.07 ((
% 102.25/17.07 (kfstsingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (theprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (kfstpairEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodfstin) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjL2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjL) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR11) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR12) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR1) =>
% 102.25/17.07 ((
% 102.25/17.07 (upairequniteq) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR2) =>
% 102.25/17.07 ((
% 102.25/17.07 (setukpairinjR) =>
% 102.25/17.07 ((
% 102.25/17.07 (ksndsingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (ksndpairEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (kpairsurjEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodsndin) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodpairmemEL) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodpairmemER) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodmempaircEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodfstpairEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodsndpairEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (cartprodpairsurjEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrI) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrSub) =>
% 102.25/17.07 ((
% 102.25/17.07 (setOfPairsIsBReln) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrERa) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrEL1) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrEL2) =>
% 102.25/17.07 ((
% 102.25/17.07 (dpsetconstrER) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcImageSingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (apProp) =>
% 102.25/17.07 ((
% 102.25/17.07 (app) =>
% 102.25/17.07 ((
% 102.25/17.07 (infuncsetfunc) =>
% 102.25/17.07 ((
% 102.25/17.07 (ap2p) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcinfuncset) =>
% 102.25/17.07 ((
% 102.25/17.07 (lamProp) =>
% 102.25/17.07 ((
% 102.25/17.07 (lamp) =>
% 102.25/17.07 ((
% 102.25/17.07 (lam2p) =>
% 102.25/17.07 ((
% 102.25/17.07 (brelnall1) =>
% 102.25/17.07 ((
% 102.25/17.07 (brelnall2) =>
% 102.25/17.07 ((
% 102.25/17.07 (ex1E2) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcGraphProp1) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcGraphProp3) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcGraphProp2) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcextLem) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcGraphProp4) =>
% 102.25/17.07 ((
% 102.25/17.07 (subbreln) =>
% 102.25/17.07 ((
% 102.25/17.07 (eqbreln) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcext) =>
% 102.25/17.07 ((
% 102.25/17.07 (funcext2) =>
% 102.25/17.07 ((
% 102.25/17.07 (ap2apEq1) =>
% 102.25/17.07 ((
% 102.25/17.07 (ap2apEq2) =>
% 102.25/17.07 ((
% 102.25/17.07 (beta1) =>
% 102.25/17.07 ((
% 102.25/17.07 (eta1) =>
% 102.25/17.07 ((
% 102.25/17.07 (lam2lamEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (beta2) =>
% 102.25/17.07 ((
% 102.25/17.07 (eta2) =>
% 102.25/17.07 ((
% 102.25/17.07 (iffalseProp1) =>
% 102.25/17.07 ((
% 102.25/17.07 (iffalseProp2) =>
% 102.25/17.07 ((
% 102.25/17.07 (iftrueProp1) =>
% 102.25/17.07 ((
% 102.25/17.07 (iftrueProp2) =>
% 102.25/17.07 ((
% 102.25/17.07 (ifSingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (ifp) =>
% 102.25/17.07 ((
% 102.25/17.07 (theeq) =>
% 102.25/17.07 ((
% 102.25/17.07 (iftrue) =>
% 102.25/17.07 ((
% 102.25/17.07 (iffalse) =>
% 102.25/17.07 ((
% 102.25/17.07 (iftrueorfalse) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (setminusT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementT_lem) =>
% 102.25/17.07 ((
% 102.25/17.07 (setextT) =>
% 102.25/17.07 ((
% 102.25/17.07 (subsetTI) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetTI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (powersetTE1) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementTI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementTE1) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectTELcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (binintersectTERcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (contrasubsetT) =>
% 102.25/17.07 ((
% 102.25/17.07 (contrasubsetT1) =>
% 102.25/17.07 ((
% 102.25/17.07 (contrasubsetT2) =>
% 102.25/17.07 ((
% 102.25/17.07 (contrasubsetT3) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementI1) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementE1) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementSub1) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementSub2) =>
% 102.25/17.07 ((
% 102.25/17.07 (doubleComplementEq) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementTnotintersectT) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementImpComplementIntersect) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementSubsetComplementIntersect) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementInPowersetComplementIntersect) =>
% 102.25/17.07 ((
% 102.25/17.07 (contraSubsetComplement) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementTcontraSubset) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionTILcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionTIRcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (inIntersectImpInUnion) =>
% 102.25/17.07 ((
% 102.25/17.07 (inIntersectImpInUnion2) =>
% 102.25/17.07 ((
% 102.25/17.07 (inIntersectImpInIntersectUnions) =>
% 102.25/17.07 ((
% 102.25/17.07 (intersectInPowersetIntersectUnions) =>
% 102.25/17.07 ((
% 102.25/17.07 (inComplementUnionImpNotIn1) =>
% 102.25/17.07 ((
% 102.25/17.07 (inComplementUnionImpInComplement1) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionTE) =>
% 102.25/17.07 ((
% 102.25/17.07 (binunionTEcontra) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2a1) =>
% 102.25/17.07 ((
% 102.25/17.07 (complementUnionInPowersetComplement) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2a2) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan1a) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan1b) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan1) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2a) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2b2) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2b) =>
% 102.25/17.07 ((
% 102.25/17.07 (demorgan2) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule0) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule1) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule2) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule3) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz13rule4) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_1) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_2) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_3) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_4) =>
% 102.25/17.07 ((
% 102.25/17.07 (woz1_5) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1all2) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1SetBreln1) =>
% 102.25/17.07 ((
% 102.25/17.07 (choice2fnsingleton) =>
% 102.25/17.07 ((
% 102.25/17.07 (setOfPairsIsBReln1) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1all1) =>
% 102.25/17.07 ((
% 102.25/17.07 (subbreln1) =>
% 102.25/17.07 ((
% 102.25/17.07 (eqbreln1) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1invprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1invI) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1invE) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1compprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1compI) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1compE) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1compEex) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionprop) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionIL) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionIR) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionI) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionE) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionEcases) =>
% 102.25/17.07 ((
% 102.25/17.07 (breln1unionCommutes) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2W) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2A) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2B) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex1) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Equiv) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1E) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1I) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncInInjFuncSet) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncInj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (leftInvIsSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjCantorThm) =>
% 102.25/17.08 ((
% 102.25/17.08 (foundation2) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself2) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSp) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSclos) =>
% 102.25/17.08 ((
% 102.25/17.08 (peano0notS) =>
% 102.25/17.08 ((
% 102.25/17.08 (peanoSinj) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (ordinalMinLem1) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y0 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (ordinal @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y1 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y2 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y2 @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @
% 102.25/17.08 Y2) =>
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
% 102.25/17.08 thf(zip_derived_cl449, plain,
% 102.25/17.08 (~ (((upairsetIR) =>
% 102.25/17.08 (((emptyE1) =>
% 102.25/17.08 (((vacuousDall) =>
% 102.25/17.08 (((quantDeMorgan1) =>
% 102.25/17.08 (((quantDeMorgan2) =>
% 102.25/17.08 (((quantDeMorgan3) =>
% 102.25/17.08 (((quantDeMorgan4) =>
% 102.25/17.08 (((prop2setI) =>
% 102.25/17.08 (((prop2set2propI) =>
% 102.25/17.08 (((notdexE) =>
% 102.25/17.08 (((notdallE) =>
% 102.25/17.08 (((exuI1) =>
% 102.25/17.08 (((exuI3) =>
% 102.25/17.08 (((exuI2) =>
% 102.25/17.08 (((inCongP) =>
% 102.25/17.08 (((in__Cong) =>
% 102.25/17.08 (((exuE3u) =>
% 102.25/17.08 (((exu__Cong) =>
% 102.25/17.08 (((setadjoin__Cong) =>
% 102.25/17.08 (((powerset__Cong) =>
% 102.25/17.08 (((setunion__Cong) =>
% 102.25/17.08 (((exuEu) =>
% 102.25/17.08 (((descr__Cong) =>
% 102.25/17.08 (((dsetconstr__Cong) =>
% 102.25/17.08 (((subsetI1) =>
% 102.25/17.08 (((eqimpsubset2) =>
% 102.25/17.08 (((eqimpsubset1) =>
% 102.25/17.08 (((subsetI2) =>
% 102.25/17.08 (((emptysetsubset) =>
% 102.25/17.08 (((subsetE) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetE2) =>
% 102.25/17.08 ((
% 102.25/17.08 (notsubsetI) =>
% 102.25/17.08 ((
% 102.25/17.08 (notequalI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (notequalI2) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetRefl) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetTrans) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub2) =>
% 102.25/17.08 ((
% 102.25/17.08 (subset2powerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (setextsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetemptysetimpeq) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (inPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetsubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepInPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepSubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairset2IR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionEcases) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionE) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectI) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset5) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset2) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset3) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectER) =>
% 102.25/17.08 ((
% 102.25/17.08 (disjointsetsI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset4) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset1) =>
% 102.25/17.08 ((
% 102.25/17.08 (bs114d) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusI) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusER) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusSubset2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusERneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusELneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusILneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusIRneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusSubset1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffE) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffI2) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffIneg1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffIneg2) =>
% 102.25/17.08 ((
% 102.25/17.08 (secondinupair) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairiskpair) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairp) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonsubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletoninpowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletoninpowunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairset2E) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairsubunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairinpowunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem3) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairin) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempair1) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempair) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionE2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton1) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1E1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1I) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1I2) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonsuniq) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL1) =>
% 102.25/17.08 ((
% 102.25/17.08 (kfstsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (theprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (kfstpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodfstin) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR11) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR12) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR1) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairequniteq) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR) =>
% 102.25/17.08 ((
% 102.25/17.08 (ksndsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (ksndpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairsurjEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodsndin) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairmemEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairmemER) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempaircEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodfstpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodsndpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairsurjEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrI) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrSub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setOfPairsIsBReln) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrERa) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrEL1) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrEL2) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrER) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcImageSingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (apProp) =>
% 102.25/17.08 ((
% 102.25/17.08 (app) =>
% 102.25/17.08 ((
% 102.25/17.08 (infuncsetfunc) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2p) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcinfuncset) =>
% 102.25/17.08 ((
% 102.25/17.08 (lamProp) =>
% 102.25/17.08 ((
% 102.25/17.08 (lamp) =>
% 102.25/17.08 ((
% 102.25/17.08 (lam2p) =>
% 102.25/17.08 ((
% 102.25/17.08 (brelnall1) =>
% 102.25/17.08 ((
% 102.25/17.08 (brelnall2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1E2) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp3) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcextLem) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp4) =>
% 102.25/17.08 ((
% 102.25/17.08 (subbreln) =>
% 102.25/17.08 ((
% 102.25/17.08 (eqbreln) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcext) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcext2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2apEq1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2apEq2) =>
% 102.25/17.08 ((
% 102.25/17.08 (beta1) =>
% 102.25/17.08 ((
% 102.25/17.08 (eta1) =>
% 102.25/17.08 ((
% 102.25/17.08 (lam2lamEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (beta2) =>
% 102.25/17.08 ((
% 102.25/17.08 (eta2) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalseProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalseProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ifSingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (ifp) =>
% 102.25/17.08 ((
% 102.25/17.08 (theeq) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrue) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalse) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueorfalse) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (setextT) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetTI) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetTI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetTE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectTELcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectTERcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT1) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT2) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT3) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementSub1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementSub2) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTnotintersectT) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementImpComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementSubsetComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementInPowersetComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (contraSubsetComplement) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTcontraSubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTILcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTIRcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInUnion) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInUnion2) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInIntersectUnions) =>
% 102.25/17.08 ((
% 102.25/17.08 (intersectInPowersetIntersectUnions) =>
% 102.25/17.08 ((
% 102.25/17.08 (inComplementUnionImpNotIn1) =>
% 102.25/17.08 ((
% 102.25/17.08 (inComplementUnionImpInComplement1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTE) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTEcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementUnionInPowersetComplement) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a2) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1a) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1b) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2b2) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2b) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule0) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule1) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule3) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule4) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_1) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_3) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_4) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_5) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1all2) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1SetBreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (choice2fnsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (setOfPairsIsBReln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1all1) =>
% 102.25/17.08 ((
% 102.25/17.08 (subbreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (eqbreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compEex) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionEcases) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionCommutes) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2W) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2A) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2B) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex1) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Equiv) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1E) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1I) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncInInjFuncSet) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncInj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (leftInvIsSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjCantorThm) =>
% 102.25/17.08 ((
% 102.25/17.08 (foundation2) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself2) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSp) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSclos) =>
% 102.25/17.08 ((
% 102.25/17.08 (peano0notS) =>
% 102.25/17.08 ((
% 102.25/17.08 (peanoSinj) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (ordinalMinLem1) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y0 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (ordinal @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y1 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y2 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y2 @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @
% 102.25/17.08 Y2) =>
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
% 102.25/17.08 thf(zip_derived_cl457, plain,
% 102.25/17.08 (~ (((emptyE1) =>
% 102.25/17.08 (((vacuousDall) =>
% 102.25/17.08 (((quantDeMorgan1) =>
% 102.25/17.08 (((quantDeMorgan2) =>
% 102.25/17.08 (((quantDeMorgan3) =>
% 102.25/17.08 (((quantDeMorgan4) =>
% 102.25/17.08 (((prop2setI) =>
% 102.25/17.08 (((prop2set2propI) =>
% 102.25/17.08 (((notdexE) =>
% 102.25/17.08 (((notdallE) =>
% 102.25/17.08 (((exuI1) =>
% 102.25/17.08 (((exuI3) =>
% 102.25/17.08 (((exuI2) =>
% 102.25/17.08 (((inCongP) =>
% 102.25/17.08 (((in__Cong) =>
% 102.25/17.08 (((exuE3u) =>
% 102.25/17.08 (((exu__Cong) =>
% 102.25/17.08 (((setadjoin__Cong) =>
% 102.25/17.08 (((powerset__Cong) =>
% 102.25/17.08 (((setunion__Cong) =>
% 102.25/17.08 (((exuEu) =>
% 102.25/17.08 (((descr__Cong) =>
% 102.25/17.08 (((dsetconstr__Cong) =>
% 102.25/17.08 (((subsetI1) =>
% 102.25/17.08 (((eqimpsubset2) =>
% 102.25/17.08 (((eqimpsubset1) =>
% 102.25/17.08 (((subsetI2) =>
% 102.25/17.08 (((emptysetsubset) =>
% 102.25/17.08 (((subsetE) =>
% 102.25/17.08 (((subsetE2) =>
% 102.25/17.08 ((
% 102.25/17.08 (notsubsetI) =>
% 102.25/17.08 ((
% 102.25/17.08 (notequalI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (notequalI2) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetRefl) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetTrans) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub2) =>
% 102.25/17.08 ((
% 102.25/17.08 (subset2powerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (setextsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetemptysetimpeq) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (inPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetsubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepInPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepSubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairset2IR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionEcases) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionE) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectI) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset5) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset2) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset3) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectER) =>
% 102.25/17.08 ((
% 102.25/17.08 (disjointsetsI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset4) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset1) =>
% 102.25/17.08 ((
% 102.25/17.08 (bs114d) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusI) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusER) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusSubset2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusERneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusELneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusILneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusIRneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusSubset1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffE) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffI2) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffIneg1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffIneg2) =>
% 102.25/17.08 ((
% 102.25/17.08 (secondinupair) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairiskpair) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairp) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonsubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletoninpowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletoninpowunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairset2E) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairsubunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairinpowunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem3) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairin) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempair1) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempair) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionE2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton1) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1E1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1I) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1I2) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonsuniq) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL1) =>
% 102.25/17.08 ((
% 102.25/17.08 (kfstsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (theprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (kfstpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodfstin) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR11) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR12) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR1) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairequniteq) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR) =>
% 102.25/17.08 ((
% 102.25/17.08 (ksndsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (ksndpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairsurjEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodsndin) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairmemEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairmemER) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempaircEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodfstpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodsndpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairsurjEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrI) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrSub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setOfPairsIsBReln) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrERa) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrEL1) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrEL2) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrER) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcImageSingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (apProp) =>
% 102.25/17.08 ((
% 102.25/17.08 (app) =>
% 102.25/17.08 ((
% 102.25/17.08 (infuncsetfunc) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2p) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcinfuncset) =>
% 102.25/17.08 ((
% 102.25/17.08 (lamProp) =>
% 102.25/17.08 ((
% 102.25/17.08 (lamp) =>
% 102.25/17.08 ((
% 102.25/17.08 (lam2p) =>
% 102.25/17.08 ((
% 102.25/17.08 (brelnall1) =>
% 102.25/17.08 ((
% 102.25/17.08 (brelnall2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1E2) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp3) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcextLem) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp4) =>
% 102.25/17.08 ((
% 102.25/17.08 (subbreln) =>
% 102.25/17.08 ((
% 102.25/17.08 (eqbreln) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcext) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcext2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2apEq1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2apEq2) =>
% 102.25/17.08 ((
% 102.25/17.08 (beta1) =>
% 102.25/17.08 ((
% 102.25/17.08 (eta1) =>
% 102.25/17.08 ((
% 102.25/17.08 (lam2lamEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (beta2) =>
% 102.25/17.08 ((
% 102.25/17.08 (eta2) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalseProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalseProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ifSingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (ifp) =>
% 102.25/17.08 ((
% 102.25/17.08 (theeq) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrue) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalse) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueorfalse) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (setextT) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetTI) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetTI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetTE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectTELcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectTERcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT1) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT2) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT3) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementSub1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementSub2) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTnotintersectT) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementImpComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementSubsetComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementInPowersetComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (contraSubsetComplement) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTcontraSubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTILcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTIRcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInUnion) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInUnion2) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInIntersectUnions) =>
% 102.25/17.08 ((
% 102.25/17.08 (intersectInPowersetIntersectUnions) =>
% 102.25/17.08 ((
% 102.25/17.08 (inComplementUnionImpNotIn1) =>
% 102.25/17.08 ((
% 102.25/17.08 (inComplementUnionImpInComplement1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTE) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTEcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementUnionInPowersetComplement) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a2) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1a) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1b) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2b2) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2b) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule0) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule1) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule3) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule4) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_1) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_3) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_4) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_5) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1all2) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1SetBreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (choice2fnsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (setOfPairsIsBReln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1all1) =>
% 102.25/17.08 ((
% 102.25/17.08 (subbreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (eqbreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compEex) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionEcases) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionCommutes) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2W) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2A) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2B) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex1) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Equiv) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1E) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1I) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncInInjFuncSet) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncInj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (leftInvIsSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjCantorThm) =>
% 102.25/17.08 ((
% 102.25/17.08 (foundation2) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself2) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSp) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSclos) =>
% 102.25/17.08 ((
% 102.25/17.08 (peano0notS) =>
% 102.25/17.08 ((
% 102.25/17.08 (peanoSinj) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (ordinalMinLem1) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y0 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (ordinal @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y1 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y2 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y2 @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @
% 102.25/17.08 Y2) =>
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
% 102.25/17.08 thf(zip_derived_cl465, plain,
% 102.25/17.08 (~ (((vacuousDall) =>
% 102.25/17.08 (((quantDeMorgan1) =>
% 102.25/17.08 (((quantDeMorgan2) =>
% 102.25/17.08 (((quantDeMorgan3) =>
% 102.25/17.08 (((quantDeMorgan4) =>
% 102.25/17.08 (((prop2setI) =>
% 102.25/17.08 (((prop2set2propI) =>
% 102.25/17.08 (((notdexE) =>
% 102.25/17.08 (((notdallE) =>
% 102.25/17.08 (((exuI1) =>
% 102.25/17.08 (((exuI3) =>
% 102.25/17.08 (((exuI2) =>
% 102.25/17.08 (((inCongP) =>
% 102.25/17.08 (((in__Cong) =>
% 102.25/17.08 (((exuE3u) =>
% 102.25/17.08 (((exu__Cong) =>
% 102.25/17.08 (((setadjoin__Cong) =>
% 102.25/17.08 (((powerset__Cong) =>
% 102.25/17.08 (((setunion__Cong) =>
% 102.25/17.08 (((exuEu) =>
% 102.25/17.08 (((descr__Cong) =>
% 102.25/17.08 (((dsetconstr__Cong) =>
% 102.25/17.08 (((subsetI1) =>
% 102.25/17.08 (((eqimpsubset2) =>
% 102.25/17.08 (((eqimpsubset1) =>
% 102.25/17.08 (((subsetI2) =>
% 102.25/17.08 (((emptysetsubset) =>
% 102.25/17.08 (((subsetE) =>
% 102.25/17.08 (((subsetE2) =>
% 102.25/17.08 (((notsubsetI) =>
% 102.25/17.08 ((
% 102.25/17.08 (notequalI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (notequalI2) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetRefl) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetTrans) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub2) =>
% 102.25/17.08 ((
% 102.25/17.08 (subset2powerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (setextsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetemptysetimpeq) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (inPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetsubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepInPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepSubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairset2IR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionEcases) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionE) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectI) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset5) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset2) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset3) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectER) =>
% 102.25/17.08 ((
% 102.25/17.08 (disjointsetsI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset4) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset1) =>
% 102.25/17.08 ((
% 102.25/17.08 (bs114d) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusI) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusER) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusSubset2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusERneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusELneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusILneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusIRneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusSubset1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffE) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffI2) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffIneg1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffIneg2) =>
% 102.25/17.08 ((
% 102.25/17.08 (secondinupair) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairiskpair) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairp) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonsubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletoninpowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletoninpowunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairset2E) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairsubunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairinpowunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem3) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairin) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempair1) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempair) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionE2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton1) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1E1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1I) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1I2) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonsuniq) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL1) =>
% 102.25/17.08 ((
% 102.25/17.08 (kfstsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (theprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (kfstpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodfstin) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR11) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR12) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR1) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairequniteq) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR) =>
% 102.25/17.08 ((
% 102.25/17.08 (ksndsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (ksndpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairsurjEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodsndin) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairmemEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairmemER) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempaircEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodfstpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodsndpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairsurjEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrI) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrSub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setOfPairsIsBReln) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrERa) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrEL1) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrEL2) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrER) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcImageSingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (apProp) =>
% 102.25/17.08 ((
% 102.25/17.08 (app) =>
% 102.25/17.08 ((
% 102.25/17.08 (infuncsetfunc) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2p) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcinfuncset) =>
% 102.25/17.08 ((
% 102.25/17.08 (lamProp) =>
% 102.25/17.08 ((
% 102.25/17.08 (lamp) =>
% 102.25/17.08 ((
% 102.25/17.08 (lam2p) =>
% 102.25/17.08 ((
% 102.25/17.08 (brelnall1) =>
% 102.25/17.08 ((
% 102.25/17.08 (brelnall2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1E2) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp3) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcextLem) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp4) =>
% 102.25/17.08 ((
% 102.25/17.08 (subbreln) =>
% 102.25/17.08 ((
% 102.25/17.08 (eqbreln) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcext) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcext2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2apEq1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2apEq2) =>
% 102.25/17.08 ((
% 102.25/17.08 (beta1) =>
% 102.25/17.08 ((
% 102.25/17.08 (eta1) =>
% 102.25/17.08 ((
% 102.25/17.08 (lam2lamEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (beta2) =>
% 102.25/17.08 ((
% 102.25/17.08 (eta2) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalseProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalseProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ifSingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (ifp) =>
% 102.25/17.08 ((
% 102.25/17.08 (theeq) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrue) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalse) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueorfalse) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (setextT) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetTI) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetTI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetTE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectTELcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectTERcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT1) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT2) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT3) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementSub1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementSub2) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTnotintersectT) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementImpComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementSubsetComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementInPowersetComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (contraSubsetComplement) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTcontraSubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTILcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTIRcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInUnion) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInUnion2) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInIntersectUnions) =>
% 102.25/17.08 ((
% 102.25/17.08 (intersectInPowersetIntersectUnions) =>
% 102.25/17.08 ((
% 102.25/17.08 (inComplementUnionImpNotIn1) =>
% 102.25/17.08 ((
% 102.25/17.08 (inComplementUnionImpInComplement1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTE) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTEcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementUnionInPowersetComplement) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a2) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1a) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1b) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2b2) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2b) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule0) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule1) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule3) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule4) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_1) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_3) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_4) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_5) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1all2) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1SetBreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (choice2fnsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (setOfPairsIsBReln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1all1) =>
% 102.25/17.08 ((
% 102.25/17.08 (subbreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (eqbreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compEex) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionEcases) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionCommutes) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2W) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2A) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2B) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex1) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Equiv) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1E) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1I) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncInInjFuncSet) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncInj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (leftInvIsSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjCantorThm) =>
% 102.25/17.08 ((
% 102.25/17.08 (foundation2) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself2) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSp) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSclos) =>
% 102.25/17.08 ((
% 102.25/17.08 (peano0notS) =>
% 102.25/17.08 ((
% 102.25/17.08 (peanoSinj) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (ordinalMinLem1) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y0 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (ordinal @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y1 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y2 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y2 @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @
% 102.25/17.08 Y2) =>
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl457])).
% 102.25/17.08 thf(zip_derived_cl471, plain,
% 102.25/17.08 (~ (((quantDeMorgan1) =>
% 102.25/17.08 (((quantDeMorgan2) =>
% 102.25/17.08 (((quantDeMorgan3) =>
% 102.25/17.08 (((quantDeMorgan4) =>
% 102.25/17.08 (((prop2setI) =>
% 102.25/17.08 (((prop2set2propI) =>
% 102.25/17.08 (((notdexE) =>
% 102.25/17.08 (((notdallE) =>
% 102.25/17.08 (((exuI1) =>
% 102.25/17.08 (((exuI3) =>
% 102.25/17.08 (((exuI2) =>
% 102.25/17.08 (((inCongP) =>
% 102.25/17.08 (((in__Cong) =>
% 102.25/17.08 (((exuE3u) =>
% 102.25/17.08 (((exu__Cong) =>
% 102.25/17.08 (((setadjoin__Cong) =>
% 102.25/17.08 (((powerset__Cong) =>
% 102.25/17.08 (((setunion__Cong) =>
% 102.25/17.08 (((exuEu) =>
% 102.25/17.08 (((descr__Cong) =>
% 102.25/17.08 (((dsetconstr__Cong) =>
% 102.25/17.08 (((subsetI1) =>
% 102.25/17.08 (((eqimpsubset2) =>
% 102.25/17.08 (((eqimpsubset1) =>
% 102.25/17.08 (((subsetI2) =>
% 102.25/17.08 (((emptysetsubset) =>
% 102.25/17.08 (((subsetE) =>
% 102.25/17.08 (((subsetE2) =>
% 102.25/17.08 (((notsubsetI) =>
% 102.25/17.08 (((notequalI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (notequalI2) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetRefl) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetTrans) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub2) =>
% 102.25/17.08 ((
% 102.25/17.08 (subset2powerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (setextsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetemptysetimpeq) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (inPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetsubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepInPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepSubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairset2IR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionEcases) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionE) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectI) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset5) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset2) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset3) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectER) =>
% 102.25/17.08 ((
% 102.25/17.08 (disjointsetsI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset4) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset1) =>
% 102.25/17.08 ((
% 102.25/17.08 (bs114d) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusI) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusER) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusSubset2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusERneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusELneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusILneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusIRneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusSubset1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffE) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffI2) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffIneg1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffIneg2) =>
% 102.25/17.08 ((
% 102.25/17.08 (secondinupair) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairiskpair) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairp) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonsubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletoninpowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletoninpowunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairset2E) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairsubunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairinpowunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem3) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairin) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempair1) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempair) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionE2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton1) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1E1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1I) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1I2) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonsuniq) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL1) =>
% 102.25/17.08 ((
% 102.25/17.08 (kfstsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (theprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (kfstpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodfstin) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR11) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR12) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR1) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairequniteq) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR) =>
% 102.25/17.08 ((
% 102.25/17.08 (ksndsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (ksndpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairsurjEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodsndin) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairmemEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairmemER) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempaircEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodfstpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodsndpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairsurjEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrI) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrSub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setOfPairsIsBReln) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrERa) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrEL1) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrEL2) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrER) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcImageSingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (apProp) =>
% 102.25/17.08 ((
% 102.25/17.08 (app) =>
% 102.25/17.08 ((
% 102.25/17.08 (infuncsetfunc) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2p) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcinfuncset) =>
% 102.25/17.08 ((
% 102.25/17.08 (lamProp) =>
% 102.25/17.08 ((
% 102.25/17.08 (lamp) =>
% 102.25/17.08 ((
% 102.25/17.08 (lam2p) =>
% 102.25/17.08 ((
% 102.25/17.08 (brelnall1) =>
% 102.25/17.08 ((
% 102.25/17.08 (brelnall2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1E2) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp3) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcextLem) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp4) =>
% 102.25/17.08 ((
% 102.25/17.08 (subbreln) =>
% 102.25/17.08 ((
% 102.25/17.08 (eqbreln) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcext) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcext2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2apEq1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2apEq2) =>
% 102.25/17.08 ((
% 102.25/17.08 (beta1) =>
% 102.25/17.08 ((
% 102.25/17.08 (eta1) =>
% 102.25/17.08 ((
% 102.25/17.08 (lam2lamEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (beta2) =>
% 102.25/17.08 ((
% 102.25/17.08 (eta2) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalseProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalseProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ifSingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (ifp) =>
% 102.25/17.08 ((
% 102.25/17.08 (theeq) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrue) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalse) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueorfalse) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (setextT) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetTI) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetTI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetTE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectTELcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectTERcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT1) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT2) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT3) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementSub1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementSub2) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTnotintersectT) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementImpComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementSubsetComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementInPowersetComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (contraSubsetComplement) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTcontraSubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTILcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTIRcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInUnion) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInUnion2) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInIntersectUnions) =>
% 102.25/17.08 ((
% 102.25/17.08 (intersectInPowersetIntersectUnions) =>
% 102.25/17.08 ((
% 102.25/17.08 (inComplementUnionImpNotIn1) =>
% 102.25/17.08 ((
% 102.25/17.08 (inComplementUnionImpInComplement1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTE) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTEcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementUnionInPowersetComplement) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a2) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1a) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1b) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2b2) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2b) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule0) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule1) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule3) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule4) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_1) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_3) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_4) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_5) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1all2) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1SetBreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (choice2fnsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (setOfPairsIsBReln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1all1) =>
% 102.25/17.08 ((
% 102.25/17.08 (subbreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (eqbreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compEex) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionEcases) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionCommutes) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2W) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2A) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2B) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex1) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Equiv) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1E) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1I) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncInInjFuncSet) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncInj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (leftInvIsSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjCantorThm) =>
% 102.25/17.08 ((
% 102.25/17.08 (foundation2) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself2) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSp) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSclos) =>
% 102.25/17.08 ((
% 102.25/17.08 (peano0notS) =>
% 102.25/17.08 ((
% 102.25/17.08 (peanoSinj) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (ordinalMinLem1) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y0 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (ordinal @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y1 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y2 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y2 @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @
% 102.25/17.08 Y2) =>
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl465])).
% 102.25/17.08 thf(zip_derived_cl478, plain,
% 102.25/17.08 (~ (((quantDeMorgan2) =>
% 102.25/17.08 (((quantDeMorgan3) =>
% 102.25/17.08 (((quantDeMorgan4) =>
% 102.25/17.08 (((prop2setI) =>
% 102.25/17.08 (((prop2set2propI) =>
% 102.25/17.08 (((notdexE) =>
% 102.25/17.08 (((notdallE) =>
% 102.25/17.08 (((exuI1) =>
% 102.25/17.08 (((exuI3) =>
% 102.25/17.08 (((exuI2) =>
% 102.25/17.08 (((inCongP) =>
% 102.25/17.08 (((in__Cong) =>
% 102.25/17.08 (((exuE3u) =>
% 102.25/17.08 (((exu__Cong) =>
% 102.25/17.08 (((setadjoin__Cong) =>
% 102.25/17.08 (((powerset__Cong) =>
% 102.25/17.08 (((setunion__Cong) =>
% 102.25/17.08 (((exuEu) =>
% 102.25/17.08 (((descr__Cong) =>
% 102.25/17.08 (((dsetconstr__Cong) =>
% 102.25/17.08 (((subsetI1) =>
% 102.25/17.08 (((eqimpsubset2) =>
% 102.25/17.08 (((eqimpsubset1) =>
% 102.25/17.08 (((subsetI2) =>
% 102.25/17.08 (((emptysetsubset) =>
% 102.25/17.08 (((subsetE) =>
% 102.25/17.08 (((subsetE2) =>
% 102.25/17.08 (((notsubsetI) =>
% 102.25/17.08 (((notequalI1) =>
% 102.25/17.08 (((notequalI2) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetRefl) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetTrans) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub2) =>
% 102.25/17.08 ((
% 102.25/17.08 (subset2powerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (setextsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetemptysetimpeq) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (inPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetsubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepInPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepSubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairset2IR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionEcases) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionE) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectI) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset5) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset2) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset3) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectER) =>
% 102.25/17.08 ((
% 102.25/17.08 (disjointsetsI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset4) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset1) =>
% 102.25/17.08 ((
% 102.25/17.08 (bs114d) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusI) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusER) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusSubset2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusERneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusELneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusILneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusIRneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusSubset1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffE) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffI2) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffIneg1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffIneg2) =>
% 102.25/17.08 ((
% 102.25/17.08 (secondinupair) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairiskpair) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairp) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonsubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletoninpowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletoninpowunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairset2E) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairsubunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairinpowunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem3) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairin) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempair1) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempair) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionE2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton1) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1E1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1I) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1I2) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonsuniq) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL1) =>
% 102.25/17.08 ((
% 102.25/17.08 (kfstsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (theprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (kfstpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodfstin) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR11) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR12) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR1) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairequniteq) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR) =>
% 102.25/17.08 ((
% 102.25/17.08 (ksndsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (ksndpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairsurjEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodsndin) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairmemEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairmemER) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempaircEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodfstpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodsndpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairsurjEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrI) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrSub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setOfPairsIsBReln) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrERa) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrEL1) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrEL2) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrER) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcImageSingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (apProp) =>
% 102.25/17.08 ((
% 102.25/17.08 (app) =>
% 102.25/17.08 ((
% 102.25/17.08 (infuncsetfunc) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2p) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcinfuncset) =>
% 102.25/17.08 ((
% 102.25/17.08 (lamProp) =>
% 102.25/17.08 ((
% 102.25/17.08 (lamp) =>
% 102.25/17.08 ((
% 102.25/17.08 (lam2p) =>
% 102.25/17.08 ((
% 102.25/17.08 (brelnall1) =>
% 102.25/17.08 ((
% 102.25/17.08 (brelnall2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1E2) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp3) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcextLem) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp4) =>
% 102.25/17.08 ((
% 102.25/17.08 (subbreln) =>
% 102.25/17.08 ((
% 102.25/17.08 (eqbreln) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcext) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcext2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2apEq1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2apEq2) =>
% 102.25/17.08 ((
% 102.25/17.08 (beta1) =>
% 102.25/17.08 ((
% 102.25/17.08 (eta1) =>
% 102.25/17.08 ((
% 102.25/17.08 (lam2lamEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (beta2) =>
% 102.25/17.08 ((
% 102.25/17.08 (eta2) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalseProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalseProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ifSingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (ifp) =>
% 102.25/17.08 ((
% 102.25/17.08 (theeq) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrue) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalse) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueorfalse) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (setextT) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetTI) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetTI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetTE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectTELcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectTERcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT1) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT2) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT3) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementSub1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementSub2) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTnotintersectT) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementImpComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementSubsetComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementInPowersetComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (contraSubsetComplement) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTcontraSubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTILcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTIRcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInUnion) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInUnion2) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInIntersectUnions) =>
% 102.25/17.08 ((
% 102.25/17.08 (intersectInPowersetIntersectUnions) =>
% 102.25/17.08 ((
% 102.25/17.08 (inComplementUnionImpNotIn1) =>
% 102.25/17.08 ((
% 102.25/17.08 (inComplementUnionImpInComplement1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTE) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTEcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementUnionInPowersetComplement) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a2) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1a) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1b) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2b2) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2b) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule0) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule1) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule3) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule4) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_1) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_3) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_4) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_5) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1all2) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1SetBreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (choice2fnsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (setOfPairsIsBReln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1all1) =>
% 102.25/17.08 ((
% 102.25/17.08 (subbreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (eqbreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compEex) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionEcases) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionCommutes) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2W) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2A) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2B) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex1) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Equiv) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1E) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1I) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncInInjFuncSet) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncInj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (leftInvIsSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjCantorThm) =>
% 102.25/17.08 ((
% 102.25/17.08 (foundation2) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself2) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSp) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSclos) =>
% 102.25/17.08 ((
% 102.25/17.08 (peano0notS) =>
% 102.25/17.08 ((
% 102.25/17.08 (peanoSinj) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (ordinalMinLem1) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y0 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (ordinal @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y1 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y2 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y2 @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @
% 102.25/17.08 Y2) =>
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl471])).
% 102.25/17.08 thf(zip_derived_cl484, plain,
% 102.25/17.08 (~ (((quantDeMorgan3) =>
% 102.25/17.08 (((quantDeMorgan4) =>
% 102.25/17.08 (((prop2setI) =>
% 102.25/17.08 (((prop2set2propI) =>
% 102.25/17.08 (((notdexE) =>
% 102.25/17.08 (((notdallE) =>
% 102.25/17.08 (((exuI1) =>
% 102.25/17.08 (((exuI3) =>
% 102.25/17.08 (((exuI2) =>
% 102.25/17.08 (((inCongP) =>
% 102.25/17.08 (((in__Cong) =>
% 102.25/17.08 (((exuE3u) =>
% 102.25/17.08 (((exu__Cong) =>
% 102.25/17.08 (((setadjoin__Cong) =>
% 102.25/17.08 (((powerset__Cong) =>
% 102.25/17.08 (((setunion__Cong) =>
% 102.25/17.08 (((exuEu) =>
% 102.25/17.08 (((descr__Cong) =>
% 102.25/17.08 (((dsetconstr__Cong) =>
% 102.25/17.08 (((subsetI1) =>
% 102.25/17.08 (((eqimpsubset2) =>
% 102.25/17.08 (((eqimpsubset1) =>
% 102.25/17.08 (((subsetI2) =>
% 102.25/17.08 (((emptysetsubset) =>
% 102.25/17.08 (((subsetE) =>
% 102.25/17.08 (((subsetE2) =>
% 102.25/17.08 (((notsubsetI) =>
% 102.25/17.08 (((notequalI1) =>
% 102.25/17.08 (((notequalI2) =>
% 102.25/17.08 (((subsetRefl) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetTrans) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub2) =>
% 102.25/17.08 ((
% 102.25/17.08 (subset2powerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (setextsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetemptysetimpeq) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (inPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetsubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepInPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepSubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairset2IR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionEcases) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionE) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectI) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset5) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset2) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset3) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectER) =>
% 102.25/17.08 ((
% 102.25/17.08 (disjointsetsI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset4) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset1) =>
% 102.25/17.08 ((
% 102.25/17.08 (bs114d) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusI) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusER) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusSubset2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusERneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusELneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusILneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusIRneg) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusSubset1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffE) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffI2) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffIneg1) =>
% 102.25/17.08 ((
% 102.25/17.08 (symdiffIneg2) =>
% 102.25/17.08 ((
% 102.25/17.08 (secondinupair) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairiskpair) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairp) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonsubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletoninpowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletoninpowunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairset2E) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairsubunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairinpowunion) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ubforcartprodlem3) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairin) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempair1) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempair) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionE2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton1) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1E1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1I) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1I2) =>
% 102.25/17.08 ((
% 102.25/17.08 (singletonsuniq) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL1) =>
% 102.25/17.08 ((
% 102.25/17.08 (kfstsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (theprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (kfstpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodfstin) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjL) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR11) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR12) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR1) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairequniteq) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setukpairinjR) =>
% 102.25/17.08 ((
% 102.25/17.08 (ksndsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (ksndpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (kpairsurjEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodsndin) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairmemEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairmemER) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodmempaircEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodfstpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodsndpairEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (cartprodpairsurjEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrI) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrSub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setOfPairsIsBReln) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrERa) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrEL1) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrEL2) =>
% 102.25/17.08 ((
% 102.25/17.08 (dpsetconstrER) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcImageSingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (apProp) =>
% 102.25/17.08 ((
% 102.25/17.08 (app) =>
% 102.25/17.08 ((
% 102.25/17.08 (infuncsetfunc) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2p) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcinfuncset) =>
% 102.25/17.08 ((
% 102.25/17.08 (lamProp) =>
% 102.25/17.08 ((
% 102.25/17.08 (lamp) =>
% 102.25/17.08 ((
% 102.25/17.08 (lam2p) =>
% 102.25/17.08 ((
% 102.25/17.08 (brelnall1) =>
% 102.25/17.08 ((
% 102.25/17.08 (brelnall2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ex1E2) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp3) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcextLem) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcGraphProp4) =>
% 102.25/17.08 ((
% 102.25/17.08 (subbreln) =>
% 102.25/17.08 ((
% 102.25/17.08 (eqbreln) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcext) =>
% 102.25/17.08 ((
% 102.25/17.08 (funcext2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2apEq1) =>
% 102.25/17.08 ((
% 102.25/17.08 (ap2apEq2) =>
% 102.25/17.08 ((
% 102.25/17.08 (beta1) =>
% 102.25/17.08 ((
% 102.25/17.08 (eta1) =>
% 102.25/17.08 ((
% 102.25/17.08 (lam2lamEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (beta2) =>
% 102.25/17.08 ((
% 102.25/17.08 (eta2) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalseProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalseProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueProp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueProp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (ifSingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (ifp) =>
% 102.25/17.08 ((
% 102.25/17.08 (theeq) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrue) =>
% 102.25/17.08 ((
% 102.25/17.08 (iffalse) =>
% 102.25/17.08 ((
% 102.25/17.08 (iftrueorfalse) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementT_lem) =>
% 102.25/17.08 ((
% 102.25/17.08 (setextT) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetTI) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetTI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetTE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectTELcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectTERcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT1) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT2) =>
% 102.25/17.08 ((
% 102.25/17.08 (contrasubsetT3) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementSub1) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementSub2) =>
% 102.25/17.08 ((
% 102.25/17.08 (doubleComplementEq) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTnotintersectT) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementImpComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementSubsetComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementInPowersetComplementIntersect) =>
% 102.25/17.08 ((
% 102.25/17.08 (contraSubsetComplement) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementTcontraSubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTILcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTIRcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInUnion) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInUnion2) =>
% 102.25/17.08 ((
% 102.25/17.08 (inIntersectImpInIntersectUnions) =>
% 102.25/17.08 ((
% 102.25/17.08 (intersectInPowersetIntersectUnions) =>
% 102.25/17.08 ((
% 102.25/17.08 (inComplementUnionImpNotIn1) =>
% 102.25/17.08 ((
% 102.25/17.08 (inComplementUnionImpInComplement1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTE) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionTEcontra) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a1) =>
% 102.25/17.08 ((
% 102.25/17.08 (complementUnionInPowersetComplement) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a2) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1a) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1b) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan1) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2a) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2b2) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2b) =>
% 102.25/17.08 ((
% 102.25/17.08 (demorgan2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule0) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule1) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule3) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz13rule4) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_1) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_2) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_3) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_4) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz1_5) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1all2) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1SetBreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (choice2fnsingleton) =>
% 102.25/17.08 ((
% 102.25/17.08 (setOfPairsIsBReln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1all1) =>
% 102.25/17.08 ((
% 102.25/17.08 (subbreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (eqbreln1) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1invE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1compEex) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionprop) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionI) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionE) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionEcases) =>
% 102.25/17.08 ((
% 102.25/17.08 (breln1unionCommutes) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2W) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2A) =>
% 102.25/17.08 ((
% 102.25/17.08 (woz2B) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Ex1) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1Equiv) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1E) =>
% 102.25/17.08 ((
% 102.25/17.08 (image1I) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncInInjFuncSet) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (injFuncSetFuncInj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncIn) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjFuncSetFuncSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (leftInvIsSurj) =>
% 102.25/17.08 ((
% 102.25/17.08 (surjCantorThm) =>
% 102.25/17.08 ((
% 102.25/17.08 (foundation2) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself) =>
% 102.25/17.08 ((
% 102.25/17.08 (notinself2) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSp) =>
% 102.25/17.08 ((
% 102.25/17.08 (omegaSclos) =>
% 102.25/17.08 ((
% 102.25/17.08 (peano0notS) =>
% 102.25/17.08 ((
% 102.25/17.08 (peanoSinj) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (transitivesetOp2) =>
% 102.25/17.08 ((
% 102.25/17.08 (setunionTransitive) =>
% 102.25/17.08 ((
% 102.25/17.08 (ordinalMinLem1) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y0 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (ordinal @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y1 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (!!) @ (
% 102.25/17.08 ^[Y2 : $i]:
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y2 @
% 102.25/17.08 Y0) =>
% 102.25/17.08 ((
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @
% 102.25/17.08 Y2) =>
% 102.25/17.08 (in @
% 102.25/17.08 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl478])).
% 102.25/17.08 thf(zip_derived_cl491, plain,
% 102.25/17.08 (~ (((quantDeMorgan4) =>
% 102.25/17.08 (((prop2setI) =>
% 102.25/17.08 (((prop2set2propI) =>
% 102.25/17.08 (((notdexE) =>
% 102.25/17.08 (((notdallE) =>
% 102.25/17.08 (((exuI1) =>
% 102.25/17.08 (((exuI3) =>
% 102.25/17.08 (((exuI2) =>
% 102.25/17.08 (((inCongP) =>
% 102.25/17.08 (((in__Cong) =>
% 102.25/17.08 (((exuE3u) =>
% 102.25/17.08 (((exu__Cong) =>
% 102.25/17.08 (((setadjoin__Cong) =>
% 102.25/17.08 (((powerset__Cong) =>
% 102.25/17.08 (((setunion__Cong) =>
% 102.25/17.08 (((exuEu) =>
% 102.25/17.08 (((descr__Cong) =>
% 102.25/17.08 (((dsetconstr__Cong) =>
% 102.25/17.08 (((subsetI1) =>
% 102.25/17.08 (((eqimpsubset2) =>
% 102.25/17.08 (((eqimpsubset1) =>
% 102.25/17.08 (((subsetI2) =>
% 102.25/17.08 (((emptysetsubset) =>
% 102.25/17.08 (((subsetE) =>
% 102.25/17.08 (((subsetE2) =>
% 102.25/17.08 (((notsubsetI) =>
% 102.25/17.08 (((notequalI1) =>
% 102.25/17.08 (((notequalI2) =>
% 102.25/17.08 (((subsetRefl) =>
% 102.25/17.08 (((subsetTrans) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub) =>
% 102.25/17.08 ((
% 102.25/17.08 (setadjoinSub2) =>
% 102.25/17.08 ((
% 102.25/17.08 (subset2powerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (setextsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (subsetemptysetimpeq) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetE1) =>
% 102.25/17.08 ((
% 102.25/17.08 (inPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (powersetsubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepInPowerset) =>
% 102.25/17.08 ((
% 102.25/17.08 (sepSubset) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIL) =>
% 102.25/17.08 ((
% 102.25/17.08 (upairset2IR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionIR) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionEcases) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionE) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binunionRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectI) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset5) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectEL) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectLsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset2) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset3) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectER) =>
% 102.25/17.08 ((
% 102.25/17.08 (disjointsetsI1) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectRsub) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset4) =>
% 102.25/17.08 ((
% 102.25/17.08 (binintersectSubset1) =>
% 102.25/17.08 ((
% 102.25/17.08 (bs114d) =>
% 102.25/17.08 ((
% 102.25/17.08 (setminusI) =>
% 102.25/17.08 ((
% 102.25/17.09 (setminusEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusER) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusERneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusELneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusILneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusIRneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffE) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI2) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg2) =>
% 102.25/17.09 ((
% 102.25/17.09 (secondinupair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairiskpair) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairp) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairset2E) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairsubunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairinpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem3) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair1) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionE2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton1) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I2) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsuniq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (theprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstin) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR11) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR12) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR1) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairequniteq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemER) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempaircEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrI) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrSub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setOfPairsIsBReln) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrERa) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrER) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcImageSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (apProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (app) =>
% 102.25/17.09 ((
% 102.25/17.09 (infuncsetfunc) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcinfuncset) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall1) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp3) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcextLem) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp4) =>
% 102.25/17.09 ((
% 102.25/17.09 (subbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (eqbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq2) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2lamEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifp) =>
% 102.25/17.09 ((
% 102.25/17.09 (theeq) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrue) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueorfalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setextT) =>
% 102.25/17.09 ((
% 102.25/17.09 (subsetTI) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTELcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTERcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT1) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT2) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT3) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementSub1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementSub2) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTnotintersectT) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementImpComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementSubsetComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementInPowersetComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (contraSubsetComplement) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTcontraSubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTILcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTIRcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInUnion) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInUnion2) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInIntersectUnions) =>
% 102.25/17.09 ((
% 102.25/17.09 (intersectInPowersetIntersectUnions) =>
% 102.25/17.09 ((
% 102.25/17.09 (inComplementUnionImpNotIn1) =>
% 102.25/17.09 ((
% 102.25/17.09 (inComplementUnionImpInComplement1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTE) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTEcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementUnionInPowersetComplement) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a2) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1a) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1b) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2b2) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2b) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule0) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule1) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule3) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule4) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_1) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_3) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_4) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_5) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1all2) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1SetBreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (choice2fnsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (setOfPairsIsBReln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1all1) =>
% 102.25/17.09 ((
% 102.25/17.09 (subbreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (eqbreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compEex) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionEcases) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionCommutes) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2Ex) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2W) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2A) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2B) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1Ex) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1Ex1) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1Equiv) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1E) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1I) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncInInjFuncSet) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncSetFuncIn) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncSetFuncInj) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjFuncSetFuncIn) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjFuncSetFuncSurj) =>
% 102.25/17.09 ((
% 102.25/17.09 (leftInvIsSurj) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjCantorThm) =>
% 102.25/17.09 ((
% 102.25/17.09 (foundation2) =>
% 102.25/17.09 ((
% 102.25/17.09 (notinself) =>
% 102.25/17.09 ((
% 102.25/17.09 (notinself2) =>
% 102.25/17.09 ((
% 102.25/17.09 (omegaSp) =>
% 102.25/17.09 ((
% 102.25/17.09 (omegaSclos) =>
% 102.25/17.09 ((
% 102.25/17.09 (peano0notS) =>
% 102.25/17.09 ((
% 102.25/17.09 (peanoSinj) =>
% 102.25/17.09 ((
% 102.25/17.09 (transitivesetOp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintTransitive) =>
% 102.25/17.09 ((
% 102.25/17.09 (transitivesetOp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionTransitive) =>
% 102.25/17.09 ((
% 102.25/17.09 (ordinalMinLem1) =>
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y0 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (ordinal @
% 102.25/17.09 Y0) =>
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y1 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y2 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (in @
% 102.25/17.09 Y2 @
% 102.25/17.09 Y0) =>
% 102.25/17.09 ((
% 102.25/17.09 (in @
% 102.25/17.09 Y1 @
% 102.25/17.09 Y2) =>
% 102.25/17.09 (in @
% 102.25/17.09 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl484])).
% 102.25/17.09 thf(zip_derived_cl501, plain,
% 102.25/17.09 (~ (((prop2setI) =>
% 102.25/17.09 (((prop2set2propI) =>
% 102.25/17.09 (((notdexE) =>
% 102.25/17.09 (((notdallE) =>
% 102.25/17.09 (((exuI1) =>
% 102.25/17.09 (((exuI3) =>
% 102.25/17.09 (((exuI2) =>
% 102.25/17.09 (((inCongP) =>
% 102.25/17.09 (((in__Cong) =>
% 102.25/17.09 (((exuE3u) =>
% 102.25/17.09 (((exu__Cong) =>
% 102.25/17.09 (((setadjoin__Cong) =>
% 102.25/17.09 (((powerset__Cong) =>
% 102.25/17.09 (((setunion__Cong) =>
% 102.25/17.09 (((exuEu) =>
% 102.25/17.09 (((descr__Cong) =>
% 102.25/17.09 (((dsetconstr__Cong) =>
% 102.25/17.09 (((subsetI1) =>
% 102.25/17.09 (((eqimpsubset2) =>
% 102.25/17.09 (((eqimpsubset1) =>
% 102.25/17.09 (((subsetI2) =>
% 102.25/17.09 (((emptysetsubset) =>
% 102.25/17.09 (((subsetE) =>
% 102.25/17.09 (((subsetE2) =>
% 102.25/17.09 (((notsubsetI) =>
% 102.25/17.09 (((notequalI1) =>
% 102.25/17.09 (((notequalI2) =>
% 102.25/17.09 (((subsetRefl) =>
% 102.25/17.09 (((subsetTrans) =>
% 102.25/17.09 (((setadjoinSub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setadjoinSub2) =>
% 102.25/17.09 ((
% 102.25/17.09 (subset2powerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (setextsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (subsetemptysetimpeq) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (inPowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetsubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (sepInPowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (sepSubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairset2IR) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionEcases) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionE) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionRsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectI) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset5) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset2) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset3) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectER) =>
% 102.25/17.09 ((
% 102.25/17.09 (disjointsetsI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectRsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset4) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset1) =>
% 102.25/17.09 ((
% 102.25/17.09 (bs114d) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusI) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusER) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusERneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusELneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusILneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusIRneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffE) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI2) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg2) =>
% 102.25/17.09 ((
% 102.25/17.09 (secondinupair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairiskpair) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairp) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairset2E) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairsubunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairinpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem3) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair1) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionE2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton1) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I2) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsuniq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (theprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstin) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR11) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR12) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR1) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairequniteq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemER) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempaircEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrI) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrSub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setOfPairsIsBReln) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrERa) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrER) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcImageSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (apProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (app) =>
% 102.25/17.09 ((
% 102.25/17.09 (infuncsetfunc) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcinfuncset) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall1) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp3) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcextLem) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp4) =>
% 102.25/17.09 ((
% 102.25/17.09 (subbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (eqbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq2) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2lamEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifp) =>
% 102.25/17.09 ((
% 102.25/17.09 (theeq) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrue) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueorfalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setextT) =>
% 102.25/17.09 ((
% 102.25/17.09 (subsetTI) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTELcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTERcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT1) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT2) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT3) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementSub1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementSub2) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTnotintersectT) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementImpComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementSubsetComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementInPowersetComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (contraSubsetComplement) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTcontraSubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTILcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTIRcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInUnion) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInUnion2) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInIntersectUnions) =>
% 102.25/17.09 ((
% 102.25/17.09 (intersectInPowersetIntersectUnions) =>
% 102.25/17.09 ((
% 102.25/17.09 (inComplementUnionImpNotIn1) =>
% 102.25/17.09 ((
% 102.25/17.09 (inComplementUnionImpInComplement1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTE) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTEcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementUnionInPowersetComplement) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a2) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1a) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1b) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2b2) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2b) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule0) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule1) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule3) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule4) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_1) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_3) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_4) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_5) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1all2) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1SetBreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (choice2fnsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (setOfPairsIsBReln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1all1) =>
% 102.25/17.09 ((
% 102.25/17.09 (subbreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (eqbreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compEex) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionEcases) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionCommutes) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2Ex) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2W) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2A) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2B) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1Ex) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1Ex1) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1Equiv) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1E) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1I) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncInInjFuncSet) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncSetFuncIn) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncSetFuncInj) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjFuncSetFuncIn) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjFuncSetFuncSurj) =>
% 102.25/17.09 ((
% 102.25/17.09 (leftInvIsSurj) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjCantorThm) =>
% 102.25/17.09 ((
% 102.25/17.09 (foundation2) =>
% 102.25/17.09 ((
% 102.25/17.09 (notinself) =>
% 102.25/17.09 ((
% 102.25/17.09 (notinself2) =>
% 102.25/17.09 ((
% 102.25/17.09 (omegaSp) =>
% 102.25/17.09 ((
% 102.25/17.09 (omegaSclos) =>
% 102.25/17.09 ((
% 102.25/17.09 (peano0notS) =>
% 102.25/17.09 ((
% 102.25/17.09 (peanoSinj) =>
% 102.25/17.09 ((
% 102.25/17.09 (transitivesetOp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintTransitive) =>
% 102.25/17.09 ((
% 102.25/17.09 (transitivesetOp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionTransitive) =>
% 102.25/17.09 ((
% 102.25/17.09 (ordinalMinLem1) =>
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y0 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (ordinal @
% 102.25/17.09 Y0) =>
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y1 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y2 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (in @
% 102.25/17.09 Y2 @
% 102.25/17.09 Y0) =>
% 102.25/17.09 ((
% 102.25/17.09 (in @
% 102.25/17.09 Y1 @
% 102.25/17.09 Y2) =>
% 102.25/17.09 (in @
% 102.25/17.09 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl491])).
% 102.25/17.09 thf(zip_derived_cl508, plain,
% 102.25/17.09 (~ (((prop2set2propI) =>
% 102.25/17.09 (((notdexE) =>
% 102.25/17.09 (((notdallE) =>
% 102.25/17.09 (((exuI1) =>
% 102.25/17.09 (((exuI3) =>
% 102.25/17.09 (((exuI2) =>
% 102.25/17.09 (((inCongP) =>
% 102.25/17.09 (((in__Cong) =>
% 102.25/17.09 (((exuE3u) =>
% 102.25/17.09 (((exu__Cong) =>
% 102.25/17.09 (((setadjoin__Cong) =>
% 102.25/17.09 (((powerset__Cong) =>
% 102.25/17.09 (((setunion__Cong) =>
% 102.25/17.09 (((exuEu) =>
% 102.25/17.09 (((descr__Cong) =>
% 102.25/17.09 (((dsetconstr__Cong) =>
% 102.25/17.09 (((subsetI1) =>
% 102.25/17.09 (((eqimpsubset2) =>
% 102.25/17.09 (((eqimpsubset1) =>
% 102.25/17.09 (((subsetI2) =>
% 102.25/17.09 (((emptysetsubset) =>
% 102.25/17.09 (((subsetE) =>
% 102.25/17.09 (((subsetE2) =>
% 102.25/17.09 (((notsubsetI) =>
% 102.25/17.09 (((notequalI1) =>
% 102.25/17.09 (((notequalI2) =>
% 102.25/17.09 (((subsetRefl) =>
% 102.25/17.09 (((subsetTrans) =>
% 102.25/17.09 (((setadjoinSub) =>
% 102.25/17.09 (((setadjoinSub2) =>
% 102.25/17.09 ((
% 102.25/17.09 (subset2powerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (setextsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (subsetemptysetimpeq) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (inPowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetsubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (sepInPowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (sepSubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairset2IR) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionEcases) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionE) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionRsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectI) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset5) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset2) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset3) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectER) =>
% 102.25/17.09 ((
% 102.25/17.09 (disjointsetsI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectRsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset4) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset1) =>
% 102.25/17.09 ((
% 102.25/17.09 (bs114d) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusI) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusER) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusERneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusELneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusILneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusIRneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffE) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI2) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg2) =>
% 102.25/17.09 ((
% 102.25/17.09 (secondinupair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairiskpair) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairp) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairset2E) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairsubunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairinpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem3) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair1) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionE2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton1) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I2) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsuniq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (theprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstin) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR11) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR12) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR1) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairequniteq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemER) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempaircEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrI) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrSub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setOfPairsIsBReln) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrERa) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrER) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcImageSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (apProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (app) =>
% 102.25/17.09 ((
% 102.25/17.09 (infuncsetfunc) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcinfuncset) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall1) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp3) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcextLem) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp4) =>
% 102.25/17.09 ((
% 102.25/17.09 (subbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (eqbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq2) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2lamEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifp) =>
% 102.25/17.09 ((
% 102.25/17.09 (theeq) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrue) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueorfalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setextT) =>
% 102.25/17.09 ((
% 102.25/17.09 (subsetTI) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTELcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTERcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT1) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT2) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT3) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementSub1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementSub2) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTnotintersectT) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementImpComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementSubsetComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementInPowersetComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (contraSubsetComplement) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTcontraSubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTILcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTIRcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInUnion) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInUnion2) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInIntersectUnions) =>
% 102.25/17.09 ((
% 102.25/17.09 (intersectInPowersetIntersectUnions) =>
% 102.25/17.09 ((
% 102.25/17.09 (inComplementUnionImpNotIn1) =>
% 102.25/17.09 ((
% 102.25/17.09 (inComplementUnionImpInComplement1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTE) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTEcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementUnionInPowersetComplement) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a2) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1a) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1b) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2b2) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2b) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule0) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule1) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule3) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule4) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_1) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_3) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_4) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_5) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1all2) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1SetBreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (choice2fnsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (setOfPairsIsBReln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1all1) =>
% 102.25/17.09 ((
% 102.25/17.09 (subbreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (eqbreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compEex) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionEcases) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionCommutes) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2Ex) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2W) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2A) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2B) =>
% 102.25/17.09 ((
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% 102.25/17.09 ((
% 102.25/17.09 (image1Ex1) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1Equiv) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1E) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1I) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncInInjFuncSet) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncSetFuncIn) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncSetFuncInj) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjFuncSetFuncIn) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjFuncSetFuncSurj) =>
% 102.25/17.09 ((
% 102.25/17.09 (leftInvIsSurj) =>
% 102.25/17.09 ((
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% 102.25/17.09 ((
% 102.25/17.09 (foundation2) =>
% 102.25/17.09 ((
% 102.25/17.09 (notinself) =>
% 102.25/17.09 ((
% 102.25/17.09 (notinself2) =>
% 102.25/17.09 ((
% 102.25/17.09 (omegaSp) =>
% 102.25/17.09 ((
% 102.25/17.09 (omegaSclos) =>
% 102.25/17.09 ((
% 102.25/17.09 (peano0notS) =>
% 102.25/17.09 ((
% 102.25/17.09 (peanoSinj) =>
% 102.25/17.09 ((
% 102.25/17.09 (transitivesetOp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintTransitive) =>
% 102.25/17.09 ((
% 102.25/17.09 (transitivesetOp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionTransitive) =>
% 102.25/17.09 ((
% 102.25/17.09 (ordinalMinLem1) =>
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y0 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (ordinal @
% 102.25/17.09 Y0) =>
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y1 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y2 : $i]:
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% 102.25/17.09 ((
% 102.25/17.09 (in @
% 102.25/17.09 Y1 @
% 102.25/17.09 Y2) =>
% 102.25/17.09 (in @
% 102.25/17.09 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl501])).
% 102.25/17.09 thf(zip_derived_cl515, plain,
% 102.25/17.09 (~ (((notdexE) =>
% 102.25/17.09 (((notdallE) =>
% 102.25/17.09 (((exuI1) =>
% 102.25/17.09 (((exuI3) =>
% 102.25/17.09 (((exuI2) =>
% 102.25/17.09 (((inCongP) =>
% 102.25/17.09 (((in__Cong) =>
% 102.25/17.09 (((exuE3u) =>
% 102.25/17.09 (((exu__Cong) =>
% 102.25/17.09 (((setadjoin__Cong) =>
% 102.25/17.09 (((powerset__Cong) =>
% 102.25/17.09 (((setunion__Cong) =>
% 102.25/17.09 (((exuEu) =>
% 102.25/17.09 (((descr__Cong) =>
% 102.25/17.09 (((dsetconstr__Cong) =>
% 102.25/17.09 (((subsetI1) =>
% 102.25/17.09 (((eqimpsubset2) =>
% 102.25/17.09 (((eqimpsubset1) =>
% 102.25/17.09 (((subsetI2) =>
% 102.25/17.09 (((emptysetsubset) =>
% 102.25/17.09 (((subsetE) =>
% 102.25/17.09 (((subsetE2) =>
% 102.25/17.09 (((notsubsetI) =>
% 102.25/17.09 (((notequalI1) =>
% 102.25/17.09 (((notequalI2) =>
% 102.25/17.09 (((subsetRefl) =>
% 102.25/17.09 (((subsetTrans) =>
% 102.25/17.09 (((setadjoinSub) =>
% 102.25/17.09 (((setadjoinSub2) =>
% 102.25/17.09 (((subset2powerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (setextsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (subsetemptysetimpeq) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (inPowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetsubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (sepInPowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (sepSubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairset2IR) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionEcases) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionE) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionRsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectI) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset5) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset2) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset3) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectER) =>
% 102.25/17.09 ((
% 102.25/17.09 (disjointsetsI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectRsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset4) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset1) =>
% 102.25/17.09 ((
% 102.25/17.09 (bs114d) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusI) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusER) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusERneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusELneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusILneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusIRneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffE) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI2) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg2) =>
% 102.25/17.09 ((
% 102.25/17.09 (secondinupair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairiskpair) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairp) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairset2E) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairsubunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairinpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem3) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair1) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionE2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton1) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I2) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsuniq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (theprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstin) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR11) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR12) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR1) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairequniteq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemER) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempaircEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrI) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrSub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setOfPairsIsBReln) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrERa) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrER) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcImageSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (apProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (app) =>
% 102.25/17.09 ((
% 102.25/17.09 (infuncsetfunc) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcinfuncset) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall1) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp3) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcextLem) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp4) =>
% 102.25/17.09 ((
% 102.25/17.09 (subbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (eqbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq2) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2lamEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifp) =>
% 102.25/17.09 ((
% 102.25/17.09 (theeq) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrue) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueorfalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setextT) =>
% 102.25/17.09 ((
% 102.25/17.09 (subsetTI) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTELcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTERcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT1) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT2) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT3) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementSub1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementSub2) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTnotintersectT) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementImpComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementSubsetComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementInPowersetComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (contraSubsetComplement) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTcontraSubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTILcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTIRcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInUnion) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInUnion2) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInIntersectUnions) =>
% 102.25/17.09 ((
% 102.25/17.09 (intersectInPowersetIntersectUnions) =>
% 102.25/17.09 ((
% 102.25/17.09 (inComplementUnionImpNotIn1) =>
% 102.25/17.09 ((
% 102.25/17.09 (inComplementUnionImpInComplement1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTE) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTEcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementUnionInPowersetComplement) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a2) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1a) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1b) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2b2) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2b) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule0) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule1) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule3) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule4) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_1) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_3) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_4) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_5) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1all2) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1SetBreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (choice2fnsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (setOfPairsIsBReln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1all1) =>
% 102.25/17.09 ((
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% 102.25/17.09 ((
% 102.25/17.09 (eqbreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compEex) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionE) =>
% 102.25/17.09 ((
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% 102.25/17.09 (breln1unionCommutes) =>
% 102.25/17.09 ((
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% 102.25/17.09 ((
% 102.25/17.09 (woz2W) =>
% 102.25/17.09 ((
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% 102.25/17.09 ((
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% 102.25/17.09 ((
% 102.25/17.09 (image1E) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1I) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncInInjFuncSet) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncSetFuncIn) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncSetFuncInj) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjFuncSetFuncIn) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjFuncSetFuncSurj) =>
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% 102.25/17.09 ((
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% 102.25/17.09 ((
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% 102.25/17.09 ((
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% 102.25/17.09 ((
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% 102.25/17.09 ((
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% 102.25/17.09 (in @
% 102.25/17.09 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl508])).
% 102.25/17.09 thf(zip_derived_cl523, plain,
% 102.25/17.09 (~ (((notdallE) =>
% 102.25/17.09 (((exuI1) =>
% 102.25/17.09 (((exuI3) =>
% 102.25/17.09 (((exuI2) =>
% 102.25/17.09 (((inCongP) =>
% 102.25/17.09 (((in__Cong) =>
% 102.25/17.09 (((exuE3u) =>
% 102.25/17.09 (((exu__Cong) =>
% 102.25/17.09 (((setadjoin__Cong) =>
% 102.25/17.09 (((powerset__Cong) =>
% 102.25/17.09 (((setunion__Cong) =>
% 102.25/17.09 (((exuEu) =>
% 102.25/17.09 (((descr__Cong) =>
% 102.25/17.09 (((dsetconstr__Cong) =>
% 102.25/17.09 (((subsetI1) =>
% 102.25/17.09 (((eqimpsubset2) =>
% 102.25/17.09 (((eqimpsubset1) =>
% 102.25/17.09 (((subsetI2) =>
% 102.25/17.09 (((emptysetsubset) =>
% 102.25/17.09 (((subsetE) =>
% 102.25/17.09 (((subsetE2) =>
% 102.25/17.09 (((notsubsetI) =>
% 102.25/17.09 (((notequalI1) =>
% 102.25/17.09 (((notequalI2) =>
% 102.25/17.09 (((subsetRefl) =>
% 102.25/17.09 (((subsetTrans) =>
% 102.25/17.09 (((setadjoinSub) =>
% 102.25/17.09 (((setadjoinSub2) =>
% 102.25/17.09 (((subset2powerset) =>
% 102.25/17.09 (((setextsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (subsetemptysetimpeq) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (inPowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetsubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (sepInPowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (sepSubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairset2IR) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionEcases) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionE) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionRsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectI) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset5) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset2) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset3) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectER) =>
% 102.25/17.09 ((
% 102.25/17.09 (disjointsetsI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectRsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset4) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset1) =>
% 102.25/17.09 ((
% 102.25/17.09 (bs114d) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusI) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusER) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusERneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusELneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusILneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusIRneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffE) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI2) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg2) =>
% 102.25/17.09 ((
% 102.25/17.09 (secondinupair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairiskpair) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairp) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairset2E) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairsubunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairinpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem3) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair1) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionE2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton1) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I2) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsuniq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (theprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstin) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR11) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR12) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR1) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairequniteq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemER) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempaircEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrI) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrSub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setOfPairsIsBReln) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrERa) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrER) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcImageSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (apProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (app) =>
% 102.25/17.09 ((
% 102.25/17.09 (infuncsetfunc) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcinfuncset) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall1) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp3) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcextLem) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp4) =>
% 102.25/17.09 ((
% 102.25/17.09 (subbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (eqbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq2) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2lamEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifp) =>
% 102.25/17.09 ((
% 102.25/17.09 (theeq) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrue) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueorfalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setextT) =>
% 102.25/17.09 ((
% 102.25/17.09 (subsetTI) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTELcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTERcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT1) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT2) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT3) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementSub1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementSub2) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTnotintersectT) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementImpComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementSubsetComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementInPowersetComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (contraSubsetComplement) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTcontraSubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTILcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTIRcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInUnion) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInUnion2) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInIntersectUnions) =>
% 102.25/17.09 ((
% 102.25/17.09 (intersectInPowersetIntersectUnions) =>
% 102.25/17.09 ((
% 102.25/17.09 (inComplementUnionImpNotIn1) =>
% 102.25/17.09 ((
% 102.25/17.09 (inComplementUnionImpInComplement1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTE) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTEcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementUnionInPowersetComplement) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a2) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1a) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1b) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2b2) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2b) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule0) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule1) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule3) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule4) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_1) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_3) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_4) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_5) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1all2) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1SetBreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (choice2fnsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (setOfPairsIsBReln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1all1) =>
% 102.25/17.09 ((
% 102.25/17.09 (subbreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (eqbreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compEex) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionEcases) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionCommutes) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2Ex) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2W) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2A) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2B) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1Ex) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1Ex1) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1Equiv) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1E) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1I) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncInInjFuncSet) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncSetFuncIn) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncSetFuncInj) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjFuncSetFuncIn) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjFuncSetFuncSurj) =>
% 102.25/17.09 ((
% 102.25/17.09 (leftInvIsSurj) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjCantorThm) =>
% 102.25/17.09 ((
% 102.25/17.09 (foundation2) =>
% 102.25/17.09 ((
% 102.25/17.09 (notinself) =>
% 102.25/17.09 ((
% 102.25/17.09 (notinself2) =>
% 102.25/17.09 ((
% 102.25/17.09 (omegaSp) =>
% 102.25/17.09 ((
% 102.25/17.09 (omegaSclos) =>
% 102.25/17.09 ((
% 102.25/17.09 (peano0notS) =>
% 102.25/17.09 ((
% 102.25/17.09 (peanoSinj) =>
% 102.25/17.09 ((
% 102.25/17.09 (transitivesetOp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintTransitive) =>
% 102.25/17.09 ((
% 102.25/17.09 (transitivesetOp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionTransitive) =>
% 102.25/17.09 ((
% 102.25/17.09 (ordinalMinLem1) =>
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y0 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (ordinal @
% 102.25/17.09 Y0) =>
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y1 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y2 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (in @
% 102.25/17.09 Y2 @
% 102.25/17.09 Y0) =>
% 102.25/17.09 ((
% 102.25/17.09 (in @
% 102.25/17.09 Y1 @
% 102.25/17.09 Y2) =>
% 102.25/17.09 (in @
% 102.25/17.09 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl515])).
% 102.25/17.09 thf(zip_derived_cl535, plain,
% 102.25/17.09 (~ (((exuI1) =>
% 102.25/17.09 (((exuI3) =>
% 102.25/17.09 (((exuI2) =>
% 102.25/17.09 (((inCongP) =>
% 102.25/17.09 (((in__Cong) =>
% 102.25/17.09 (((exuE3u) =>
% 102.25/17.09 (((exu__Cong) =>
% 102.25/17.09 (((setadjoin__Cong) =>
% 102.25/17.09 (((powerset__Cong) =>
% 102.25/17.09 (((setunion__Cong) =>
% 102.25/17.09 (((exuEu) =>
% 102.25/17.09 (((descr__Cong) =>
% 102.25/17.09 (((dsetconstr__Cong) =>
% 102.25/17.09 (((subsetI1) =>
% 102.25/17.09 (((eqimpsubset2) =>
% 102.25/17.09 (((eqimpsubset1) =>
% 102.25/17.09 (((subsetI2) =>
% 102.25/17.09 (((emptysetsubset) =>
% 102.25/17.09 (((subsetE) =>
% 102.25/17.09 (((subsetE2) =>
% 102.25/17.09 (((notsubsetI) =>
% 102.25/17.09 (((notequalI1) =>
% 102.25/17.09 (((notequalI2) =>
% 102.25/17.09 (((subsetRefl) =>
% 102.25/17.09 (((subsetTrans) =>
% 102.25/17.09 (((setadjoinSub) =>
% 102.25/17.09 (((setadjoinSub2) =>
% 102.25/17.09 (((subset2powerset) =>
% 102.25/17.09 (((setextsub) =>
% 102.25/17.09 (((subsetemptysetimpeq) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (inPowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetsubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (sepInPowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (sepSubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairset2IR) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionEcases) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionE) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionRsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectI) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset5) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset2) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset3) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectER) =>
% 102.25/17.09 ((
% 102.25/17.09 (disjointsetsI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectRsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset4) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset1) =>
% 102.25/17.09 ((
% 102.25/17.09 (bs114d) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusI) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusER) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusERneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusELneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusILneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusIRneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffE) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI2) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg2) =>
% 102.25/17.09 ((
% 102.25/17.09 (secondinupair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairiskpair) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairp) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairset2E) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairsubunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairinpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem3) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair1) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionE2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton1) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I2) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsuniq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (theprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstin) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR11) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR12) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR1) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairequniteq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemER) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempaircEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrI) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrSub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setOfPairsIsBReln) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrERa) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrER) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcImageSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (apProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (app) =>
% 102.25/17.09 ((
% 102.25/17.09 (infuncsetfunc) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcinfuncset) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall1) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp3) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcextLem) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp4) =>
% 102.25/17.09 ((
% 102.25/17.09 (subbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (eqbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq2) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2lamEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifp) =>
% 102.25/17.09 ((
% 102.25/17.09 (theeq) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrue) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueorfalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setextT) =>
% 102.25/17.09 ((
% 102.25/17.09 (subsetTI) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTELcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTERcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT1) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT2) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT3) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementSub1) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementSub2) =>
% 102.25/17.09 ((
% 102.25/17.09 (doubleComplementEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTnotintersectT) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementImpComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementSubsetComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementInPowersetComplementIntersect) =>
% 102.25/17.09 ((
% 102.25/17.09 (contraSubsetComplement) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTcontraSubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTILcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTIRcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInUnion) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInUnion2) =>
% 102.25/17.09 ((
% 102.25/17.09 (inIntersectImpInIntersectUnions) =>
% 102.25/17.09 ((
% 102.25/17.09 (intersectInPowersetIntersectUnions) =>
% 102.25/17.09 ((
% 102.25/17.09 (inComplementUnionImpNotIn1) =>
% 102.25/17.09 ((
% 102.25/17.09 (inComplementUnionImpInComplement1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTE) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionTEcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementUnionInPowersetComplement) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a2) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1a) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1b) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan1) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2a) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2b2) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2b) =>
% 102.25/17.09 ((
% 102.25/17.09 (demorgan2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule0) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule1) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule3) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz13rule4) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_1) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_2) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_3) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_4) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz1_5) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1all2) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1SetBreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (choice2fnsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (setOfPairsIsBReln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1all1) =>
% 102.25/17.09 ((
% 102.25/17.09 (subbreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (eqbreln1) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1invE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1compEex) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionI) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionE) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionEcases) =>
% 102.25/17.09 ((
% 102.25/17.09 (breln1unionCommutes) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2Ex) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2W) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2A) =>
% 102.25/17.09 ((
% 102.25/17.09 (woz2B) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1Ex) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1Ex1) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1Equiv) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1E) =>
% 102.25/17.09 ((
% 102.25/17.09 (image1I) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncInInjFuncSet) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncSetFuncIn) =>
% 102.25/17.09 ((
% 102.25/17.09 (injFuncSetFuncInj) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjFuncSetFuncIn) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjFuncSetFuncSurj) =>
% 102.25/17.09 ((
% 102.25/17.09 (leftInvIsSurj) =>
% 102.25/17.09 ((
% 102.25/17.09 (surjCantorThm) =>
% 102.25/17.09 ((
% 102.25/17.09 (foundation2) =>
% 102.25/17.09 ((
% 102.25/17.09 (notinself) =>
% 102.25/17.09 ((
% 102.25/17.09 (notinself2) =>
% 102.25/17.09 ((
% 102.25/17.09 (omegaSp) =>
% 102.25/17.09 ((
% 102.25/17.09 (omegaSclos) =>
% 102.25/17.09 ((
% 102.25/17.09 (peano0notS) =>
% 102.25/17.09 ((
% 102.25/17.09 (peanoSinj) =>
% 102.25/17.09 ((
% 102.25/17.09 (transitivesetOp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintTransitive) =>
% 102.25/17.09 ((
% 102.25/17.09 (transitivesetOp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionTransitive) =>
% 102.25/17.09 ((
% 102.25/17.09 (ordinalMinLem1) =>
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y0 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (ordinal @
% 102.25/17.09 Y0) =>
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y1 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (!!) @ (
% 102.25/17.09 ^[Y2 : $i]:
% 102.25/17.09 ((
% 102.25/17.09 (in @
% 102.25/17.09 Y2 @
% 102.25/17.09 Y0) =>
% 102.25/17.09 ((
% 102.25/17.09 (in @
% 102.25/17.09 Y1 @
% 102.25/17.09 Y2) =>
% 102.25/17.09 (in @
% 102.25/17.09 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl523])).
% 102.25/17.09 thf(zip_derived_cl550, plain,
% 102.25/17.09 (~ (((exuI3) =>
% 102.25/17.09 (((exuI2) =>
% 102.25/17.09 (((inCongP) =>
% 102.25/17.09 (((in__Cong) =>
% 102.25/17.09 (((exuE3u) =>
% 102.25/17.09 (((exu__Cong) =>
% 102.25/17.09 (((setadjoin__Cong) =>
% 102.25/17.09 (((powerset__Cong) =>
% 102.25/17.09 (((setunion__Cong) =>
% 102.25/17.09 (((exuEu) =>
% 102.25/17.09 (((descr__Cong) =>
% 102.25/17.09 (((dsetconstr__Cong) =>
% 102.25/17.09 (((subsetI1) =>
% 102.25/17.09 (((eqimpsubset2) =>
% 102.25/17.09 (((eqimpsubset1) =>
% 102.25/17.09 (((subsetI2) =>
% 102.25/17.09 (((emptysetsubset) =>
% 102.25/17.09 (((subsetE) =>
% 102.25/17.09 (((subsetE2) =>
% 102.25/17.09 (((notsubsetI) =>
% 102.25/17.09 (((notequalI1) =>
% 102.25/17.09 (((notequalI2) =>
% 102.25/17.09 (((subsetRefl) =>
% 102.25/17.09 (((subsetTrans) =>
% 102.25/17.09 (((setadjoinSub) =>
% 102.25/17.09 (((setadjoinSub2) =>
% 102.25/17.09 (((subset2powerset) =>
% 102.25/17.09 (((setextsub) =>
% 102.25/17.09 (((subsetemptysetimpeq) =>
% 102.25/17.09 (((powersetI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (inPowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetsubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (sepInPowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (sepSubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairset2IR) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionEcases) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionE) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionRsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectI) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset5) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset2) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset3) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectER) =>
% 102.25/17.09 ((
% 102.25/17.09 (disjointsetsI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectRsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset4) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectSubset1) =>
% 102.25/17.09 ((
% 102.25/17.09 (bs114d) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusI) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusER) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusERneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusELneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusILneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusIRneg) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusLsub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusSubset1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffE) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffI2) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg1) =>
% 102.25/17.09 ((
% 102.25/17.09 (symdiffIneg2) =>
% 102.25/17.09 ((
% 102.25/17.09 (secondinupair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairIR) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairiskpair) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairp) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsubset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowerset) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletoninpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairset2E) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairsubunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairinpowunion) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ubforcartprodlem3) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair1) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempair) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionE2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton1) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setunionsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1I2) =>
% 102.25/17.09 ((
% 102.25/17.09 (singletonsuniq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (theprop) =>
% 102.25/17.09 ((
% 102.25/17.09 (kfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstin) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjL) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR11) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR12) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR1) =>
% 102.25/17.09 ((
% 102.25/17.09 (upairequniteq) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR2) =>
% 102.25/17.09 ((
% 102.25/17.09 (setukpairinjR) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndsingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ksndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (kpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndin) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemEL) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairmemER) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodmempaircEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodfstpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodsndpairEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (cartprodpairsurjEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrI) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrSub) =>
% 102.25/17.09 ((
% 102.25/17.09 (setOfPairsIsBReln) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrERa) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL1) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrEL2) =>
% 102.25/17.09 ((
% 102.25/17.09 (dpsetconstrER) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcImageSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (apProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (app) =>
% 102.25/17.09 ((
% 102.25/17.09 (infuncsetfunc) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcinfuncset) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamProp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lamp) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2p) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall1) =>
% 102.25/17.09 ((
% 102.25/17.09 (brelnall2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ex1E2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp3) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcextLem) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcGraphProp4) =>
% 102.25/17.09 ((
% 102.25/17.09 (subbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (eqbreln) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext) =>
% 102.25/17.09 ((
% 102.25/17.09 (funcext2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq1) =>
% 102.25/17.09 ((
% 102.25/17.09 (ap2apEq2) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta1) =>
% 102.25/17.09 ((
% 102.25/17.09 (lam2lamEq) =>
% 102.25/17.09 ((
% 102.25/17.09 (beta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (eta2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalseProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp1) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueProp2) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifSingleton) =>
% 102.25/17.09 ((
% 102.25/17.09 (ifp) =>
% 102.25/17.09 ((
% 102.25/17.09 (theeq) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrue) =>
% 102.25/17.09 ((
% 102.25/17.09 (iffalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (iftrueorfalse) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (binunionT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setminusT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementT_lem) =>
% 102.25/17.09 ((
% 102.25/17.09 (setextT) =>
% 102.25/17.09 ((
% 102.25/17.09 (subsetTI) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (powersetTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTI1) =>
% 102.25/17.09 ((
% 102.25/17.09 (complementTE1) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTELcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (binintersectTERcontra) =>
% 102.25/17.09 ((
% 102.25/17.09 (contrasubsetT) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT1) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT2) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT3) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub2) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTnotintersectT) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementImpComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementSubsetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementInPowersetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (contraSubsetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTcontraSubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTILcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTIRcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion2) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (intersectInPowersetIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpNotIn1) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpInComplement1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTEcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementUnionInPowersetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule0) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_5) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all2) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1SetBreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (choice2fnsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (setOfPairsIsBReln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all1) =>
% 102.25/17.10 ((
% 102.25/17.10 (subbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (eqbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compEex) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionCommutes) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2W) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2A) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2B) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex1) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Equiv) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1E) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1I) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncInInjFuncSet) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncInj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (leftInvIsSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjCantorThm) =>
% 102.25/17.10 ((
% 102.25/17.10 (foundation2) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself2) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSp) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSclos) =>
% 102.25/17.10 ((
% 102.25/17.10 (peano0notS) =>
% 102.25/17.10 ((
% 102.25/17.10 (peanoSinj) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (ordinalMinLem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y0 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (ordinal @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y1 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y2 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y2 @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @
% 102.25/17.10 Y2) =>
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl535])).
% 102.25/17.10 thf(zip_derived_cl560, plain,
% 102.25/17.10 (~ (((exuI2) =>
% 102.25/17.10 (((inCongP) =>
% 102.25/17.10 (((in__Cong) =>
% 102.25/17.10 (((exuE3u) =>
% 102.25/17.10 (((exu__Cong) =>
% 102.25/17.10 (((setadjoin__Cong) =>
% 102.25/17.10 (((powerset__Cong) =>
% 102.25/17.10 (((setunion__Cong) =>
% 102.25/17.10 (((exuEu) =>
% 102.25/17.10 (((descr__Cong) =>
% 102.25/17.10 (((dsetconstr__Cong) =>
% 102.25/17.10 (((subsetI1) =>
% 102.25/17.10 (((eqimpsubset2) =>
% 102.25/17.10 (((eqimpsubset1) =>
% 102.25/17.10 (((subsetI2) =>
% 102.25/17.10 (((emptysetsubset) =>
% 102.25/17.10 (((subsetE) =>
% 102.25/17.10 (((subsetE2) =>
% 102.25/17.10 (((notsubsetI) =>
% 102.25/17.10 (((notequalI1) =>
% 102.25/17.10 (((notequalI2) =>
% 102.25/17.10 (((subsetRefl) =>
% 102.25/17.10 (((subsetTrans) =>
% 102.25/17.10 (((setadjoinSub) =>
% 102.25/17.10 (((setadjoinSub2) =>
% 102.25/17.10 (((subset2powerset) =>
% 102.25/17.10 (((setextsub) =>
% 102.25/17.10 (((subsetemptysetimpeq) =>
% 102.25/17.10 (((powersetI1) =>
% 102.25/17.10 (((powersetE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (inPowerset) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetsubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (sepInPowerset) =>
% 102.25/17.10 ((
% 102.25/17.10 (sepSubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairset2IR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectI) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset5) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset3) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectER) =>
% 102.25/17.10 ((
% 102.25/17.10 (disjointsetsI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset4) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (bs114d) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusI) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusER) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusERneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusELneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusILneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusIRneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffE) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI2) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg2) =>
% 102.25/17.10 ((
% 102.25/17.10 (secondinupair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairiskpair) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairp) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonsubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowerset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairset2E) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairsubunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairinpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem3) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairin) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair1) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionE2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton1) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1E1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1I) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1I2) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonsuniq) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL1) =>
% 102.25/17.10 ((
% 102.25/17.10 (kfstsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (theprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (kfstpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodfstin) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR11) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR12) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR1) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairequniteq) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR) =>
% 102.25/17.10 ((
% 102.25/17.10 (ksndsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (ksndpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairsurjEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodsndin) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairmemEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairmemER) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempaircEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodfstpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodsndpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairsurjEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrI) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrSub) =>
% 102.25/17.10 ((
% 102.25/17.10 (setOfPairsIsBReln) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrERa) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrEL1) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrEL2) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrER) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcImageSingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (apProp) =>
% 102.25/17.10 ((
% 102.25/17.10 (app) =>
% 102.25/17.10 ((
% 102.25/17.10 (infuncsetfunc) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2p) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcinfuncset) =>
% 102.25/17.10 ((
% 102.25/17.10 (lamProp) =>
% 102.25/17.10 ((
% 102.25/17.10 (lamp) =>
% 102.25/17.10 ((
% 102.25/17.10 (lam2p) =>
% 102.25/17.10 ((
% 102.25/17.10 (brelnall1) =>
% 102.25/17.10 ((
% 102.25/17.10 (brelnall2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1E2) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp3) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcextLem) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp4) =>
% 102.25/17.10 ((
% 102.25/17.10 (subbreln) =>
% 102.25/17.10 ((
% 102.25/17.10 (eqbreln) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcext) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcext2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2apEq1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2apEq2) =>
% 102.25/17.10 ((
% 102.25/17.10 (beta1) =>
% 102.25/17.10 ((
% 102.25/17.10 (eta1) =>
% 102.25/17.10 ((
% 102.25/17.10 (lam2lamEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (beta2) =>
% 102.25/17.10 ((
% 102.25/17.10 (eta2) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalseProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalseProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ifSingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (ifp) =>
% 102.25/17.10 ((
% 102.25/17.10 (theeq) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrue) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalse) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueorfalse) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (setextT) =>
% 102.25/17.10 ((
% 102.25/17.10 (subsetTI) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetTI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetTE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectTELcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectTERcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT1) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT2) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT3) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub2) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTnotintersectT) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementImpComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementSubsetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementInPowersetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (contraSubsetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTcontraSubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTILcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTIRcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion2) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (intersectInPowersetIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpNotIn1) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpInComplement1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTEcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementUnionInPowersetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule0) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_5) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all2) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1SetBreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (choice2fnsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (setOfPairsIsBReln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all1) =>
% 102.25/17.10 ((
% 102.25/17.10 (subbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (eqbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compEex) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionCommutes) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2W) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2A) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2B) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex1) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Equiv) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1E) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1I) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncInInjFuncSet) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncInj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (leftInvIsSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjCantorThm) =>
% 102.25/17.10 ((
% 102.25/17.10 (foundation2) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself2) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSp) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSclos) =>
% 102.25/17.10 ((
% 102.25/17.10 (peano0notS) =>
% 102.25/17.10 ((
% 102.25/17.10 (peanoSinj) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (ordinalMinLem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y0 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (ordinal @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y1 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y2 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y2 @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @
% 102.25/17.10 Y2) =>
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl550])).
% 102.25/17.10 thf(zip_derived_cl568, plain,
% 102.25/17.10 (~ (((inCongP) =>
% 102.25/17.10 (((in__Cong) =>
% 102.25/17.10 (((exuE3u) =>
% 102.25/17.10 (((exu__Cong) =>
% 102.25/17.10 (((setadjoin__Cong) =>
% 102.25/17.10 (((powerset__Cong) =>
% 102.25/17.10 (((setunion__Cong) =>
% 102.25/17.10 (((exuEu) =>
% 102.25/17.10 (((descr__Cong) =>
% 102.25/17.10 (((dsetconstr__Cong) =>
% 102.25/17.10 (((subsetI1) =>
% 102.25/17.10 (((eqimpsubset2) =>
% 102.25/17.10 (((eqimpsubset1) =>
% 102.25/17.10 (((subsetI2) =>
% 102.25/17.10 (((emptysetsubset) =>
% 102.25/17.10 (((subsetE) =>
% 102.25/17.10 (((subsetE2) =>
% 102.25/17.10 (((notsubsetI) =>
% 102.25/17.10 (((notequalI1) =>
% 102.25/17.10 (((notequalI2) =>
% 102.25/17.10 (((subsetRefl) =>
% 102.25/17.10 (((subsetTrans) =>
% 102.25/17.10 (((setadjoinSub) =>
% 102.25/17.10 (((setadjoinSub2) =>
% 102.25/17.10 (((subset2powerset) =>
% 102.25/17.10 (((setextsub) =>
% 102.25/17.10 (((subsetemptysetimpeq) =>
% 102.25/17.10 (((powersetI1) =>
% 102.25/17.10 (((powersetE1) =>
% 102.25/17.10 (((inPowerset) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetsubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (sepInPowerset) =>
% 102.25/17.10 ((
% 102.25/17.10 (sepSubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairset2IR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectI) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset5) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset3) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectER) =>
% 102.25/17.10 ((
% 102.25/17.10 (disjointsetsI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset4) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (bs114d) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusI) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusER) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusERneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusELneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusILneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusIRneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffE) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI2) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg2) =>
% 102.25/17.10 ((
% 102.25/17.10 (secondinupair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairiskpair) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairp) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonsubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowerset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairset2E) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairsubunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairinpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem3) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairin) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair1) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionE2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton1) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1E1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1I) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1I2) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonsuniq) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL1) =>
% 102.25/17.10 ((
% 102.25/17.10 (kfstsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (theprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (kfstpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodfstin) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR11) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR12) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR1) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairequniteq) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR) =>
% 102.25/17.10 ((
% 102.25/17.10 (ksndsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (ksndpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairsurjEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodsndin) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairmemEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairmemER) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempaircEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodfstpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodsndpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairsurjEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrI) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrSub) =>
% 102.25/17.10 ((
% 102.25/17.10 (setOfPairsIsBReln) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrERa) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrEL1) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrEL2) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrER) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcImageSingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (apProp) =>
% 102.25/17.10 ((
% 102.25/17.10 (app) =>
% 102.25/17.10 ((
% 102.25/17.10 (infuncsetfunc) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2p) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcinfuncset) =>
% 102.25/17.10 ((
% 102.25/17.10 (lamProp) =>
% 102.25/17.10 ((
% 102.25/17.10 (lamp) =>
% 102.25/17.10 ((
% 102.25/17.10 (lam2p) =>
% 102.25/17.10 ((
% 102.25/17.10 (brelnall1) =>
% 102.25/17.10 ((
% 102.25/17.10 (brelnall2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1E2) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp3) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcextLem) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp4) =>
% 102.25/17.10 ((
% 102.25/17.10 (subbreln) =>
% 102.25/17.10 ((
% 102.25/17.10 (eqbreln) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcext) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcext2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2apEq1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2apEq2) =>
% 102.25/17.10 ((
% 102.25/17.10 (beta1) =>
% 102.25/17.10 ((
% 102.25/17.10 (eta1) =>
% 102.25/17.10 ((
% 102.25/17.10 (lam2lamEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (beta2) =>
% 102.25/17.10 ((
% 102.25/17.10 (eta2) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalseProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalseProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ifSingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (ifp) =>
% 102.25/17.10 ((
% 102.25/17.10 (theeq) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrue) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalse) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueorfalse) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (setextT) =>
% 102.25/17.10 ((
% 102.25/17.10 (subsetTI) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetTI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetTE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectTELcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectTERcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT1) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT2) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT3) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub2) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTnotintersectT) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementImpComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementSubsetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementInPowersetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (contraSubsetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTcontraSubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTILcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTIRcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion2) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (intersectInPowersetIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpNotIn1) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpInComplement1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTEcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementUnionInPowersetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule0) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_5) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all2) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1SetBreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (choice2fnsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (setOfPairsIsBReln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all1) =>
% 102.25/17.10 ((
% 102.25/17.10 (subbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (eqbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compEex) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionCommutes) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2W) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2A) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2B) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex1) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Equiv) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1E) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1I) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncInInjFuncSet) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncInj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (leftInvIsSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjCantorThm) =>
% 102.25/17.10 ((
% 102.25/17.10 (foundation2) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself2) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSp) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSclos) =>
% 102.25/17.10 ((
% 102.25/17.10 (peano0notS) =>
% 102.25/17.10 ((
% 102.25/17.10 (peanoSinj) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (ordinalMinLem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y0 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (ordinal @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y1 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y2 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y2 @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @
% 102.25/17.10 Y2) =>
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl560])).
% 102.25/17.10 thf(zip_derived_cl578, plain,
% 102.25/17.10 (~ (((in__Cong) =>
% 102.25/17.10 (((exuE3u) =>
% 102.25/17.10 (((exu__Cong) =>
% 102.25/17.10 (((setadjoin__Cong) =>
% 102.25/17.10 (((powerset__Cong) =>
% 102.25/17.10 (((setunion__Cong) =>
% 102.25/17.10 (((exuEu) =>
% 102.25/17.10 (((descr__Cong) =>
% 102.25/17.10 (((dsetconstr__Cong) =>
% 102.25/17.10 (((subsetI1) =>
% 102.25/17.10 (((eqimpsubset2) =>
% 102.25/17.10 (((eqimpsubset1) =>
% 102.25/17.10 (((subsetI2) =>
% 102.25/17.10 (((emptysetsubset) =>
% 102.25/17.10 (((subsetE) =>
% 102.25/17.10 (((subsetE2) =>
% 102.25/17.10 (((notsubsetI) =>
% 102.25/17.10 (((notequalI1) =>
% 102.25/17.10 (((notequalI2) =>
% 102.25/17.10 (((subsetRefl) =>
% 102.25/17.10 (((subsetTrans) =>
% 102.25/17.10 (((setadjoinSub) =>
% 102.25/17.10 (((setadjoinSub2) =>
% 102.25/17.10 (((subset2powerset) =>
% 102.25/17.10 (((setextsub) =>
% 102.25/17.10 (((subsetemptysetimpeq) =>
% 102.25/17.10 (((powersetI1) =>
% 102.25/17.10 (((powersetE1) =>
% 102.25/17.10 (((inPowerset) =>
% 102.25/17.10 (((powersetsubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (sepInPowerset) =>
% 102.25/17.10 ((
% 102.25/17.10 (sepSubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairset2IR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectI) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset5) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset3) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectER) =>
% 102.25/17.10 ((
% 102.25/17.10 (disjointsetsI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset4) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (bs114d) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusI) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusER) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusERneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusELneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusILneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusIRneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffE) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI2) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg2) =>
% 102.25/17.10 ((
% 102.25/17.10 (secondinupair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairiskpair) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairp) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonsubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowerset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairset2E) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairsubunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairinpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem3) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairin) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair1) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionE2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton1) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1E1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1I) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1I2) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonsuniq) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL1) =>
% 102.25/17.10 ((
% 102.25/17.10 (kfstsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (theprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (kfstpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodfstin) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR11) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR12) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR1) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairequniteq) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR) =>
% 102.25/17.10 ((
% 102.25/17.10 (ksndsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (ksndpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairsurjEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodsndin) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairmemEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairmemER) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempaircEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodfstpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodsndpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairsurjEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrI) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrSub) =>
% 102.25/17.10 ((
% 102.25/17.10 (setOfPairsIsBReln) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrERa) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrEL1) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrEL2) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrER) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcImageSingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (apProp) =>
% 102.25/17.10 ((
% 102.25/17.10 (app) =>
% 102.25/17.10 ((
% 102.25/17.10 (infuncsetfunc) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2p) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcinfuncset) =>
% 102.25/17.10 ((
% 102.25/17.10 (lamProp) =>
% 102.25/17.10 ((
% 102.25/17.10 (lamp) =>
% 102.25/17.10 ((
% 102.25/17.10 (lam2p) =>
% 102.25/17.10 ((
% 102.25/17.10 (brelnall1) =>
% 102.25/17.10 ((
% 102.25/17.10 (brelnall2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1E2) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp3) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcextLem) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp4) =>
% 102.25/17.10 ((
% 102.25/17.10 (subbreln) =>
% 102.25/17.10 ((
% 102.25/17.10 (eqbreln) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcext) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcext2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2apEq1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2apEq2) =>
% 102.25/17.10 ((
% 102.25/17.10 (beta1) =>
% 102.25/17.10 ((
% 102.25/17.10 (eta1) =>
% 102.25/17.10 ((
% 102.25/17.10 (lam2lamEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (beta2) =>
% 102.25/17.10 ((
% 102.25/17.10 (eta2) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalseProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalseProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ifSingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (ifp) =>
% 102.25/17.10 ((
% 102.25/17.10 (theeq) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrue) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalse) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueorfalse) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (setextT) =>
% 102.25/17.10 ((
% 102.25/17.10 (subsetTI) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetTI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetTE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectTELcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectTERcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT1) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT2) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT3) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub2) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTnotintersectT) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementImpComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementSubsetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementInPowersetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (contraSubsetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTcontraSubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTILcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTIRcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion2) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (intersectInPowersetIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpNotIn1) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpInComplement1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTEcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementUnionInPowersetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule0) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_5) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all2) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1SetBreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (choice2fnsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (setOfPairsIsBReln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all1) =>
% 102.25/17.10 ((
% 102.25/17.10 (subbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (eqbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compEex) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionCommutes) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2W) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2A) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2B) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex1) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Equiv) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1E) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1I) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncInInjFuncSet) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncInj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (leftInvIsSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjCantorThm) =>
% 102.25/17.10 ((
% 102.25/17.10 (foundation2) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself2) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSp) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSclos) =>
% 102.25/17.10 ((
% 102.25/17.10 (peano0notS) =>
% 102.25/17.10 ((
% 102.25/17.10 (peanoSinj) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (ordinalMinLem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y0 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (ordinal @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y1 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y2 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y2 @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @
% 102.25/17.10 Y2) =>
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl568])).
% 102.25/17.10 thf(zip_derived_cl588, plain,
% 102.25/17.10 (~ (((exuE3u) =>
% 102.25/17.10 (((exu__Cong) =>
% 102.25/17.10 (((setadjoin__Cong) =>
% 102.25/17.10 (((powerset__Cong) =>
% 102.25/17.10 (((setunion__Cong) =>
% 102.25/17.10 (((exuEu) =>
% 102.25/17.10 (((descr__Cong) =>
% 102.25/17.10 (((dsetconstr__Cong) =>
% 102.25/17.10 (((subsetI1) =>
% 102.25/17.10 (((eqimpsubset2) =>
% 102.25/17.10 (((eqimpsubset1) =>
% 102.25/17.10 (((subsetI2) =>
% 102.25/17.10 (((emptysetsubset) =>
% 102.25/17.10 (((subsetE) =>
% 102.25/17.10 (((subsetE2) =>
% 102.25/17.10 (((notsubsetI) =>
% 102.25/17.10 (((notequalI1) =>
% 102.25/17.10 (((notequalI2) =>
% 102.25/17.10 (((subsetRefl) =>
% 102.25/17.10 (((subsetTrans) =>
% 102.25/17.10 (((setadjoinSub) =>
% 102.25/17.10 (((setadjoinSub2) =>
% 102.25/17.10 (((subset2powerset) =>
% 102.25/17.10 (((setextsub) =>
% 102.25/17.10 (((subsetemptysetimpeq) =>
% 102.25/17.10 (((powersetI1) =>
% 102.25/17.10 (((powersetE1) =>
% 102.25/17.10 (((inPowerset) =>
% 102.25/17.10 (((powersetsubset) =>
% 102.25/17.10 (((sepInPowerset) =>
% 102.25/17.10 ((
% 102.25/17.10 (sepSubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairset2IR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectI) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset5) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset3) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectER) =>
% 102.25/17.10 ((
% 102.25/17.10 (disjointsetsI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset4) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (bs114d) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusI) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusER) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusERneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusELneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusILneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusIRneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffE) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI2) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg2) =>
% 102.25/17.10 ((
% 102.25/17.10 (secondinupair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairiskpair) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairp) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonsubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowerset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairset2E) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairsubunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairinpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem3) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairin) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair1) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionE2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton1) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1E1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1I) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1I2) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonsuniq) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL1) =>
% 102.25/17.10 ((
% 102.25/17.10 (kfstsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (theprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (kfstpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodfstin) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR11) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR12) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR1) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairequniteq) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR) =>
% 102.25/17.10 ((
% 102.25/17.10 (ksndsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (ksndpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairsurjEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodsndin) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairmemEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairmemER) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempaircEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodfstpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodsndpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairsurjEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrI) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrSub) =>
% 102.25/17.10 ((
% 102.25/17.10 (setOfPairsIsBReln) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrERa) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrEL1) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrEL2) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrER) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcImageSingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (apProp) =>
% 102.25/17.10 ((
% 102.25/17.10 (app) =>
% 102.25/17.10 ((
% 102.25/17.10 (infuncsetfunc) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2p) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcinfuncset) =>
% 102.25/17.10 ((
% 102.25/17.10 (lamProp) =>
% 102.25/17.10 ((
% 102.25/17.10 (lamp) =>
% 102.25/17.10 ((
% 102.25/17.10 (lam2p) =>
% 102.25/17.10 ((
% 102.25/17.10 (brelnall1) =>
% 102.25/17.10 ((
% 102.25/17.10 (brelnall2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1E2) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp3) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcextLem) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp4) =>
% 102.25/17.10 ((
% 102.25/17.10 (subbreln) =>
% 102.25/17.10 ((
% 102.25/17.10 (eqbreln) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcext) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcext2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2apEq1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2apEq2) =>
% 102.25/17.10 ((
% 102.25/17.10 (beta1) =>
% 102.25/17.10 ((
% 102.25/17.10 (eta1) =>
% 102.25/17.10 ((
% 102.25/17.10 (lam2lamEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (beta2) =>
% 102.25/17.10 ((
% 102.25/17.10 (eta2) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalseProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalseProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ifSingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (ifp) =>
% 102.25/17.10 ((
% 102.25/17.10 (theeq) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrue) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalse) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueorfalse) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (setextT) =>
% 102.25/17.10 ((
% 102.25/17.10 (subsetTI) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetTI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetTE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectTELcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectTERcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT1) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT2) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT3) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub2) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTnotintersectT) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementImpComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementSubsetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementInPowersetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (contraSubsetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTcontraSubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTILcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTIRcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion2) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (intersectInPowersetIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpNotIn1) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpInComplement1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTEcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementUnionInPowersetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule0) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_5) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all2) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1SetBreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (choice2fnsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (setOfPairsIsBReln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all1) =>
% 102.25/17.10 ((
% 102.25/17.10 (subbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (eqbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compEex) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionCommutes) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2W) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2A) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2B) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex1) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Equiv) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1E) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1I) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncInInjFuncSet) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncInj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (leftInvIsSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjCantorThm) =>
% 102.25/17.10 ((
% 102.25/17.10 (foundation2) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself2) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSp) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSclos) =>
% 102.25/17.10 ((
% 102.25/17.10 (peano0notS) =>
% 102.25/17.10 ((
% 102.25/17.10 (peanoSinj) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (ordinalMinLem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y0 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (ordinal @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y1 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y2 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y2 @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @
% 102.25/17.10 Y2) =>
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 102.25/17.10 thf(zip_derived_cl598, plain,
% 102.25/17.10 (~ (((exu__Cong) =>
% 102.25/17.10 (((setadjoin__Cong) =>
% 102.25/17.10 (((powerset__Cong) =>
% 102.25/17.10 (((setunion__Cong) =>
% 102.25/17.10 (((exuEu) =>
% 102.25/17.10 (((descr__Cong) =>
% 102.25/17.10 (((dsetconstr__Cong) =>
% 102.25/17.10 (((subsetI1) =>
% 102.25/17.10 (((eqimpsubset2) =>
% 102.25/17.10 (((eqimpsubset1) =>
% 102.25/17.10 (((subsetI2) =>
% 102.25/17.10 (((emptysetsubset) =>
% 102.25/17.10 (((subsetE) =>
% 102.25/17.10 (((subsetE2) =>
% 102.25/17.10 (((notsubsetI) =>
% 102.25/17.10 (((notequalI1) =>
% 102.25/17.10 (((notequalI2) =>
% 102.25/17.10 (((subsetRefl) =>
% 102.25/17.10 (((subsetTrans) =>
% 102.25/17.10 (((setadjoinSub) =>
% 102.25/17.10 (((setadjoinSub2) =>
% 102.25/17.10 (((subset2powerset) =>
% 102.25/17.10 (((setextsub) =>
% 102.25/17.10 (((subsetemptysetimpeq) =>
% 102.25/17.10 (((powersetI1) =>
% 102.25/17.10 (((powersetE1) =>
% 102.25/17.10 (((inPowerset) =>
% 102.25/17.10 (((powersetsubset) =>
% 102.25/17.10 (((sepInPowerset) =>
% 102.25/17.10 (((sepSubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairset2IR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectI) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset5) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset3) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectER) =>
% 102.25/17.10 ((
% 102.25/17.10 (disjointsetsI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset4) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (bs114d) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusI) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusER) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusERneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusELneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusILneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusIRneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffE) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI2) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg2) =>
% 102.25/17.10 ((
% 102.25/17.10 (secondinupair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairiskpair) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairp) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonsubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowerset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairset2E) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairsubunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairinpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem3) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairin) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair1) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionE2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton1) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1E1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1I) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1I2) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonsuniq) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL1) =>
% 102.25/17.10 ((
% 102.25/17.10 (kfstsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (theprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (kfstpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodfstin) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR11) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR12) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR1) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairequniteq) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR) =>
% 102.25/17.10 ((
% 102.25/17.10 (ksndsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (ksndpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairsurjEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodsndin) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairmemEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairmemER) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempaircEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodfstpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodsndpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairsurjEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrI) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrSub) =>
% 102.25/17.10 ((
% 102.25/17.10 (setOfPairsIsBReln) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrERa) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrEL1) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrEL2) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrER) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcImageSingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (apProp) =>
% 102.25/17.10 ((
% 102.25/17.10 (app) =>
% 102.25/17.10 ((
% 102.25/17.10 (infuncsetfunc) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2p) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcinfuncset) =>
% 102.25/17.10 ((
% 102.25/17.10 (lamProp) =>
% 102.25/17.10 ((
% 102.25/17.10 (lamp) =>
% 102.25/17.10 ((
% 102.25/17.10 (lam2p) =>
% 102.25/17.10 ((
% 102.25/17.10 (brelnall1) =>
% 102.25/17.10 ((
% 102.25/17.10 (brelnall2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1E2) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp3) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcextLem) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp4) =>
% 102.25/17.10 ((
% 102.25/17.10 (subbreln) =>
% 102.25/17.10 ((
% 102.25/17.10 (eqbreln) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcext) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcext2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2apEq1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2apEq2) =>
% 102.25/17.10 ((
% 102.25/17.10 (beta1) =>
% 102.25/17.10 ((
% 102.25/17.10 (eta1) =>
% 102.25/17.10 ((
% 102.25/17.10 (lam2lamEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (beta2) =>
% 102.25/17.10 ((
% 102.25/17.10 (eta2) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalseProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalseProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ifSingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (ifp) =>
% 102.25/17.10 ((
% 102.25/17.10 (theeq) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrue) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalse) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueorfalse) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (setextT) =>
% 102.25/17.10 ((
% 102.25/17.10 (subsetTI) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetTI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetTE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectTELcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectTERcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT1) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT2) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT3) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub2) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTnotintersectT) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementImpComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementSubsetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementInPowersetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (contraSubsetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTcontraSubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTILcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTIRcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion2) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (intersectInPowersetIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpNotIn1) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpInComplement1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTEcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementUnionInPowersetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule0) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_5) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all2) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1SetBreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (choice2fnsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (setOfPairsIsBReln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all1) =>
% 102.25/17.10 ((
% 102.25/17.10 (subbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (eqbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compEex) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionCommutes) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2W) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2A) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2B) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex1) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Equiv) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1E) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1I) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncInInjFuncSet) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncInj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (leftInvIsSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjCantorThm) =>
% 102.25/17.10 ((
% 102.25/17.10 (foundation2) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself2) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSp) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSclos) =>
% 102.25/17.10 ((
% 102.25/17.10 (peano0notS) =>
% 102.25/17.10 ((
% 102.25/17.10 (peanoSinj) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (ordinalMinLem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y0 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (ordinal @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y1 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y2 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y2 @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @
% 102.25/17.10 Y2) =>
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl588])).
% 102.25/17.10 thf(zip_derived_cl609, plain,
% 102.25/17.10 (~ (((setadjoin__Cong) =>
% 102.25/17.10 (((powerset__Cong) =>
% 102.25/17.10 (((setunion__Cong) =>
% 102.25/17.10 (((exuEu) =>
% 102.25/17.10 (((descr__Cong) =>
% 102.25/17.10 (((dsetconstr__Cong) =>
% 102.25/17.10 (((subsetI1) =>
% 102.25/17.10 (((eqimpsubset2) =>
% 102.25/17.10 (((eqimpsubset1) =>
% 102.25/17.10 (((subsetI2) =>
% 102.25/17.10 (((emptysetsubset) =>
% 102.25/17.10 (((subsetE) =>
% 102.25/17.10 (((subsetE2) =>
% 102.25/17.10 (((notsubsetI) =>
% 102.25/17.10 (((notequalI1) =>
% 102.25/17.10 (((notequalI2) =>
% 102.25/17.10 (((subsetRefl) =>
% 102.25/17.10 (((subsetTrans) =>
% 102.25/17.10 (((setadjoinSub) =>
% 102.25/17.10 (((setadjoinSub2) =>
% 102.25/17.10 (((subset2powerset) =>
% 102.25/17.10 (((setextsub) =>
% 102.25/17.10 (((subsetemptysetimpeq) =>
% 102.25/17.10 (((powersetI1) =>
% 102.25/17.10 (((powersetE1) =>
% 102.25/17.10 (((inPowerset) =>
% 102.25/17.10 (((powersetsubset) =>
% 102.25/17.10 (((sepInPowerset) =>
% 102.25/17.10 (((sepSubset) =>
% 102.25/17.10 (((binunionIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairset2IR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectI) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset5) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset3) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectER) =>
% 102.25/17.10 ((
% 102.25/17.10 (disjointsetsI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset4) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (bs114d) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusI) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusER) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusERneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusELneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusILneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusIRneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffE) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI2) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg2) =>
% 102.25/17.10 ((
% 102.25/17.10 (secondinupair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairiskpair) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairp) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonsubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowerset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairset2E) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairsubunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairinpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem3) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairin) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair1) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionE2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton1) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1E1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1I) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1I2) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonsuniq) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL1) =>
% 102.25/17.10 ((
% 102.25/17.10 (kfstsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (theprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (kfstpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodfstin) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR11) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR12) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR1) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairequniteq) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairinjR) =>
% 102.25/17.10 ((
% 102.25/17.10 (ksndsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (ksndpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairsurjEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodsndin) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairmemEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairmemER) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempaircEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodfstpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodsndpairEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairsurjEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrI) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrSub) =>
% 102.25/17.10 ((
% 102.25/17.10 (setOfPairsIsBReln) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrERa) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrEL1) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrEL2) =>
% 102.25/17.10 ((
% 102.25/17.10 (dpsetconstrER) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcImageSingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (apProp) =>
% 102.25/17.10 ((
% 102.25/17.10 (app) =>
% 102.25/17.10 ((
% 102.25/17.10 (infuncsetfunc) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2p) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcinfuncset) =>
% 102.25/17.10 ((
% 102.25/17.10 (lamProp) =>
% 102.25/17.10 ((
% 102.25/17.10 (lamp) =>
% 102.25/17.10 ((
% 102.25/17.10 (lam2p) =>
% 102.25/17.10 ((
% 102.25/17.10 (brelnall1) =>
% 102.25/17.10 ((
% 102.25/17.10 (brelnall2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1E2) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp3) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcextLem) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcGraphProp4) =>
% 102.25/17.10 ((
% 102.25/17.10 (subbreln) =>
% 102.25/17.10 ((
% 102.25/17.10 (eqbreln) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcext) =>
% 102.25/17.10 ((
% 102.25/17.10 (funcext2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2apEq1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ap2apEq2) =>
% 102.25/17.10 ((
% 102.25/17.10 (beta1) =>
% 102.25/17.10 ((
% 102.25/17.10 (eta1) =>
% 102.25/17.10 ((
% 102.25/17.10 (lam2lamEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (beta2) =>
% 102.25/17.10 ((
% 102.25/17.10 (eta2) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalseProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalseProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueProp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueProp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ifSingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (ifp) =>
% 102.25/17.10 ((
% 102.25/17.10 (theeq) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrue) =>
% 102.25/17.10 ((
% 102.25/17.10 (iffalse) =>
% 102.25/17.10 ((
% 102.25/17.10 (iftrueorfalse) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementT_lem) =>
% 102.25/17.10 ((
% 102.25/17.10 (setextT) =>
% 102.25/17.10 ((
% 102.25/17.10 (subsetTI) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetTI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (powersetTE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectTELcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectTERcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT1) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT2) =>
% 102.25/17.10 ((
% 102.25/17.10 (contrasubsetT3) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementE1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub1) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementSub2) =>
% 102.25/17.10 ((
% 102.25/17.10 (doubleComplementEq) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTnotintersectT) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementImpComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementSubsetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementInPowersetComplementIntersect) =>
% 102.25/17.10 ((
% 102.25/17.10 (contraSubsetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementTcontraSubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTILcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTIRcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInUnion2) =>
% 102.25/17.10 ((
% 102.25/17.10 (inIntersectImpInIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (intersectInPowersetIntersectUnions) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpNotIn1) =>
% 102.25/17.10 ((
% 102.25/17.10 (inComplementUnionImpInComplement1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionTEcontra) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a1) =>
% 102.25/17.10 ((
% 102.25/17.10 (complementUnionInPowersetComplement) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan1) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2a) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b2) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2b) =>
% 102.25/17.10 ((
% 102.25/17.10 (demorgan2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule0) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz13rule4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_1) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_2) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_3) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_4) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz1_5) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all2) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1SetBreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (choice2fnsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (setOfPairsIsBReln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1all1) =>
% 102.25/17.10 ((
% 102.25/17.10 (subbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (eqbreln1) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1invE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1compEex) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionI) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (breln1unionCommutes) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2W) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2A) =>
% 102.25/17.10 ((
% 102.25/17.10 (woz2B) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Ex1) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1Equiv) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1E) =>
% 102.25/17.10 ((
% 102.25/17.10 (image1I) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncInInjFuncSet) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (injFuncSetFuncInj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncIn) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjFuncSetFuncSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (leftInvIsSurj) =>
% 102.25/17.10 ((
% 102.25/17.10 (surjCantorThm) =>
% 102.25/17.10 ((
% 102.25/17.10 (foundation2) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself) =>
% 102.25/17.10 ((
% 102.25/17.10 (notinself2) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSp) =>
% 102.25/17.10 ((
% 102.25/17.10 (omegaSclos) =>
% 102.25/17.10 ((
% 102.25/17.10 (peano0notS) =>
% 102.25/17.10 ((
% 102.25/17.10 (peanoSinj) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (transitivesetOp2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionTransitive) =>
% 102.25/17.10 ((
% 102.25/17.10 (ordinalMinLem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y0 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (ordinal @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y1 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (!!) @ (
% 102.25/17.10 ^[Y2 : $i]:
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y2 @
% 102.25/17.10 Y0) =>
% 102.25/17.10 ((
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @
% 102.25/17.10 Y2) =>
% 102.25/17.10 (in @
% 102.25/17.10 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.10 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl598])).
% 102.25/17.10 thf(zip_derived_cl623, plain,
% 102.25/17.10 (~ (((powerset__Cong) =>
% 102.25/17.10 (((setunion__Cong) =>
% 102.25/17.10 (((exuEu) =>
% 102.25/17.10 (((descr__Cong) =>
% 102.25/17.10 (((dsetconstr__Cong) =>
% 102.25/17.10 (((subsetI1) =>
% 102.25/17.10 (((eqimpsubset2) =>
% 102.25/17.10 (((eqimpsubset1) =>
% 102.25/17.10 (((subsetI2) =>
% 102.25/17.10 (((emptysetsubset) =>
% 102.25/17.10 (((subsetE) =>
% 102.25/17.10 (((subsetE2) =>
% 102.25/17.10 (((notsubsetI) =>
% 102.25/17.10 (((notequalI1) =>
% 102.25/17.10 (((notequalI2) =>
% 102.25/17.10 (((subsetRefl) =>
% 102.25/17.10 (((subsetTrans) =>
% 102.25/17.10 (((setadjoinSub) =>
% 102.25/17.10 (((setadjoinSub2) =>
% 102.25/17.10 (((subset2powerset) =>
% 102.25/17.10 (((setextsub) =>
% 102.25/17.10 (((subsetemptysetimpeq) =>
% 102.25/17.10 (((powersetI1) =>
% 102.25/17.10 (((powersetE1) =>
% 102.25/17.10 (((inPowerset) =>
% 102.25/17.10 (((powersetsubset) =>
% 102.25/17.10 (((sepInPowerset) =>
% 102.25/17.10 (((sepSubset) =>
% 102.25/17.10 (((binunionIL) =>
% 102.25/17.10 (((upairset2IR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionEcases) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionE) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binunionRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectI) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset5) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset3) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectER) =>
% 102.25/17.10 ((
% 102.25/17.10 (disjointsetsI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectRsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset4) =>
% 102.25/17.10 ((
% 102.25/17.10 (binintersectSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (bs114d) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusI) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusEL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusER) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusERneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusELneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusILneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusIRneg) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusLsub) =>
% 102.25/17.10 ((
% 102.25/17.10 (setminusSubset1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffE) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffI2) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg1) =>
% 102.25/17.10 ((
% 102.25/17.10 (symdiffIneg2) =>
% 102.25/17.10 ((
% 102.25/17.10 (secondinupair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIL) =>
% 102.25/17.10 ((
% 102.25/17.10 (setukpairIR) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairiskpair) =>
% 102.25/17.10 ((
% 102.25/17.10 (kpairp) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonsubset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowerset) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletoninpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairset2E) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairsubunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (upairinpowunion) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem2) =>
% 102.25/17.10 ((
% 102.25/17.10 (ubforcartprodlem3) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodpairin) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair1) =>
% 102.25/17.10 ((
% 102.25/17.10 (cartprodmempair) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionE2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton1) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton2) =>
% 102.25/17.10 ((
% 102.25/17.10 (setunionsingleton) =>
% 102.25/17.10 ((
% 102.25/17.10 (singletonprop) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1E1) =>
% 102.25/17.10 ((
% 102.25/17.10 (ex1I) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1I2) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonsuniq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (theprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstin) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR11) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR12) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR1) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairequniteq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndin) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemER) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempaircEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrI) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrSub) =>
% 102.25/17.11 ((
% 102.25/17.11 (setOfPairsIsBReln) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrERa) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrER) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcImageSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (apProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (app) =>
% 102.25/17.11 ((
% 102.25/17.11 (infuncsetfunc) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcinfuncset) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall1) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1E2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp3) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcextLem) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp4) =>
% 102.25/17.11 ((
% 102.25/17.11 (subbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (eqbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq2) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2lamEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifp) =>
% 102.25/17.11 ((
% 102.25/17.11 (theeq) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrue) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalse) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueorfalse) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (setextT) =>
% 102.25/17.11 ((
% 102.25/17.11 (subsetTI) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTELcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTERcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT1) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT2) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT3) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub2) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTnotintersectT) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementImpComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementSubsetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementInPowersetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (contraSubsetComplement) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTcontraSubset) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTILcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTIRcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInUnion) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInUnion2) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInIntersectUnions) =>
% 102.25/17.11 ((
% 102.25/17.11 (intersectInPowersetIntersectUnions) =>
% 102.25/17.11 ((
% 102.25/17.11 (inComplementUnionImpNotIn1) =>
% 102.25/17.11 ((
% 102.25/17.11 (inComplementUnionImpInComplement1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTE) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTEcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementUnionInPowersetComplement) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a2) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1a) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1b) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2b2) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2b) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule0) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule1) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule3) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule4) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_1) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_3) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_4) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_5) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1all2) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1SetBreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (choice2fnsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (setOfPairsIsBReln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1all1) =>
% 102.25/17.11 ((
% 102.25/17.11 (subbreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (eqbreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compEex) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionIL) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionIR) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionEcases) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionCommutes) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2Ex) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2W) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2A) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2B) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Ex) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Ex1) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Equiv) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1E) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1I) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncInInjFuncSet) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncSetFuncIn) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncSetFuncInj) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjFuncSetFuncIn) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjFuncSetFuncSurj) =>
% 102.25/17.11 ((
% 102.25/17.11 (leftInvIsSurj) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjCantorThm) =>
% 102.25/17.11 ((
% 102.25/17.11 (foundation2) =>
% 102.25/17.11 ((
% 102.25/17.11 (notinself) =>
% 102.25/17.11 ((
% 102.25/17.11 (notinself2) =>
% 102.25/17.11 ((
% 102.25/17.11 (omegaSp) =>
% 102.25/17.11 ((
% 102.25/17.11 (omegaSclos) =>
% 102.25/17.11 ((
% 102.25/17.11 (peano0notS) =>
% 102.25/17.11 ((
% 102.25/17.11 (peanoSinj) =>
% 102.25/17.11 ((
% 102.25/17.11 (transitivesetOp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintTransitive) =>
% 102.25/17.11 ((
% 102.25/17.11 (transitivesetOp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionTransitive) =>
% 102.25/17.11 ((
% 102.25/17.11 (ordinalMinLem1) =>
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y0 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (ordinal @
% 102.25/17.11 Y0) =>
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y1 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y2 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (in @
% 102.25/17.11 Y2 @
% 102.25/17.11 Y0) =>
% 102.25/17.11 ((
% 102.25/17.11 (in @
% 102.25/17.11 Y1 @
% 102.25/17.11 Y2) =>
% 102.25/17.11 (in @
% 102.25/17.11 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl609])).
% 102.25/17.11 thf(zip_derived_cl637, plain,
% 102.25/17.11 (~ (((setunion__Cong) =>
% 102.25/17.11 (((exuEu) =>
% 102.25/17.11 (((descr__Cong) =>
% 102.25/17.11 (((dsetconstr__Cong) =>
% 102.25/17.11 (((subsetI1) =>
% 102.25/17.11 (((eqimpsubset2) =>
% 102.25/17.11 (((eqimpsubset1) =>
% 102.25/17.11 (((subsetI2) =>
% 102.25/17.11 (((emptysetsubset) =>
% 102.25/17.11 (((subsetE) =>
% 102.25/17.11 (((subsetE2) =>
% 102.25/17.11 (((notsubsetI) =>
% 102.25/17.11 (((notequalI1) =>
% 102.25/17.11 (((notequalI2) =>
% 102.25/17.11 (((subsetRefl) =>
% 102.25/17.11 (((subsetTrans) =>
% 102.25/17.11 (((setadjoinSub) =>
% 102.25/17.11 (((setadjoinSub2) =>
% 102.25/17.11 (((subset2powerset) =>
% 102.25/17.11 (((setextsub) =>
% 102.25/17.11 (((subsetemptysetimpeq) =>
% 102.25/17.11 (((powersetI1) =>
% 102.25/17.11 (((powersetE1) =>
% 102.25/17.11 (((inPowerset) =>
% 102.25/17.11 (((powersetsubset) =>
% 102.25/17.11 (((sepInPowerset) =>
% 102.25/17.11 (((sepSubset) =>
% 102.25/17.11 (((binunionIL) =>
% 102.25/17.11 (((upairset2IR) =>
% 102.25/17.11 (((binunionIR) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionEcases) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionE) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionRsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectI) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset5) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset2) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset3) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectER) =>
% 102.25/17.11 ((
% 102.25/17.11 (disjointsetsI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectRsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset4) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset1) =>
% 102.25/17.11 ((
% 102.25/17.11 (bs114d) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusI) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusER) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusSubset2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusERneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusELneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusILneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusIRneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusSubset1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffE) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffI2) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffIneg1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffIneg2) =>
% 102.25/17.11 ((
% 102.25/17.11 (secondinupair) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairIL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairIR) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairiskpair) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairp) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonsubset) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletoninpowerset) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletoninpowunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairset2E) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairsubunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairinpowunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem3) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairin) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempair1) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempair) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionE2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton1) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1E1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1I) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1I2) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonsuniq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (theprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstin) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR11) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR12) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR1) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairequniteq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndin) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemER) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempaircEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrI) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrSub) =>
% 102.25/17.11 ((
% 102.25/17.11 (setOfPairsIsBReln) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrERa) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrER) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcImageSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (apProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (app) =>
% 102.25/17.11 ((
% 102.25/17.11 (infuncsetfunc) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcinfuncset) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall1) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1E2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp3) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcextLem) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp4) =>
% 102.25/17.11 ((
% 102.25/17.11 (subbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (eqbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq2) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2lamEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifp) =>
% 102.25/17.11 ((
% 102.25/17.11 (theeq) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrue) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalse) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueorfalse) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (setextT) =>
% 102.25/17.11 ((
% 102.25/17.11 (subsetTI) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTELcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTERcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT1) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT2) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT3) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub2) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTnotintersectT) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementImpComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementSubsetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementInPowersetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (contraSubsetComplement) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTcontraSubset) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTILcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTIRcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInUnion) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInUnion2) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInIntersectUnions) =>
% 102.25/17.11 ((
% 102.25/17.11 (intersectInPowersetIntersectUnions) =>
% 102.25/17.11 ((
% 102.25/17.11 (inComplementUnionImpNotIn1) =>
% 102.25/17.11 ((
% 102.25/17.11 (inComplementUnionImpInComplement1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTE) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTEcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementUnionInPowersetComplement) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a2) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1a) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1b) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2b2) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2b) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule0) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule1) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule3) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule4) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_1) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_3) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_4) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_5) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1all2) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1SetBreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (choice2fnsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (setOfPairsIsBReln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1all1) =>
% 102.25/17.11 ((
% 102.25/17.11 (subbreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (eqbreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compEex) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionIL) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionIR) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionEcases) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionCommutes) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2Ex) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2W) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2A) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2B) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Ex) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Ex1) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Equiv) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1E) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1I) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncInInjFuncSet) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncSetFuncIn) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncSetFuncInj) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjFuncSetFuncIn) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjFuncSetFuncSurj) =>
% 102.25/17.11 ((
% 102.25/17.11 (leftInvIsSurj) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjCantorThm) =>
% 102.25/17.11 ((
% 102.25/17.11 (foundation2) =>
% 102.25/17.11 ((
% 102.25/17.11 (notinself) =>
% 102.25/17.11 ((
% 102.25/17.11 (notinself2) =>
% 102.25/17.11 ((
% 102.25/17.11 (omegaSp) =>
% 102.25/17.11 ((
% 102.25/17.11 (omegaSclos) =>
% 102.25/17.11 ((
% 102.25/17.11 (peano0notS) =>
% 102.25/17.11 ((
% 102.25/17.11 (peanoSinj) =>
% 102.25/17.11 ((
% 102.25/17.11 (transitivesetOp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintTransitive) =>
% 102.25/17.11 ((
% 102.25/17.11 (transitivesetOp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionTransitive) =>
% 102.25/17.11 ((
% 102.25/17.11 (ordinalMinLem1) =>
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y0 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (ordinal @
% 102.25/17.11 Y0) =>
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y1 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y2 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (in @
% 102.25/17.11 Y2 @
% 102.25/17.11 Y0) =>
% 102.25/17.11 ((
% 102.25/17.11 (in @
% 102.25/17.11 Y1 @
% 102.25/17.11 Y2) =>
% 102.25/17.11 (in @
% 102.25/17.11 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl623])).
% 102.25/17.11 thf(zip_derived_cl652, plain,
% 102.25/17.11 (~ (((exuEu) =>
% 102.25/17.11 (((descr__Cong) =>
% 102.25/17.11 (((dsetconstr__Cong) =>
% 102.25/17.11 (((subsetI1) =>
% 102.25/17.11 (((eqimpsubset2) =>
% 102.25/17.11 (((eqimpsubset1) =>
% 102.25/17.11 (((subsetI2) =>
% 102.25/17.11 (((emptysetsubset) =>
% 102.25/17.11 (((subsetE) =>
% 102.25/17.11 (((subsetE2) =>
% 102.25/17.11 (((notsubsetI) =>
% 102.25/17.11 (((notequalI1) =>
% 102.25/17.11 (((notequalI2) =>
% 102.25/17.11 (((subsetRefl) =>
% 102.25/17.11 (((subsetTrans) =>
% 102.25/17.11 (((setadjoinSub) =>
% 102.25/17.11 (((setadjoinSub2) =>
% 102.25/17.11 (((subset2powerset) =>
% 102.25/17.11 (((setextsub) =>
% 102.25/17.11 (((subsetemptysetimpeq) =>
% 102.25/17.11 (((powersetI1) =>
% 102.25/17.11 (((powersetE1) =>
% 102.25/17.11 (((inPowerset) =>
% 102.25/17.11 (((powersetsubset) =>
% 102.25/17.11 (((sepInPowerset) =>
% 102.25/17.11 (((sepSubset) =>
% 102.25/17.11 (((binunionIL) =>
% 102.25/17.11 (((upairset2IR) =>
% 102.25/17.11 (((binunionIR) =>
% 102.25/17.11 (((binunionEcases) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionE) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionRsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectI) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset5) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset2) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset3) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectER) =>
% 102.25/17.11 ((
% 102.25/17.11 (disjointsetsI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectRsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset4) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset1) =>
% 102.25/17.11 ((
% 102.25/17.11 (bs114d) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusI) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusER) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusSubset2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusERneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusELneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusILneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusIRneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusSubset1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffE) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffI2) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffIneg1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffIneg2) =>
% 102.25/17.11 ((
% 102.25/17.11 (secondinupair) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairIL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairIR) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairiskpair) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairp) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonsubset) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletoninpowerset) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletoninpowunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairset2E) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairsubunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairinpowunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem3) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairin) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempair1) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempair) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionE2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton1) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1E1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1I) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1I2) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonsuniq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (theprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstin) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR11) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR12) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR1) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairequniteq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndin) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemER) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempaircEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrI) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrSub) =>
% 102.25/17.11 ((
% 102.25/17.11 (setOfPairsIsBReln) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrERa) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrER) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcImageSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (apProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (app) =>
% 102.25/17.11 ((
% 102.25/17.11 (infuncsetfunc) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcinfuncset) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall1) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1E2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp3) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcextLem) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp4) =>
% 102.25/17.11 ((
% 102.25/17.11 (subbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (eqbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq2) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2lamEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifp) =>
% 102.25/17.11 ((
% 102.25/17.11 (theeq) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrue) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalse) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueorfalse) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (setextT) =>
% 102.25/17.11 ((
% 102.25/17.11 (subsetTI) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTELcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTERcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT1) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT2) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT3) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub2) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTnotintersectT) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementImpComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementSubsetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementInPowersetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (contraSubsetComplement) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTcontraSubset) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTILcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTIRcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInUnion) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInUnion2) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInIntersectUnions) =>
% 102.25/17.11 ((
% 102.25/17.11 (intersectInPowersetIntersectUnions) =>
% 102.25/17.11 ((
% 102.25/17.11 (inComplementUnionImpNotIn1) =>
% 102.25/17.11 ((
% 102.25/17.11 (inComplementUnionImpInComplement1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTE) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTEcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementUnionInPowersetComplement) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a2) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1a) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1b) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2b2) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2b) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule0) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule1) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule3) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule4) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_1) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_3) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_4) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_5) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1all2) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1SetBreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (choice2fnsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (setOfPairsIsBReln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1all1) =>
% 102.25/17.11 ((
% 102.25/17.11 (subbreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (eqbreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compEex) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionIL) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionIR) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionEcases) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionCommutes) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2Ex) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2W) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2A) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2B) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Ex) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Ex1) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Equiv) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1E) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1I) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncInInjFuncSet) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncSetFuncIn) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncSetFuncInj) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjFuncSetFuncIn) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjFuncSetFuncSurj) =>
% 102.25/17.11 ((
% 102.25/17.11 (leftInvIsSurj) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjCantorThm) =>
% 102.25/17.11 ((
% 102.25/17.11 (foundation2) =>
% 102.25/17.11 ((
% 102.25/17.11 (notinself) =>
% 102.25/17.11 ((
% 102.25/17.11 (notinself2) =>
% 102.25/17.11 ((
% 102.25/17.11 (omegaSp) =>
% 102.25/17.11 ((
% 102.25/17.11 (omegaSclos) =>
% 102.25/17.11 ((
% 102.25/17.11 (peano0notS) =>
% 102.25/17.11 ((
% 102.25/17.11 (peanoSinj) =>
% 102.25/17.11 ((
% 102.25/17.11 (transitivesetOp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintTransitive) =>
% 102.25/17.11 ((
% 102.25/17.11 (transitivesetOp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionTransitive) =>
% 102.25/17.11 ((
% 102.25/17.11 (ordinalMinLem1) =>
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y0 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (ordinal @
% 102.25/17.11 Y0) =>
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y1 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y2 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (in @
% 102.25/17.11 Y2 @
% 102.25/17.11 Y0) =>
% 102.25/17.11 ((
% 102.25/17.11 (in @
% 102.25/17.11 Y1 @
% 102.25/17.11 Y2) =>
% 102.25/17.11 (in @
% 102.25/17.11 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl637])).
% 102.25/17.11 thf(zip_derived_cl664, plain,
% 102.25/17.11 (~ (((descr__Cong) =>
% 102.25/17.11 (((dsetconstr__Cong) =>
% 102.25/17.11 (((subsetI1) =>
% 102.25/17.11 (((eqimpsubset2) =>
% 102.25/17.11 (((eqimpsubset1) =>
% 102.25/17.11 (((subsetI2) =>
% 102.25/17.11 (((emptysetsubset) =>
% 102.25/17.11 (((subsetE) =>
% 102.25/17.11 (((subsetE2) =>
% 102.25/17.11 (((notsubsetI) =>
% 102.25/17.11 (((notequalI1) =>
% 102.25/17.11 (((notequalI2) =>
% 102.25/17.11 (((subsetRefl) =>
% 102.25/17.11 (((subsetTrans) =>
% 102.25/17.11 (((setadjoinSub) =>
% 102.25/17.11 (((setadjoinSub2) =>
% 102.25/17.11 (((subset2powerset) =>
% 102.25/17.11 (((setextsub) =>
% 102.25/17.11 (((subsetemptysetimpeq) =>
% 102.25/17.11 (((powersetI1) =>
% 102.25/17.11 (((powersetE1) =>
% 102.25/17.11 (((inPowerset) =>
% 102.25/17.11 (((powersetsubset) =>
% 102.25/17.11 (((sepInPowerset) =>
% 102.25/17.11 (((sepSubset) =>
% 102.25/17.11 (((binunionIL) =>
% 102.25/17.11 (((upairset2IR) =>
% 102.25/17.11 (((binunionIR) =>
% 102.25/17.11 (((binunionEcases) =>
% 102.25/17.11 (((binunionE) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionRsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectI) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset5) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset2) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset3) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectER) =>
% 102.25/17.11 ((
% 102.25/17.11 (disjointsetsI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectRsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset4) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset1) =>
% 102.25/17.11 ((
% 102.25/17.11 (bs114d) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusI) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusER) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusSubset2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusERneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusELneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusILneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusIRneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusSubset1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffE) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffI2) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffIneg1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffIneg2) =>
% 102.25/17.11 ((
% 102.25/17.11 (secondinupair) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairIL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairIR) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairiskpair) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairp) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonsubset) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletoninpowerset) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletoninpowunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairset2E) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairsubunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairinpowunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem3) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairin) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempair1) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempair) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionE2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton1) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1E1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1I) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1I2) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonsuniq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (theprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstin) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR11) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR12) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR1) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairequniteq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndin) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemER) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempaircEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrI) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrSub) =>
% 102.25/17.11 ((
% 102.25/17.11 (setOfPairsIsBReln) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrERa) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrER) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcImageSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (apProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (app) =>
% 102.25/17.11 ((
% 102.25/17.11 (infuncsetfunc) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcinfuncset) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall1) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1E2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp3) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcextLem) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp4) =>
% 102.25/17.11 ((
% 102.25/17.11 (subbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (eqbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq2) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2lamEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifp) =>
% 102.25/17.11 ((
% 102.25/17.11 (theeq) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrue) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalse) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueorfalse) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusT_lem) =>
% 102.25/17.11 ((
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% 102.25/17.11 ((
% 102.25/17.11 (setextT) =>
% 102.25/17.11 ((
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% 102.25/17.11 ((
% 102.25/17.11 (powersetTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTELcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTERcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT1) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT2) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT3) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub2) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTnotintersectT) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementImpComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementSubsetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementInPowersetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (contraSubsetComplement) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTcontraSubset) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTILcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTIRcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInUnion) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInUnion2) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInIntersectUnions) =>
% 102.25/17.11 ((
% 102.25/17.11 (intersectInPowersetIntersectUnions) =>
% 102.25/17.11 ((
% 102.25/17.11 (inComplementUnionImpNotIn1) =>
% 102.25/17.11 ((
% 102.25/17.11 (inComplementUnionImpInComplement1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTE) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTEcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementUnionInPowersetComplement) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a2) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1a) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1b) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2b2) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2b) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule0) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule1) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule3) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule4) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_1) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_3) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_4) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_5) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1all2) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1SetBreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (choice2fnsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (setOfPairsIsBReln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1all1) =>
% 102.25/17.11 ((
% 102.25/17.11 (subbreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (eqbreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compEex) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionIL) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionIR) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionEcases) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionCommutes) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2Ex) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2W) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2A) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2B) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Ex) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Ex1) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Equiv) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1E) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1I) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncInInjFuncSet) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncSetFuncIn) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncSetFuncInj) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjFuncSetFuncIn) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjFuncSetFuncSurj) =>
% 102.25/17.11 ((
% 102.25/17.11 (leftInvIsSurj) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjCantorThm) =>
% 102.25/17.11 ((
% 102.25/17.11 (foundation2) =>
% 102.25/17.11 ((
% 102.25/17.11 (notinself) =>
% 102.25/17.11 ((
% 102.25/17.11 (notinself2) =>
% 102.25/17.11 ((
% 102.25/17.11 (omegaSp) =>
% 102.25/17.11 ((
% 102.25/17.11 (omegaSclos) =>
% 102.25/17.11 ((
% 102.25/17.11 (peano0notS) =>
% 102.25/17.11 ((
% 102.25/17.11 (peanoSinj) =>
% 102.25/17.11 ((
% 102.25/17.11 (transitivesetOp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintTransitive) =>
% 102.25/17.11 ((
% 102.25/17.11 (transitivesetOp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionTransitive) =>
% 102.25/17.11 ((
% 102.25/17.11 (ordinalMinLem1) =>
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y0 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (ordinal @
% 102.25/17.11 Y0) =>
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y1 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y2 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (in @
% 102.25/17.11 Y2 @
% 102.25/17.11 Y0) =>
% 102.25/17.11 ((
% 102.25/17.11 (in @
% 102.25/17.11 Y1 @
% 102.25/17.11 Y2) =>
% 102.25/17.11 (in @
% 102.25/17.11 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl652])).
% 102.25/17.11 thf(zip_derived_cl681, plain,
% 102.25/17.11 (~ (((dsetconstr__Cong) =>
% 102.25/17.11 (((subsetI1) =>
% 102.25/17.11 (((eqimpsubset2) =>
% 102.25/17.11 (((eqimpsubset1) =>
% 102.25/17.11 (((subsetI2) =>
% 102.25/17.11 (((emptysetsubset) =>
% 102.25/17.11 (((subsetE) =>
% 102.25/17.11 (((subsetE2) =>
% 102.25/17.11 (((notsubsetI) =>
% 102.25/17.11 (((notequalI1) =>
% 102.25/17.11 (((notequalI2) =>
% 102.25/17.11 (((subsetRefl) =>
% 102.25/17.11 (((subsetTrans) =>
% 102.25/17.11 (((setadjoinSub) =>
% 102.25/17.11 (((setadjoinSub2) =>
% 102.25/17.11 (((subset2powerset) =>
% 102.25/17.11 (((setextsub) =>
% 102.25/17.11 (((subsetemptysetimpeq) =>
% 102.25/17.11 (((powersetI1) =>
% 102.25/17.11 (((powersetE1) =>
% 102.25/17.11 (((inPowerset) =>
% 102.25/17.11 (((powersetsubset) =>
% 102.25/17.11 (((sepInPowerset) =>
% 102.25/17.11 (((sepSubset) =>
% 102.25/17.11 (((binunionIL) =>
% 102.25/17.11 (((upairset2IR) =>
% 102.25/17.11 (((binunionIR) =>
% 102.25/17.11 (((binunionEcases) =>
% 102.25/17.11 (((binunionE) =>
% 102.25/17.11 (((binunionLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionRsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectI) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset5) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset2) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset3) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectER) =>
% 102.25/17.11 ((
% 102.25/17.11 (disjointsetsI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectRsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset4) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset1) =>
% 102.25/17.11 ((
% 102.25/17.11 (bs114d) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusI) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusER) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusSubset2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusERneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusELneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusILneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusIRneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusSubset1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffE) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffI2) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffIneg1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffIneg2) =>
% 102.25/17.11 ((
% 102.25/17.11 (secondinupair) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairIL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairIR) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairiskpair) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairp) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonsubset) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletoninpowerset) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletoninpowunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairset2E) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairsubunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairinpowunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem3) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairin) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempair1) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempair) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionE2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton1) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1E1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1I) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1I2) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonsuniq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (theprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstin) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR11) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR12) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR1) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairequniteq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndin) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemER) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempaircEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrI) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrSub) =>
% 102.25/17.11 ((
% 102.25/17.11 (setOfPairsIsBReln) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrERa) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrER) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcImageSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (apProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (app) =>
% 102.25/17.11 ((
% 102.25/17.11 (infuncsetfunc) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcinfuncset) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall1) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1E2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp3) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcextLem) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp4) =>
% 102.25/17.11 ((
% 102.25/17.11 (subbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (eqbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq2) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2lamEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifp) =>
% 102.25/17.11 ((
% 102.25/17.11 (theeq) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrue) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalse) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueorfalse) =>
% 102.25/17.11 ((
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% 102.25/17.11 ((
% 102.25/17.11 (binunionT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (setextT) =>
% 102.25/17.11 ((
% 102.25/17.11 (subsetTI) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTELcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTERcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT1) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT2) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT3) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub2) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTnotintersectT) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementImpComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementSubsetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementInPowersetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (contraSubsetComplement) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTcontraSubset) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTILcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTIRcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInUnion) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInUnion2) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInIntersectUnions) =>
% 102.25/17.11 ((
% 102.25/17.11 (intersectInPowersetIntersectUnions) =>
% 102.25/17.11 ((
% 102.25/17.11 (inComplementUnionImpNotIn1) =>
% 102.25/17.11 ((
% 102.25/17.11 (inComplementUnionImpInComplement1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTE) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTEcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementUnionInPowersetComplement) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a2) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1a) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1b) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2b2) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2b) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule0) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule1) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule3) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule4) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_1) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_3) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_4) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_5) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1all2) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1SetBreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (choice2fnsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (setOfPairsIsBReln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1all1) =>
% 102.25/17.11 ((
% 102.25/17.11 (subbreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (eqbreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compEex) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionIL) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionIR) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionEcases) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionCommutes) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2Ex) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2W) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2A) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2B) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Ex) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Ex1) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Equiv) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1E) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1I) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncInInjFuncSet) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncSetFuncIn) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncSetFuncInj) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjFuncSetFuncIn) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjFuncSetFuncSurj) =>
% 102.25/17.11 ((
% 102.25/17.11 (leftInvIsSurj) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjCantorThm) =>
% 102.25/17.11 ((
% 102.25/17.11 (foundation2) =>
% 102.25/17.11 ((
% 102.25/17.11 (notinself) =>
% 102.25/17.11 ((
% 102.25/17.11 (notinself2) =>
% 102.25/17.11 ((
% 102.25/17.11 (omegaSp) =>
% 102.25/17.11 ((
% 102.25/17.11 (omegaSclos) =>
% 102.25/17.11 ((
% 102.25/17.11 (peano0notS) =>
% 102.25/17.11 ((
% 102.25/17.11 (peanoSinj) =>
% 102.25/17.11 ((
% 102.25/17.11 (transitivesetOp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintTransitive) =>
% 102.25/17.11 ((
% 102.25/17.11 (transitivesetOp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionTransitive) =>
% 102.25/17.11 ((
% 102.25/17.11 (ordinalMinLem1) =>
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y0 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (ordinal @
% 102.25/17.11 Y0) =>
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y1 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y2 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (in @
% 102.25/17.11 Y2 @
% 102.25/17.11 Y0) =>
% 102.25/17.11 ((
% 102.25/17.11 (in @
% 102.25/17.11 Y1 @
% 102.25/17.11 Y2) =>
% 102.25/17.11 (in @
% 102.25/17.11 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl664])).
% 102.25/17.11 thf(zip_derived_cl698, plain,
% 102.25/17.11 (~ (((subsetI1) =>
% 102.25/17.11 (((eqimpsubset2) =>
% 102.25/17.11 (((eqimpsubset1) =>
% 102.25/17.11 (((subsetI2) =>
% 102.25/17.11 (((emptysetsubset) =>
% 102.25/17.11 (((subsetE) =>
% 102.25/17.11 (((subsetE2) =>
% 102.25/17.11 (((notsubsetI) =>
% 102.25/17.11 (((notequalI1) =>
% 102.25/17.11 (((notequalI2) =>
% 102.25/17.11 (((subsetRefl) =>
% 102.25/17.11 (((subsetTrans) =>
% 102.25/17.11 (((setadjoinSub) =>
% 102.25/17.11 (((setadjoinSub2) =>
% 102.25/17.11 (((subset2powerset) =>
% 102.25/17.11 (((setextsub) =>
% 102.25/17.11 (((subsetemptysetimpeq) =>
% 102.25/17.11 (((powersetI1) =>
% 102.25/17.11 (((powersetE1) =>
% 102.25/17.11 (((inPowerset) =>
% 102.25/17.11 (((powersetsubset) =>
% 102.25/17.11 (((sepInPowerset) =>
% 102.25/17.11 (((sepSubset) =>
% 102.25/17.11 (((binunionIL) =>
% 102.25/17.11 (((upairset2IR) =>
% 102.25/17.11 (((binunionIR) =>
% 102.25/17.11 (((binunionEcases) =>
% 102.25/17.11 (((binunionE) =>
% 102.25/17.11 (((binunionLsub) =>
% 102.25/17.11 (((binunionRsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectI) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset5) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset2) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset3) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectER) =>
% 102.25/17.11 ((
% 102.25/17.11 (disjointsetsI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectRsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset4) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset1) =>
% 102.25/17.11 ((
% 102.25/17.11 (bs114d) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusI) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusER) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusSubset2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusERneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusELneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusILneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusIRneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusSubset1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffE) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffI2) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffIneg1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffIneg2) =>
% 102.25/17.11 ((
% 102.25/17.11 (secondinupair) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairIL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairIR) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairiskpair) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairp) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonsubset) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletoninpowerset) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletoninpowunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairset2E) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairsubunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairinpowunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem3) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairin) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempair1) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempair) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionE2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton1) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1E1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1I) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1I2) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonsuniq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (theprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstin) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR11) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR12) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR1) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairequniteq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndin) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemER) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempaircEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrI) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrSub) =>
% 102.25/17.11 ((
% 102.25/17.11 (setOfPairsIsBReln) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrERa) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrER) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcImageSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (apProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (app) =>
% 102.25/17.11 ((
% 102.25/17.11 (infuncsetfunc) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcinfuncset) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall1) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1E2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp3) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcextLem) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp4) =>
% 102.25/17.11 ((
% 102.25/17.11 (subbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (eqbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq2) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2lamEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifp) =>
% 102.25/17.11 ((
% 102.25/17.11 (theeq) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrue) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalse) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueorfalse) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (setextT) =>
% 102.25/17.11 ((
% 102.25/17.11 (subsetTI) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTELcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTERcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT1) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT2) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT3) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub2) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTnotintersectT) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementImpComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementSubsetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementInPowersetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (contraSubsetComplement) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTcontraSubset) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTILcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTIRcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInUnion) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInUnion2) =>
% 102.25/17.11 ((
% 102.25/17.11 (inIntersectImpInIntersectUnions) =>
% 102.25/17.11 ((
% 102.25/17.11 (intersectInPowersetIntersectUnions) =>
% 102.25/17.11 ((
% 102.25/17.11 (inComplementUnionImpNotIn1) =>
% 102.25/17.11 ((
% 102.25/17.11 (inComplementUnionImpInComplement1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTE) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTEcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementUnionInPowersetComplement) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a2) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1a) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1b) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan1) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2a) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2b2) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2b) =>
% 102.25/17.11 ((
% 102.25/17.11 (demorgan2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule0) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule1) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule3) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz13rule4) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_1) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_2) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_3) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_4) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz1_5) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1all2) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1SetBreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (choice2fnsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (setOfPairsIsBReln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1all1) =>
% 102.25/17.11 ((
% 102.25/17.11 (subbreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (eqbreln1) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1invE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1compEex) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionIL) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionIR) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionI) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionE) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionEcases) =>
% 102.25/17.11 ((
% 102.25/17.11 (breln1unionCommutes) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2Ex) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2W) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2A) =>
% 102.25/17.11 ((
% 102.25/17.11 (woz2B) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Ex) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Ex1) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1Equiv) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1E) =>
% 102.25/17.11 ((
% 102.25/17.11 (image1I) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncInInjFuncSet) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncSetFuncIn) =>
% 102.25/17.11 ((
% 102.25/17.11 (injFuncSetFuncInj) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjFuncSetFuncIn) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjFuncSetFuncSurj) =>
% 102.25/17.11 ((
% 102.25/17.11 (leftInvIsSurj) =>
% 102.25/17.11 ((
% 102.25/17.11 (surjCantorThm) =>
% 102.25/17.11 ((
% 102.25/17.11 (foundation2) =>
% 102.25/17.11 ((
% 102.25/17.11 (notinself) =>
% 102.25/17.11 ((
% 102.25/17.11 (notinself2) =>
% 102.25/17.11 ((
% 102.25/17.11 (omegaSp) =>
% 102.25/17.11 ((
% 102.25/17.11 (omegaSclos) =>
% 102.25/17.11 ((
% 102.25/17.11 (peano0notS) =>
% 102.25/17.11 ((
% 102.25/17.11 (peanoSinj) =>
% 102.25/17.11 ((
% 102.25/17.11 (transitivesetOp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintTransitive) =>
% 102.25/17.11 ((
% 102.25/17.11 (transitivesetOp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionTransitive) =>
% 102.25/17.11 ((
% 102.25/17.11 (ordinalMinLem1) =>
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y0 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (ordinal @
% 102.25/17.11 Y0) =>
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y1 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (!!) @ (
% 102.25/17.11 ^[Y2 : $i]:
% 102.25/17.11 ((
% 102.25/17.11 (in @
% 102.25/17.11 Y2 @
% 102.25/17.11 Y0) =>
% 102.25/17.11 ((
% 102.25/17.11 (in @
% 102.25/17.11 Y1 @
% 102.25/17.11 Y2) =>
% 102.25/17.11 (in @
% 102.25/17.11 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.25/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl681])).
% 102.25/17.11 thf(zip_derived_cl712, plain,
% 102.25/17.11 (~ (((eqimpsubset2) =>
% 102.25/17.11 (((eqimpsubset1) =>
% 102.25/17.11 (((subsetI2) =>
% 102.25/17.11 (((emptysetsubset) =>
% 102.25/17.11 (((subsetE) =>
% 102.25/17.11 (((subsetE2) =>
% 102.25/17.11 (((notsubsetI) =>
% 102.25/17.11 (((notequalI1) =>
% 102.25/17.11 (((notequalI2) =>
% 102.25/17.11 (((subsetRefl) =>
% 102.25/17.11 (((subsetTrans) =>
% 102.25/17.11 (((setadjoinSub) =>
% 102.25/17.11 (((setadjoinSub2) =>
% 102.25/17.11 (((subset2powerset) =>
% 102.25/17.11 (((setextsub) =>
% 102.25/17.11 (((subsetemptysetimpeq) =>
% 102.25/17.11 (((powersetI1) =>
% 102.25/17.11 (((powersetE1) =>
% 102.25/17.11 (((inPowerset) =>
% 102.25/17.11 (((powersetsubset) =>
% 102.25/17.11 (((sepInPowerset) =>
% 102.25/17.11 (((sepSubset) =>
% 102.25/17.11 (((binunionIL) =>
% 102.25/17.11 (((upairset2IR) =>
% 102.25/17.11 (((binunionIR) =>
% 102.25/17.11 (((binunionEcases) =>
% 102.25/17.11 (((binunionE) =>
% 102.25/17.11 (((binunionLsub) =>
% 102.25/17.11 (((binunionRsub) =>
% 102.25/17.11 (((binintersectI) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset5) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset2) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset3) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectER) =>
% 102.25/17.11 ((
% 102.25/17.11 (disjointsetsI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectRsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset4) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectSubset1) =>
% 102.25/17.11 ((
% 102.25/17.11 (bs114d) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusI) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusER) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusSubset2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusERneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusELneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusILneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusIRneg) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusLsub) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusSubset1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffE) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffI2) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffIneg1) =>
% 102.25/17.11 ((
% 102.25/17.11 (symdiffIneg2) =>
% 102.25/17.11 ((
% 102.25/17.11 (secondinupair) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairIL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairIR) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairiskpair) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairp) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonsubset) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletoninpowerset) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletoninpowunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairset2E) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairsubunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairinpowunion) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ubforcartprodlem3) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairin) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempair1) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempair) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionE2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton1) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setunionsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1E1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1I) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1I2) =>
% 102.25/17.11 ((
% 102.25/17.11 (singletonsuniq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (theprop) =>
% 102.25/17.11 ((
% 102.25/17.11 (kfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstin) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjL) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR11) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR12) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR1) =>
% 102.25/17.11 ((
% 102.25/17.11 (upairequniteq) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR2) =>
% 102.25/17.11 ((
% 102.25/17.11 (setukpairinjR) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndsingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ksndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (kpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndin) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemEL) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairmemER) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodmempaircEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodfstpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodsndpairEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (cartprodpairsurjEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrI) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrSub) =>
% 102.25/17.11 ((
% 102.25/17.11 (setOfPairsIsBReln) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrERa) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL1) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrEL2) =>
% 102.25/17.11 ((
% 102.25/17.11 (dpsetconstrER) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcImageSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (apProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (app) =>
% 102.25/17.11 ((
% 102.25/17.11 (infuncsetfunc) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcinfuncset) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamProp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lamp) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2p) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall1) =>
% 102.25/17.11 ((
% 102.25/17.11 (brelnall2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ex1E2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp3) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcextLem) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcGraphProp4) =>
% 102.25/17.11 ((
% 102.25/17.11 (subbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (eqbreln) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext) =>
% 102.25/17.11 ((
% 102.25/17.11 (funcext2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq1) =>
% 102.25/17.11 ((
% 102.25/17.11 (ap2apEq2) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta1) =>
% 102.25/17.11 ((
% 102.25/17.11 (lam2lamEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (beta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (eta2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalseProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp1) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueProp2) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifSingleton) =>
% 102.25/17.11 ((
% 102.25/17.11 (ifp) =>
% 102.25/17.11 ((
% 102.25/17.11 (theeq) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrue) =>
% 102.25/17.11 ((
% 102.25/17.11 (iffalse) =>
% 102.25/17.11 ((
% 102.25/17.11 (iftrueorfalse) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (setminusT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementT_lem) =>
% 102.25/17.11 ((
% 102.25/17.11 (setextT) =>
% 102.25/17.11 ((
% 102.25/17.11 (subsetTI) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (powersetTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTELcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (binintersectTERcontra) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT1) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT2) =>
% 102.25/17.11 ((
% 102.25/17.11 (contrasubsetT3) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementI1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementE1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub1) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementSub2) =>
% 102.25/17.11 ((
% 102.25/17.11 (doubleComplementEq) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTnotintersectT) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementImpComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementSubsetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementInPowersetComplementIntersect) =>
% 102.25/17.11 ((
% 102.25/17.11 (contraSubsetComplement) =>
% 102.25/17.11 ((
% 102.25/17.11 (complementTcontraSubset) =>
% 102.25/17.11 ((
% 102.25/17.11 (binunionTILcontra) =>
% 102.48/17.11 ((
% 102.48/17.11 (binunionTIRcontra) =>
% 102.48/17.11 ((
% 102.48/17.11 (inIntersectImpInUnion) =>
% 102.48/17.11 ((
% 102.48/17.11 (inIntersectImpInUnion2) =>
% 102.48/17.11 ((
% 102.48/17.11 (inIntersectImpInIntersectUnions) =>
% 102.48/17.11 ((
% 102.48/17.11 (intersectInPowersetIntersectUnions) =>
% 102.48/17.11 ((
% 102.48/17.11 (inComplementUnionImpNotIn1) =>
% 102.48/17.11 ((
% 102.48/17.11 (inComplementUnionImpInComplement1) =>
% 102.48/17.11 ((
% 102.48/17.11 (binunionTE) =>
% 102.48/17.11 ((
% 102.48/17.11 (binunionTEcontra) =>
% 102.48/17.11 ((
% 102.48/17.11 (demorgan2a1) =>
% 102.48/17.11 ((
% 102.48/17.11 (complementUnionInPowersetComplement) =>
% 102.48/17.11 ((
% 102.48/17.11 (demorgan2a2) =>
% 102.48/17.11 ((
% 102.48/17.11 (demorgan1a) =>
% 102.48/17.11 ((
% 102.48/17.11 (demorgan1b) =>
% 102.48/17.11 ((
% 102.48/17.11 (demorgan1) =>
% 102.48/17.11 ((
% 102.48/17.11 (demorgan2a) =>
% 102.48/17.11 ((
% 102.48/17.11 (demorgan2b2) =>
% 102.48/17.11 ((
% 102.48/17.11 (demorgan2b) =>
% 102.48/17.11 ((
% 102.48/17.11 (demorgan2) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz13rule0) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz13rule1) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz13rule2) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz13rule3) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz13rule4) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz1_1) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz1_2) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz1_3) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz1_4) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz1_5) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1all2) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1SetBreln1) =>
% 102.48/17.11 ((
% 102.48/17.11 (choice2fnsingleton) =>
% 102.48/17.11 ((
% 102.48/17.11 (setOfPairsIsBReln1) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1all1) =>
% 102.48/17.11 ((
% 102.48/17.11 (subbreln1) =>
% 102.48/17.11 ((
% 102.48/17.11 (eqbreln1) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1invprop) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1invI) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1invE) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1compprop) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1compI) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1compE) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1compEex) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1unionprop) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1unionIL) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1unionIR) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1unionI) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1unionE) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1unionEcases) =>
% 102.48/17.11 ((
% 102.48/17.11 (breln1unionCommutes) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz2Ex) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz2W) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz2A) =>
% 102.48/17.11 ((
% 102.48/17.11 (woz2B) =>
% 102.48/17.11 ((
% 102.48/17.11 (image1Ex) =>
% 102.48/17.11 ((
% 102.48/17.11 (image1Ex1) =>
% 102.48/17.11 ((
% 102.48/17.11 (image1Equiv) =>
% 102.48/17.11 ((
% 102.48/17.11 (image1E) =>
% 102.48/17.11 ((
% 102.48/17.11 (image1I) =>
% 102.48/17.11 ((
% 102.48/17.11 (injFuncInInjFuncSet) =>
% 102.48/17.11 ((
% 102.48/17.11 (injFuncSetFuncIn) =>
% 102.48/17.11 ((
% 102.48/17.11 (injFuncSetFuncInj) =>
% 102.48/17.11 ((
% 102.48/17.11 (surjFuncSetFuncIn) =>
% 102.48/17.11 ((
% 102.48/17.11 (surjFuncSetFuncSurj) =>
% 102.48/17.11 ((
% 102.48/17.11 (leftInvIsSurj) =>
% 102.48/17.11 ((
% 102.48/17.11 (surjCantorThm) =>
% 102.48/17.11 ((
% 102.48/17.11 (foundation2) =>
% 102.48/17.11 ((
% 102.48/17.11 (notinself) =>
% 102.48/17.11 ((
% 102.48/17.11 (notinself2) =>
% 102.48/17.11 ((
% 102.48/17.11 (omegaSp) =>
% 102.48/17.11 ((
% 102.48/17.11 (omegaSclos) =>
% 102.48/17.11 ((
% 102.48/17.11 (peano0notS) =>
% 102.48/17.11 ((
% 102.48/17.11 (peanoSinj) =>
% 102.48/17.11 ((
% 102.48/17.11 (transitivesetOp1) =>
% 102.48/17.11 ((
% 102.48/17.11 (binintTransitive) =>
% 102.48/17.11 ((
% 102.48/17.11 (transitivesetOp2) =>
% 102.48/17.11 ((
% 102.48/17.11 (setunionTransitive) =>
% 102.48/17.11 ((
% 102.48/17.11 (ordinalMinLem1) =>
% 102.48/17.11 ((
% 102.48/17.11 (!!) @ (
% 102.48/17.11 ^[Y0 : $i]:
% 102.48/17.11 ((
% 102.48/17.11 (ordinal @
% 102.48/17.11 Y0) =>
% 102.48/17.11 ((
% 102.48/17.11 (!!) @ (
% 102.48/17.11 ^[Y1 : $i]:
% 102.48/17.11 ((
% 102.48/17.11 (!!) @ (
% 102.48/17.11 ^[Y2 : $i]:
% 102.48/17.11 ((
% 102.48/17.11 (in @
% 102.48/17.11 Y2 @
% 102.48/17.11 Y0) =>
% 102.48/17.11 ((
% 102.48/17.11 (in @
% 102.48/17.11 Y1 @
% 102.48/17.11 Y2) =>
% 102.48/17.11 (in @
% 102.48/17.11 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.11 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl698])).
% 102.48/17.11 thf(zip_derived_cl725, plain,
% 102.48/17.11 (~ (((eqimpsubset1) =>
% 102.48/17.11 (((subsetI2) =>
% 102.48/17.11 (((emptysetsubset) =>
% 102.48/17.11 (((subsetE) =>
% 102.48/17.11 (((subsetE2) =>
% 102.48/17.11 (((notsubsetI) =>
% 102.48/17.11 (((notequalI1) =>
% 102.48/17.11 (((notequalI2) =>
% 102.48/17.11 (((subsetRefl) =>
% 102.48/17.11 (((subsetTrans) =>
% 102.48/17.11 (((setadjoinSub) =>
% 102.48/17.11 (((setadjoinSub2) =>
% 102.48/17.11 (((subset2powerset) =>
% 102.48/17.11 (((setextsub) =>
% 102.48/17.11 (((subsetemptysetimpeq) =>
% 102.48/17.11 (((powersetI1) =>
% 102.48/17.11 (((powersetE1) =>
% 102.48/17.11 (((inPowerset) =>
% 102.48/17.11 (((powersetsubset) =>
% 102.48/17.11 (((sepInPowerset) =>
% 102.48/17.11 (((sepSubset) =>
% 102.48/17.11 (((binunionIL) =>
% 102.48/17.11 (((upairset2IR) =>
% 102.48/17.11 (((binunionIR) =>
% 102.48/17.11 (((binunionEcases) =>
% 102.48/17.11 (((binunionE) =>
% 102.48/17.11 (((binunionLsub) =>
% 102.48/17.11 (((binunionRsub) =>
% 102.48/17.11 (((binintersectI) =>
% 102.48/17.11 (((binintersectSubset5) =>
% 102.48/17.11 ((
% 102.48/17.11 (binintersectEL) =>
% 102.48/17.11 ((
% 102.48/17.11 (binintersectLsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset2) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset3) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectER) =>
% 102.48/17.12 ((
% 102.48/17.12 (disjointsetsI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectRsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset4) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (bs114d) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusI) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusER) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusERneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusELneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusILneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusIRneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusLsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffE) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI2) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg2) =>
% 102.48/17.12 ((
% 102.48/17.12 (secondinupair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairiskpair) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairp) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowerset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairset2E) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairsubunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairinpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem3) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair1) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionE2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton1) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I2) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsuniq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (theprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstin) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR11) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR12) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR1) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairequniteq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemER) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempaircEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrI) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrSub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrERa) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrER) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcImageSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (apProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (app) =>
% 102.48/17.12 ((
% 102.48/17.12 (infuncsetfunc) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcinfuncset) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall1) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp3) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcextLem) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp4) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq2) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2lamEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifp) =>
% 102.48/17.12 ((
% 102.48/17.12 (theeq) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrue) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueorfalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setextT) =>
% 102.48/17.12 ((
% 102.48/17.12 (subsetTI) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTELcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTERcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT1) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT2) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT3) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub2) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTnotintersectT) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementImpComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementSubsetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementInPowersetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (contraSubsetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTcontraSubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTILcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTIRcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion2) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (intersectInPowersetIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpNotIn1) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpInComplement1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTE) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTEcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementUnionInPowersetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule0) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_5) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all2) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1SetBreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (choice2fnsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all1) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compEex) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionEcases) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionCommutes) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2W) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2A) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2B) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex1) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Equiv) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1E) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncInInjFuncSet) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncInj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (leftInvIsSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjCantorThm) =>
% 102.48/17.12 ((
% 102.48/17.12 (foundation2) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself2) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSp) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSclos) =>
% 102.48/17.12 ((
% 102.48/17.12 (peano0notS) =>
% 102.48/17.12 ((
% 102.48/17.12 (peanoSinj) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (ordinalMinLem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y0 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (ordinal @
% 102.48/17.12 Y0) =>
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y1 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y2 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (in @
% 102.48/17.12 Y2 @
% 102.48/17.12 Y0) =>
% 102.48/17.12 ((
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @
% 102.48/17.12 Y2) =>
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl712])).
% 102.48/17.12 thf(zip_derived_cl735, plain,
% 102.48/17.12 (~ (((subsetI2) =>
% 102.48/17.12 (((emptysetsubset) =>
% 102.48/17.12 (((subsetE) =>
% 102.48/17.12 (((subsetE2) =>
% 102.48/17.12 (((notsubsetI) =>
% 102.48/17.12 (((notequalI1) =>
% 102.48/17.12 (((notequalI2) =>
% 102.48/17.12 (((subsetRefl) =>
% 102.48/17.12 (((subsetTrans) =>
% 102.48/17.12 (((setadjoinSub) =>
% 102.48/17.12 (((setadjoinSub2) =>
% 102.48/17.12 (((subset2powerset) =>
% 102.48/17.12 (((setextsub) =>
% 102.48/17.12 (((subsetemptysetimpeq) =>
% 102.48/17.12 (((powersetI1) =>
% 102.48/17.12 (((powersetE1) =>
% 102.48/17.12 (((inPowerset) =>
% 102.48/17.12 (((powersetsubset) =>
% 102.48/17.12 (((sepInPowerset) =>
% 102.48/17.12 (((sepSubset) =>
% 102.48/17.12 (((binunionIL) =>
% 102.48/17.12 (((upairset2IR) =>
% 102.48/17.12 (((binunionIR) =>
% 102.48/17.12 (((binunionEcases) =>
% 102.48/17.12 (((binunionE) =>
% 102.48/17.12 (((binunionLsub) =>
% 102.48/17.12 (((binunionRsub) =>
% 102.48/17.12 (((binintersectI) =>
% 102.48/17.12 (((binintersectSubset5) =>
% 102.48/17.12 (((binintersectEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectLsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset2) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset3) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectER) =>
% 102.48/17.12 ((
% 102.48/17.12 (disjointsetsI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectRsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset4) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (bs114d) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusI) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusER) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusERneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusELneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusILneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusIRneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusLsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffE) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI2) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg2) =>
% 102.48/17.12 ((
% 102.48/17.12 (secondinupair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairiskpair) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairp) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowerset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairset2E) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairsubunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairinpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem3) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair1) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionE2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton1) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I2) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsuniq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (theprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstin) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR11) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR12) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR1) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairequniteq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemER) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempaircEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrI) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrSub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrERa) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrER) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcImageSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (apProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (app) =>
% 102.48/17.12 ((
% 102.48/17.12 (infuncsetfunc) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcinfuncset) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall1) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp3) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcextLem) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp4) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq2) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2lamEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifp) =>
% 102.48/17.12 ((
% 102.48/17.12 (theeq) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrue) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueorfalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setextT) =>
% 102.48/17.12 ((
% 102.48/17.12 (subsetTI) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTELcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTERcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT1) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT2) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT3) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub2) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTnotintersectT) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementImpComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementSubsetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementInPowersetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (contraSubsetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTcontraSubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTILcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTIRcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion2) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (intersectInPowersetIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpNotIn1) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpInComplement1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTE) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTEcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementUnionInPowersetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule0) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_5) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all2) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1SetBreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (choice2fnsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all1) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compEex) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionEcases) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionCommutes) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2W) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2A) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2B) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex1) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Equiv) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1E) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncInInjFuncSet) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncInj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (leftInvIsSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjCantorThm) =>
% 102.48/17.12 ((
% 102.48/17.12 (foundation2) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself2) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSp) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSclos) =>
% 102.48/17.12 ((
% 102.48/17.12 (peano0notS) =>
% 102.48/17.12 ((
% 102.48/17.12 (peanoSinj) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (ordinalMinLem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y0 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (ordinal @
% 102.48/17.12 Y0) =>
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y1 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y2 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (in @
% 102.48/17.12 Y2 @
% 102.48/17.12 Y0) =>
% 102.48/17.12 ((
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @
% 102.48/17.12 Y2) =>
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl725])).
% 102.48/17.12 thf(zip_derived_cl746, plain,
% 102.48/17.12 (~ (((emptysetsubset) =>
% 102.48/17.12 (((subsetE) =>
% 102.48/17.12 (((subsetE2) =>
% 102.48/17.12 (((notsubsetI) =>
% 102.48/17.12 (((notequalI1) =>
% 102.48/17.12 (((notequalI2) =>
% 102.48/17.12 (((subsetRefl) =>
% 102.48/17.12 (((subsetTrans) =>
% 102.48/17.12 (((setadjoinSub) =>
% 102.48/17.12 (((setadjoinSub2) =>
% 102.48/17.12 (((subset2powerset) =>
% 102.48/17.12 (((setextsub) =>
% 102.48/17.12 (((subsetemptysetimpeq) =>
% 102.48/17.12 (((powersetI1) =>
% 102.48/17.12 (((powersetE1) =>
% 102.48/17.12 (((inPowerset) =>
% 102.48/17.12 (((powersetsubset) =>
% 102.48/17.12 (((sepInPowerset) =>
% 102.48/17.12 (((sepSubset) =>
% 102.48/17.12 (((binunionIL) =>
% 102.48/17.12 (((upairset2IR) =>
% 102.48/17.12 (((binunionIR) =>
% 102.48/17.12 (((binunionEcases) =>
% 102.48/17.12 (((binunionE) =>
% 102.48/17.12 (((binunionLsub) =>
% 102.48/17.12 (((binunionRsub) =>
% 102.48/17.12 (((binintersectI) =>
% 102.48/17.12 (((binintersectSubset5) =>
% 102.48/17.12 (((binintersectEL) =>
% 102.48/17.12 (((binintersectLsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset2) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset3) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectER) =>
% 102.48/17.12 ((
% 102.48/17.12 (disjointsetsI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectRsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset4) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (bs114d) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusI) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusER) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusERneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusELneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusILneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusIRneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusLsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffE) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI2) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg2) =>
% 102.48/17.12 ((
% 102.48/17.12 (secondinupair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairiskpair) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairp) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowerset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairset2E) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairsubunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairinpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem3) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair1) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionE2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton1) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I2) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsuniq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (theprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstin) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR11) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR12) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR1) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairequniteq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemER) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempaircEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrI) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrSub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrERa) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrER) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcImageSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (apProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (app) =>
% 102.48/17.12 ((
% 102.48/17.12 (infuncsetfunc) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcinfuncset) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall1) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp3) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcextLem) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp4) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq2) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2lamEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifp) =>
% 102.48/17.12 ((
% 102.48/17.12 (theeq) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrue) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueorfalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setextT) =>
% 102.48/17.12 ((
% 102.48/17.12 (subsetTI) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTELcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTERcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT1) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT2) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT3) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub2) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTnotintersectT) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementImpComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementSubsetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementInPowersetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (contraSubsetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTcontraSubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTILcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTIRcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion2) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (intersectInPowersetIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpNotIn1) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpInComplement1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTE) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTEcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementUnionInPowersetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule0) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_5) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all2) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1SetBreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (choice2fnsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all1) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compEex) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionEcases) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionCommutes) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2W) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2A) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2B) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex1) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Equiv) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1E) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncInInjFuncSet) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncInj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (leftInvIsSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjCantorThm) =>
% 102.48/17.12 ((
% 102.48/17.12 (foundation2) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself2) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSp) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSclos) =>
% 102.48/17.12 ((
% 102.48/17.12 (peano0notS) =>
% 102.48/17.12 ((
% 102.48/17.12 (peanoSinj) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (ordinalMinLem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y0 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (ordinal @
% 102.48/17.12 Y0) =>
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y1 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y2 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (in @
% 102.48/17.12 Y2 @
% 102.48/17.12 Y0) =>
% 102.48/17.12 ((
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @
% 102.48/17.12 Y2) =>
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl735])).
% 102.48/17.12 thf(zip_derived_cl758, plain,
% 102.48/17.12 (~ (((subsetE) =>
% 102.48/17.12 (((subsetE2) =>
% 102.48/17.12 (((notsubsetI) =>
% 102.48/17.12 (((notequalI1) =>
% 102.48/17.12 (((notequalI2) =>
% 102.48/17.12 (((subsetRefl) =>
% 102.48/17.12 (((subsetTrans) =>
% 102.48/17.12 (((setadjoinSub) =>
% 102.48/17.12 (((setadjoinSub2) =>
% 102.48/17.12 (((subset2powerset) =>
% 102.48/17.12 (((setextsub) =>
% 102.48/17.12 (((subsetemptysetimpeq) =>
% 102.48/17.12 (((powersetI1) =>
% 102.48/17.12 (((powersetE1) =>
% 102.48/17.12 (((inPowerset) =>
% 102.48/17.12 (((powersetsubset) =>
% 102.48/17.12 (((sepInPowerset) =>
% 102.48/17.12 (((sepSubset) =>
% 102.48/17.12 (((binunionIL) =>
% 102.48/17.12 (((upairset2IR) =>
% 102.48/17.12 (((binunionIR) =>
% 102.48/17.12 (((binunionEcases) =>
% 102.48/17.12 (((binunionE) =>
% 102.48/17.12 (((binunionLsub) =>
% 102.48/17.12 (((binunionRsub) =>
% 102.48/17.12 (((binintersectI) =>
% 102.48/17.12 (((binintersectSubset5) =>
% 102.48/17.12 (((binintersectEL) =>
% 102.48/17.12 (((binintersectLsub) =>
% 102.48/17.12 (((binintersectSubset2) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset3) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectER) =>
% 102.48/17.12 ((
% 102.48/17.12 (disjointsetsI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectRsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset4) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (bs114d) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusI) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusER) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusERneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusELneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusILneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusIRneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusLsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffE) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI2) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg2) =>
% 102.48/17.12 ((
% 102.48/17.12 (secondinupair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairiskpair) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairp) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowerset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairset2E) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairsubunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairinpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem3) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair1) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionE2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton1) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I2) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsuniq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (theprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstin) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR11) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR12) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR1) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairequniteq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemER) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempaircEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrI) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrSub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrERa) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrER) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcImageSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (apProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (app) =>
% 102.48/17.12 ((
% 102.48/17.12 (infuncsetfunc) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcinfuncset) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall1) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp3) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcextLem) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp4) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq2) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2lamEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifp) =>
% 102.48/17.12 ((
% 102.48/17.12 (theeq) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrue) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueorfalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setextT) =>
% 102.48/17.12 ((
% 102.48/17.12 (subsetTI) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTELcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTERcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT1) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT2) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT3) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub2) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTnotintersectT) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementImpComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementSubsetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementInPowersetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (contraSubsetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTcontraSubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTILcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTIRcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion2) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (intersectInPowersetIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpNotIn1) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpInComplement1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTE) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTEcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementUnionInPowersetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule0) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_5) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all2) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1SetBreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (choice2fnsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all1) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compEex) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionEcases) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionCommutes) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2W) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2A) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2B) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex1) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Equiv) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1E) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncInInjFuncSet) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncInj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (leftInvIsSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjCantorThm) =>
% 102.48/17.12 ((
% 102.48/17.12 (foundation2) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself2) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSp) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSclos) =>
% 102.48/17.12 ((
% 102.48/17.12 (peano0notS) =>
% 102.48/17.12 ((
% 102.48/17.12 (peanoSinj) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (ordinalMinLem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y0 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (ordinal @
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% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y1 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y2 : $i]:
% 102.48/17.12 ((
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% 102.48/17.12 Y0) =>
% 102.48/17.12 ((
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @
% 102.48/17.12 Y2) =>
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl746])).
% 102.48/17.12 thf(zip_derived_cl770, plain,
% 102.48/17.12 (~ (((subsetE2) =>
% 102.48/17.12 (((notsubsetI) =>
% 102.48/17.12 (((notequalI1) =>
% 102.48/17.12 (((notequalI2) =>
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% 102.48/17.12 (((subsetTrans) =>
% 102.48/17.12 (((setadjoinSub) =>
% 102.48/17.12 (((setadjoinSub2) =>
% 102.48/17.12 (((subset2powerset) =>
% 102.48/17.12 (((setextsub) =>
% 102.48/17.12 (((subsetemptysetimpeq) =>
% 102.48/17.12 (((powersetI1) =>
% 102.48/17.12 (((powersetE1) =>
% 102.48/17.12 (((inPowerset) =>
% 102.48/17.12 (((powersetsubset) =>
% 102.48/17.12 (((sepInPowerset) =>
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% 102.48/17.12 (((binunionIL) =>
% 102.48/17.12 (((upairset2IR) =>
% 102.48/17.12 (((binunionIR) =>
% 102.48/17.12 (((binunionEcases) =>
% 102.48/17.12 (((binunionE) =>
% 102.48/17.12 (((binunionLsub) =>
% 102.48/17.12 (((binunionRsub) =>
% 102.48/17.12 (((binintersectI) =>
% 102.48/17.12 (((binintersectSubset5) =>
% 102.48/17.12 (((binintersectEL) =>
% 102.48/17.12 (((binintersectLsub) =>
% 102.48/17.12 (((binintersectSubset2) =>
% 102.48/17.12 (((binintersectSubset3) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectER) =>
% 102.48/17.12 ((
% 102.48/17.12 (disjointsetsI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectRsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset4) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (bs114d) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusI) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusER) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusERneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusELneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusILneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusIRneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusLsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffE) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI2) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg2) =>
% 102.48/17.12 ((
% 102.48/17.12 (secondinupair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairiskpair) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairp) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowerset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairset2E) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairsubunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairinpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem3) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair1) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionE2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton1) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I2) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsuniq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (theprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstin) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR11) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR12) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR1) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairequniteq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemER) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempaircEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrI) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrSub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrERa) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrER) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcImageSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (apProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (app) =>
% 102.48/17.12 ((
% 102.48/17.12 (infuncsetfunc) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcinfuncset) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall1) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp3) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcextLem) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp4) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq2) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2lamEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifp) =>
% 102.48/17.12 ((
% 102.48/17.12 (theeq) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrue) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueorfalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setextT) =>
% 102.48/17.12 ((
% 102.48/17.12 (subsetTI) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTELcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTERcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT1) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT2) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT3) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub2) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTnotintersectT) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementImpComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementSubsetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementInPowersetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (contraSubsetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTcontraSubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTILcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTIRcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion2) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (intersectInPowersetIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpNotIn1) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpInComplement1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTE) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTEcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementUnionInPowersetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule0) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_5) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all2) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1SetBreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (choice2fnsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all1) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compEex) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionEcases) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionCommutes) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2W) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2A) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2B) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex1) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Equiv) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1E) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncInInjFuncSet) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncInj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (leftInvIsSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjCantorThm) =>
% 102.48/17.12 ((
% 102.48/17.12 (foundation2) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself2) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSp) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSclos) =>
% 102.48/17.12 ((
% 102.48/17.12 (peano0notS) =>
% 102.48/17.12 ((
% 102.48/17.12 (peanoSinj) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (ordinalMinLem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y0 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (ordinal @
% 102.48/17.12 Y0) =>
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y1 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y2 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (in @
% 102.48/17.12 Y2 @
% 102.48/17.12 Y0) =>
% 102.48/17.12 ((
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @
% 102.48/17.12 Y2) =>
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl758])).
% 102.48/17.12 thf(zip_derived_cl783, plain,
% 102.48/17.12 (~ (((notsubsetI) =>
% 102.48/17.12 (((notequalI1) =>
% 102.48/17.12 (((notequalI2) =>
% 102.48/17.12 (((subsetRefl) =>
% 102.48/17.12 (((subsetTrans) =>
% 102.48/17.12 (((setadjoinSub) =>
% 102.48/17.12 (((setadjoinSub2) =>
% 102.48/17.12 (((subset2powerset) =>
% 102.48/17.12 (((setextsub) =>
% 102.48/17.12 (((subsetemptysetimpeq) =>
% 102.48/17.12 (((powersetI1) =>
% 102.48/17.12 (((powersetE1) =>
% 102.48/17.12 (((inPowerset) =>
% 102.48/17.12 (((powersetsubset) =>
% 102.48/17.12 (((sepInPowerset) =>
% 102.48/17.12 (((sepSubset) =>
% 102.48/17.12 (((binunionIL) =>
% 102.48/17.12 (((upairset2IR) =>
% 102.48/17.12 (((binunionIR) =>
% 102.48/17.12 (((binunionEcases) =>
% 102.48/17.12 (((binunionE) =>
% 102.48/17.12 (((binunionLsub) =>
% 102.48/17.12 (((binunionRsub) =>
% 102.48/17.12 (((binintersectI) =>
% 102.48/17.12 (((binintersectSubset5) =>
% 102.48/17.12 (((binintersectEL) =>
% 102.48/17.12 (((binintersectLsub) =>
% 102.48/17.12 (((binintersectSubset2) =>
% 102.48/17.12 (((binintersectSubset3) =>
% 102.48/17.12 (((binintersectER) =>
% 102.48/17.12 ((
% 102.48/17.12 (disjointsetsI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectRsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset4) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (bs114d) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusI) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusER) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusERneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusELneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusILneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusIRneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusLsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffE) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI2) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg2) =>
% 102.48/17.12 ((
% 102.48/17.12 (secondinupair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairiskpair) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairp) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowerset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairset2E) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairsubunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairinpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem3) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair1) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionE2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton1) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I2) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsuniq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (theprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstin) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR11) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR12) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR1) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairequniteq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemER) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempaircEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrI) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrSub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrERa) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrER) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcImageSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (apProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (app) =>
% 102.48/17.12 ((
% 102.48/17.12 (infuncsetfunc) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcinfuncset) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall1) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp3) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcextLem) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp4) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq2) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2lamEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifp) =>
% 102.48/17.12 ((
% 102.48/17.12 (theeq) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrue) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueorfalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setextT) =>
% 102.48/17.12 ((
% 102.48/17.12 (subsetTI) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTELcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTERcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT1) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT2) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT3) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub2) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTnotintersectT) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementImpComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementSubsetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementInPowersetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (contraSubsetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTcontraSubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTILcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTIRcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion2) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (intersectInPowersetIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpNotIn1) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpInComplement1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTE) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTEcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementUnionInPowersetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule0) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_5) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all2) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1SetBreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (choice2fnsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all1) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compEex) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionEcases) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionCommutes) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2W) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2A) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2B) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex1) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Equiv) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1E) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncInInjFuncSet) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncInj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (leftInvIsSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjCantorThm) =>
% 102.48/17.12 ((
% 102.48/17.12 (foundation2) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself2) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSp) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSclos) =>
% 102.48/17.12 ((
% 102.48/17.12 (peano0notS) =>
% 102.48/17.12 ((
% 102.48/17.12 (peanoSinj) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (ordinalMinLem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y0 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (ordinal @
% 102.48/17.12 Y0) =>
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y1 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y2 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (in @
% 102.48/17.12 Y2 @
% 102.48/17.12 Y0) =>
% 102.48/17.12 ((
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @
% 102.48/17.12 Y2) =>
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl770])).
% 102.48/17.12 thf(zip_derived_cl795, plain,
% 102.48/17.12 (~ (((notequalI1) =>
% 102.48/17.12 (((notequalI2) =>
% 102.48/17.12 (((subsetRefl) =>
% 102.48/17.12 (((subsetTrans) =>
% 102.48/17.12 (((setadjoinSub) =>
% 102.48/17.12 (((setadjoinSub2) =>
% 102.48/17.12 (((subset2powerset) =>
% 102.48/17.12 (((setextsub) =>
% 102.48/17.12 (((subsetemptysetimpeq) =>
% 102.48/17.12 (((powersetI1) =>
% 102.48/17.12 (((powersetE1) =>
% 102.48/17.12 (((inPowerset) =>
% 102.48/17.12 (((powersetsubset) =>
% 102.48/17.12 (((sepInPowerset) =>
% 102.48/17.12 (((sepSubset) =>
% 102.48/17.12 (((binunionIL) =>
% 102.48/17.12 (((upairset2IR) =>
% 102.48/17.12 (((binunionIR) =>
% 102.48/17.12 (((binunionEcases) =>
% 102.48/17.12 (((binunionE) =>
% 102.48/17.12 (((binunionLsub) =>
% 102.48/17.12 (((binunionRsub) =>
% 102.48/17.12 (((binintersectI) =>
% 102.48/17.12 (((binintersectSubset5) =>
% 102.48/17.12 (((binintersectEL) =>
% 102.48/17.12 (((binintersectLsub) =>
% 102.48/17.12 (((binintersectSubset2) =>
% 102.48/17.12 (((binintersectSubset3) =>
% 102.48/17.12 (((binintersectER) =>
% 102.48/17.12 (((disjointsetsI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectRsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset4) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (bs114d) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusI) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusER) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusERneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusELneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusILneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusIRneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusLsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffE) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffI2) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg1) =>
% 102.48/17.12 ((
% 102.48/17.12 (symdiffIneg2) =>
% 102.48/17.12 ((
% 102.48/17.12 (secondinupair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairiskpair) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairp) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowerset) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletoninpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairset2E) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairsubunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairinpowunion) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ubforcartprodlem3) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair1) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempair) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionE2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton1) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1I2) =>
% 102.48/17.12 ((
% 102.48/17.12 (singletonsuniq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (theprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (kfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstin) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR11) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR12) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR1) =>
% 102.48/17.12 ((
% 102.48/17.12 (upairequniteq) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setukpairinjR) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ksndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (kpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndin) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairmemER) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodmempaircEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodfstpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodsndpairEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (cartprodpairsurjEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrI) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrSub) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrERa) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL1) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrEL2) =>
% 102.48/17.12 ((
% 102.48/17.12 (dpsetconstrER) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcImageSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (apProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (app) =>
% 102.48/17.12 ((
% 102.48/17.12 (infuncsetfunc) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcinfuncset) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamProp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lamp) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2p) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall1) =>
% 102.48/17.12 ((
% 102.48/17.12 (brelnall2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ex1E2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp3) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcextLem) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcGraphProp4) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext) =>
% 102.48/17.12 ((
% 102.48/17.12 (funcext2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq1) =>
% 102.48/17.12 ((
% 102.48/17.12 (ap2apEq2) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta1) =>
% 102.48/17.12 ((
% 102.48/17.12 (lam2lamEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (beta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (eta2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalseProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueProp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifSingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (ifp) =>
% 102.48/17.12 ((
% 102.48/17.12 (theeq) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrue) =>
% 102.48/17.12 ((
% 102.48/17.12 (iffalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (iftrueorfalse) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementT_lem) =>
% 102.48/17.12 ((
% 102.48/17.12 (setextT) =>
% 102.48/17.12 ((
% 102.48/17.12 (subsetTI) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (powersetTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTELcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectTERcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT1) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT2) =>
% 102.48/17.12 ((
% 102.48/17.12 (contrasubsetT3) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementI1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementE1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub1) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementSub2) =>
% 102.48/17.12 ((
% 102.48/17.12 (doubleComplementEq) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTnotintersectT) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementImpComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementSubsetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementInPowersetComplementIntersect) =>
% 102.48/17.12 ((
% 102.48/17.12 (contraSubsetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementTcontraSubset) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTILcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTIRcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInUnion2) =>
% 102.48/17.12 ((
% 102.48/17.12 (inIntersectImpInIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (intersectInPowersetIntersectUnions) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpNotIn1) =>
% 102.48/17.12 ((
% 102.48/17.12 (inComplementUnionImpInComplement1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTE) =>
% 102.48/17.12 ((
% 102.48/17.12 (binunionTEcontra) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a1) =>
% 102.48/17.12 ((
% 102.48/17.12 (complementUnionInPowersetComplement) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan1) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2a) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b2) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2b) =>
% 102.48/17.12 ((
% 102.48/17.12 (demorgan2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule0) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz13rule4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_1) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_2) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_3) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_4) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz1_5) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all2) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1SetBreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (choice2fnsingleton) =>
% 102.48/17.12 ((
% 102.48/17.12 (setOfPairsIsBReln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1all1) =>
% 102.48/17.12 ((
% 102.48/17.12 (subbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (eqbreln1) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1invE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1compEex) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionprop) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIL) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionIR) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionI) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionE) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionEcases) =>
% 102.48/17.12 ((
% 102.48/17.12 (breln1unionCommutes) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2W) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2A) =>
% 102.48/17.12 ((
% 102.48/17.12 (woz2B) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Ex1) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1Equiv) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1E) =>
% 102.48/17.12 ((
% 102.48/17.12 (image1I) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncInInjFuncSet) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (injFuncSetFuncInj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncIn) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjFuncSetFuncSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (leftInvIsSurj) =>
% 102.48/17.12 ((
% 102.48/17.12 (surjCantorThm) =>
% 102.48/17.12 ((
% 102.48/17.12 (foundation2) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself) =>
% 102.48/17.12 ((
% 102.48/17.12 (notinself2) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSp) =>
% 102.48/17.12 ((
% 102.48/17.12 (omegaSclos) =>
% 102.48/17.12 ((
% 102.48/17.12 (peano0notS) =>
% 102.48/17.12 ((
% 102.48/17.12 (peanoSinj) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp1) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (transitivesetOp2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setunionTransitive) =>
% 102.48/17.12 ((
% 102.48/17.12 (ordinalMinLem1) =>
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y0 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (ordinal @
% 102.48/17.12 Y0) =>
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y1 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (!!) @ (
% 102.48/17.12 ^[Y2 : $i]:
% 102.48/17.12 ((
% 102.48/17.12 (in @
% 102.48/17.12 Y2 @
% 102.48/17.12 Y0) =>
% 102.48/17.12 ((
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @
% 102.48/17.12 Y2) =>
% 102.48/17.12 (in @
% 102.48/17.12 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.12 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl783])).
% 102.48/17.12 thf(zip_derived_cl805, plain,
% 102.48/17.12 (~ (((notequalI2) =>
% 102.48/17.12 (((subsetRefl) =>
% 102.48/17.12 (((subsetTrans) =>
% 102.48/17.12 (((setadjoinSub) =>
% 102.48/17.12 (((setadjoinSub2) =>
% 102.48/17.12 (((subset2powerset) =>
% 102.48/17.12 (((setextsub) =>
% 102.48/17.12 (((subsetemptysetimpeq) =>
% 102.48/17.12 (((powersetI1) =>
% 102.48/17.12 (((powersetE1) =>
% 102.48/17.12 (((inPowerset) =>
% 102.48/17.12 (((powersetsubset) =>
% 102.48/17.12 (((sepInPowerset) =>
% 102.48/17.12 (((sepSubset) =>
% 102.48/17.12 (((binunionIL) =>
% 102.48/17.12 (((upairset2IR) =>
% 102.48/17.12 (((binunionIR) =>
% 102.48/17.12 (((binunionEcases) =>
% 102.48/17.12 (((binunionE) =>
% 102.48/17.12 (((binunionLsub) =>
% 102.48/17.12 (((binunionRsub) =>
% 102.48/17.12 (((binintersectI) =>
% 102.48/17.12 (((binintersectSubset5) =>
% 102.48/17.12 (((binintersectEL) =>
% 102.48/17.12 (((binintersectLsub) =>
% 102.48/17.12 (((binintersectSubset2) =>
% 102.48/17.12 (((binintersectSubset3) =>
% 102.48/17.12 (((binintersectER) =>
% 102.48/17.12 (((disjointsetsI1) =>
% 102.48/17.12 (((binintersectRsub) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset4) =>
% 102.48/17.12 ((
% 102.48/17.12 (binintersectSubset1) =>
% 102.48/17.12 ((
% 102.48/17.12 (bs114d) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusI) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusEL) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusER) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusSubset2) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusERneg) =>
% 102.48/17.12 ((
% 102.48/17.12 (setminusELneg) =>
% 102.48/17.12 ((
% 102.48/17.13 (setminusILneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusIRneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusLsub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffE) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI2) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg2) =>
% 102.48/17.13 ((
% 102.48/17.13 (secondinupair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairiskpair) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairp) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowerset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairset2E) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairsubunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairinpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem3) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair1) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionE2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton1) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I2) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsuniq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (theprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstin) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR11) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR12) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR1) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairequniteq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemEL) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemER) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempaircEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrI) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrSub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrERa) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrER) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcImageSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (apProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (app) =>
% 102.48/17.13 ((
% 102.48/17.13 (infuncsetfunc) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcinfuncset) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall1) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp3) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcextLem) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp4) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq2) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2lamEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifp) =>
% 102.48/17.13 ((
% 102.48/17.13 (theeq) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrue) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueorfalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setextT) =>
% 102.48/17.13 ((
% 102.48/17.13 (subsetTI) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTELcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTERcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT1) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT2) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT3) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub2) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTnotintersectT) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementImpComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementSubsetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementInPowersetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (contraSubsetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTcontraSubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTILcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTIRcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion2) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (intersectInPowersetIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpNotIn1) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpInComplement1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTE) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTEcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementUnionInPowersetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule0) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_5) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all2) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1SetBreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (choice2fnsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all1) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compEex) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionEcases) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionCommutes) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2W) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2A) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2B) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex1) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Equiv) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1E) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncInInjFuncSet) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncInj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (leftInvIsSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjCantorThm) =>
% 102.48/17.13 ((
% 102.48/17.13 (foundation2) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself2) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSp) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSclos) =>
% 102.48/17.13 ((
% 102.48/17.13 (peano0notS) =>
% 102.48/17.13 ((
% 102.48/17.13 (peanoSinj) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (ordinalMinLem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y0 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (ordinal @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y1 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y2 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (in @
% 102.48/17.13 Y2 @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @
% 102.48/17.13 Y2) =>
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl795])).
% 102.48/17.13 thf(zip_derived_cl813, plain,
% 102.48/17.13 (~ (((subsetRefl) =>
% 102.48/17.13 (((subsetTrans) =>
% 102.48/17.13 (((setadjoinSub) =>
% 102.48/17.13 (((setadjoinSub2) =>
% 102.48/17.13 (((subset2powerset) =>
% 102.48/17.13 (((setextsub) =>
% 102.48/17.13 (((subsetemptysetimpeq) =>
% 102.48/17.13 (((powersetI1) =>
% 102.48/17.13 (((powersetE1) =>
% 102.48/17.13 (((inPowerset) =>
% 102.48/17.13 (((powersetsubset) =>
% 102.48/17.13 (((sepInPowerset) =>
% 102.48/17.13 (((sepSubset) =>
% 102.48/17.13 (((binunionIL) =>
% 102.48/17.13 (((upairset2IR) =>
% 102.48/17.13 (((binunionIR) =>
% 102.48/17.13 (((binunionEcases) =>
% 102.48/17.13 (((binunionE) =>
% 102.48/17.13 (((binunionLsub) =>
% 102.48/17.13 (((binunionRsub) =>
% 102.48/17.13 (((binintersectI) =>
% 102.48/17.13 (((binintersectSubset5) =>
% 102.48/17.13 (((binintersectEL) =>
% 102.48/17.13 (((binintersectLsub) =>
% 102.48/17.13 (((binintersectSubset2) =>
% 102.48/17.13 (((binintersectSubset3) =>
% 102.48/17.13 (((binintersectER) =>
% 102.48/17.13 (((disjointsetsI1) =>
% 102.48/17.13 (((binintersectRsub) =>
% 102.48/17.13 (((binintersectSubset4) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectSubset1) =>
% 102.48/17.13 ((
% 102.48/17.13 (bs114d) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusI) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusEL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusER) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusERneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusELneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusILneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusIRneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusLsub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffE) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI2) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg2) =>
% 102.48/17.13 ((
% 102.48/17.13 (secondinupair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairiskpair) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairp) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowerset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairset2E) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairsubunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairinpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem3) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair1) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionE2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton1) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I2) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsuniq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (theprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstin) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR11) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR12) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR1) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairequniteq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemEL) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemER) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempaircEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrI) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrSub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrERa) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrER) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcImageSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (apProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (app) =>
% 102.48/17.13 ((
% 102.48/17.13 (infuncsetfunc) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcinfuncset) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall1) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp3) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcextLem) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp4) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq2) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2lamEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifp) =>
% 102.48/17.13 ((
% 102.48/17.13 (theeq) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrue) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueorfalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setextT) =>
% 102.48/17.13 ((
% 102.48/17.13 (subsetTI) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTELcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTERcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT1) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT2) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT3) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub2) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTnotintersectT) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementImpComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementSubsetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementInPowersetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (contraSubsetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTcontraSubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTILcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTIRcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion2) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (intersectInPowersetIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpNotIn1) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpInComplement1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTE) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTEcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementUnionInPowersetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule0) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_5) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all2) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1SetBreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (choice2fnsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all1) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compEex) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionEcases) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionCommutes) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2W) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2A) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2B) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex1) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Equiv) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1E) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncInInjFuncSet) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncInj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (leftInvIsSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjCantorThm) =>
% 102.48/17.13 ((
% 102.48/17.13 (foundation2) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself2) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSp) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSclos) =>
% 102.48/17.13 ((
% 102.48/17.13 (peano0notS) =>
% 102.48/17.13 ((
% 102.48/17.13 (peanoSinj) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (ordinalMinLem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y0 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (ordinal @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y1 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y2 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (in @
% 102.48/17.13 Y2 @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @
% 102.48/17.13 Y2) =>
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl805])).
% 102.48/17.13 thf(zip_derived_cl823, plain,
% 102.48/17.13 (~ (((subsetTrans) =>
% 102.48/17.13 (((setadjoinSub) =>
% 102.48/17.13 (((setadjoinSub2) =>
% 102.48/17.13 (((subset2powerset) =>
% 102.48/17.13 (((setextsub) =>
% 102.48/17.13 (((subsetemptysetimpeq) =>
% 102.48/17.13 (((powersetI1) =>
% 102.48/17.13 (((powersetE1) =>
% 102.48/17.13 (((inPowerset) =>
% 102.48/17.13 (((powersetsubset) =>
% 102.48/17.13 (((sepInPowerset) =>
% 102.48/17.13 (((sepSubset) =>
% 102.48/17.13 (((binunionIL) =>
% 102.48/17.13 (((upairset2IR) =>
% 102.48/17.13 (((binunionIR) =>
% 102.48/17.13 (((binunionEcases) =>
% 102.48/17.13 (((binunionE) =>
% 102.48/17.13 (((binunionLsub) =>
% 102.48/17.13 (((binunionRsub) =>
% 102.48/17.13 (((binintersectI) =>
% 102.48/17.13 (((binintersectSubset5) =>
% 102.48/17.13 (((binintersectEL) =>
% 102.48/17.13 (((binintersectLsub) =>
% 102.48/17.13 (((binintersectSubset2) =>
% 102.48/17.13 (((binintersectSubset3) =>
% 102.48/17.13 (((binintersectER) =>
% 102.48/17.13 (((disjointsetsI1) =>
% 102.48/17.13 (((binintersectRsub) =>
% 102.48/17.13 (((binintersectSubset4) =>
% 102.48/17.13 (((binintersectSubset1) =>
% 102.48/17.13 ((
% 102.48/17.13 (bs114d) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusI) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusEL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusER) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusERneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusELneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusILneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusIRneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusLsub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffE) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI2) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg2) =>
% 102.48/17.13 ((
% 102.48/17.13 (secondinupair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairiskpair) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairp) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowerset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairset2E) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairsubunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairinpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem3) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair1) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionE2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton1) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I2) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsuniq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (theprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstin) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR11) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR12) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR1) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairequniteq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemEL) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemER) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempaircEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrI) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrSub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrERa) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrER) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcImageSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (apProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (app) =>
% 102.48/17.13 ((
% 102.48/17.13 (infuncsetfunc) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcinfuncset) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall1) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp3) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcextLem) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp4) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq2) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2lamEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifp) =>
% 102.48/17.13 ((
% 102.48/17.13 (theeq) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrue) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueorfalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setextT) =>
% 102.48/17.13 ((
% 102.48/17.13 (subsetTI) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTELcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTERcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT1) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT2) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT3) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub2) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTnotintersectT) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementImpComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementSubsetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementInPowersetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (contraSubsetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTcontraSubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTILcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTIRcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion2) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (intersectInPowersetIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpNotIn1) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpInComplement1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTE) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTEcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementUnionInPowersetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule0) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_5) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all2) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1SetBreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (choice2fnsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all1) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compEex) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionEcases) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionCommutes) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2W) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2A) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2B) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex1) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Equiv) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1E) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncInInjFuncSet) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncInj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (leftInvIsSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjCantorThm) =>
% 102.48/17.13 ((
% 102.48/17.13 (foundation2) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself2) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSp) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSclos) =>
% 102.48/17.13 ((
% 102.48/17.13 (peano0notS) =>
% 102.48/17.13 ((
% 102.48/17.13 (peanoSinj) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (ordinalMinLem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y0 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (ordinal @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y1 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y2 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (in @
% 102.48/17.13 Y2 @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @
% 102.48/17.13 Y2) =>
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl813])).
% 102.48/17.13 thf(zip_derived_cl833, plain,
% 102.48/17.13 (~ (((setadjoinSub) =>
% 102.48/17.13 (((setadjoinSub2) =>
% 102.48/17.13 (((subset2powerset) =>
% 102.48/17.13 (((setextsub) =>
% 102.48/17.13 (((subsetemptysetimpeq) =>
% 102.48/17.13 (((powersetI1) =>
% 102.48/17.13 (((powersetE1) =>
% 102.48/17.13 (((inPowerset) =>
% 102.48/17.13 (((powersetsubset) =>
% 102.48/17.13 (((sepInPowerset) =>
% 102.48/17.13 (((sepSubset) =>
% 102.48/17.13 (((binunionIL) =>
% 102.48/17.13 (((upairset2IR) =>
% 102.48/17.13 (((binunionIR) =>
% 102.48/17.13 (((binunionEcases) =>
% 102.48/17.13 (((binunionE) =>
% 102.48/17.13 (((binunionLsub) =>
% 102.48/17.13 (((binunionRsub) =>
% 102.48/17.13 (((binintersectI) =>
% 102.48/17.13 (((binintersectSubset5) =>
% 102.48/17.13 (((binintersectEL) =>
% 102.48/17.13 (((binintersectLsub) =>
% 102.48/17.13 (((binintersectSubset2) =>
% 102.48/17.13 (((binintersectSubset3) =>
% 102.48/17.13 (((binintersectER) =>
% 102.48/17.13 (((disjointsetsI1) =>
% 102.48/17.13 (((binintersectRsub) =>
% 102.48/17.13 (((binintersectSubset4) =>
% 102.48/17.13 (((binintersectSubset1) =>
% 102.48/17.13 (((bs114d) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusI) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusEL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusER) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusERneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusELneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusILneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusIRneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusLsub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffE) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI2) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg2) =>
% 102.48/17.13 ((
% 102.48/17.13 (secondinupair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairiskpair) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairp) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowerset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairset2E) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairsubunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairinpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem3) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair1) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionE2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton1) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I2) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsuniq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (theprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstin) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR11) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR12) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR1) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairequniteq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemEL) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemER) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempaircEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrI) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrSub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrERa) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrER) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcImageSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (apProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (app) =>
% 102.48/17.13 ((
% 102.48/17.13 (infuncsetfunc) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcinfuncset) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall1) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp3) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcextLem) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp4) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq2) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2lamEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifp) =>
% 102.48/17.13 ((
% 102.48/17.13 (theeq) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrue) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueorfalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setextT) =>
% 102.48/17.13 ((
% 102.48/17.13 (subsetTI) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTELcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTERcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT1) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT2) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT3) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub2) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTnotintersectT) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementImpComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementSubsetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementInPowersetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (contraSubsetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTcontraSubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTILcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTIRcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion2) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (intersectInPowersetIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpNotIn1) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpInComplement1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTE) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTEcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementUnionInPowersetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule0) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_5) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all2) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1SetBreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (choice2fnsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all1) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compEex) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionEcases) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionCommutes) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2W) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2A) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2B) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex1) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Equiv) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1E) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncInInjFuncSet) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncInj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (leftInvIsSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjCantorThm) =>
% 102.48/17.13 ((
% 102.48/17.13 (foundation2) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself2) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSp) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSclos) =>
% 102.48/17.13 ((
% 102.48/17.13 (peano0notS) =>
% 102.48/17.13 ((
% 102.48/17.13 (peanoSinj) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (ordinalMinLem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y0 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (ordinal @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y1 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y2 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (in @
% 102.48/17.13 Y2 @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @
% 102.48/17.13 Y2) =>
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl823])).
% 102.48/17.13 thf(zip_derived_cl843, plain,
% 102.48/17.13 (~ (((setadjoinSub2) =>
% 102.48/17.13 (((subset2powerset) =>
% 102.48/17.13 (((setextsub) =>
% 102.48/17.13 (((subsetemptysetimpeq) =>
% 102.48/17.13 (((powersetI1) =>
% 102.48/17.13 (((powersetE1) =>
% 102.48/17.13 (((inPowerset) =>
% 102.48/17.13 (((powersetsubset) =>
% 102.48/17.13 (((sepInPowerset) =>
% 102.48/17.13 (((sepSubset) =>
% 102.48/17.13 (((binunionIL) =>
% 102.48/17.13 (((upairset2IR) =>
% 102.48/17.13 (((binunionIR) =>
% 102.48/17.13 (((binunionEcases) =>
% 102.48/17.13 (((binunionE) =>
% 102.48/17.13 (((binunionLsub) =>
% 102.48/17.13 (((binunionRsub) =>
% 102.48/17.13 (((binintersectI) =>
% 102.48/17.13 (((binintersectSubset5) =>
% 102.48/17.13 (((binintersectEL) =>
% 102.48/17.13 (((binintersectLsub) =>
% 102.48/17.13 (((binintersectSubset2) =>
% 102.48/17.13 (((binintersectSubset3) =>
% 102.48/17.13 (((binintersectER) =>
% 102.48/17.13 (((disjointsetsI1) =>
% 102.48/17.13 (((binintersectRsub) =>
% 102.48/17.13 (((binintersectSubset4) =>
% 102.48/17.13 (((binintersectSubset1) =>
% 102.48/17.13 (((bs114d) =>
% 102.48/17.13 (((setminusI) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusEL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusER) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusERneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusELneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusILneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusIRneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusLsub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffE) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI2) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg2) =>
% 102.48/17.13 ((
% 102.48/17.13 (secondinupair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairiskpair) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairp) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowerset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairset2E) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairsubunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairinpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem3) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair1) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionE2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton1) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I2) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsuniq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (theprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstin) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR11) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR12) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR1) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairequniteq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemEL) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemER) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempaircEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrI) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrSub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrERa) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrER) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcImageSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (apProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (app) =>
% 102.48/17.13 ((
% 102.48/17.13 (infuncsetfunc) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcinfuncset) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall1) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp3) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcextLem) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp4) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq2) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2lamEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifp) =>
% 102.48/17.13 ((
% 102.48/17.13 (theeq) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrue) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueorfalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setextT) =>
% 102.48/17.13 ((
% 102.48/17.13 (subsetTI) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTELcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTERcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT1) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT2) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT3) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub2) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTnotintersectT) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementImpComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementSubsetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementInPowersetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (contraSubsetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTcontraSubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTILcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTIRcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion2) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (intersectInPowersetIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpNotIn1) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpInComplement1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTE) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTEcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementUnionInPowersetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule0) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_5) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all2) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1SetBreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (choice2fnsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all1) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compEex) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionEcases) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionCommutes) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2W) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2A) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2B) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex1) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Equiv) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1E) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncInInjFuncSet) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncInj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (leftInvIsSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjCantorThm) =>
% 102.48/17.13 ((
% 102.48/17.13 (foundation2) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself2) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSp) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSclos) =>
% 102.48/17.13 ((
% 102.48/17.13 (peano0notS) =>
% 102.48/17.13 ((
% 102.48/17.13 (peanoSinj) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (ordinalMinLem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y0 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (ordinal @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y1 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y2 : $i]:
% 102.48/17.13 ((
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% 102.48/17.13 Y2 @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @
% 102.48/17.13 Y2) =>
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl833])).
% 102.48/17.13 thf(zip_derived_cl851, plain,
% 102.48/17.13 (~ (((subset2powerset) =>
% 102.48/17.13 (((setextsub) =>
% 102.48/17.13 (((subsetemptysetimpeq) =>
% 102.48/17.13 (((powersetI1) =>
% 102.48/17.13 (((powersetE1) =>
% 102.48/17.13 (((inPowerset) =>
% 102.48/17.13 (((powersetsubset) =>
% 102.48/17.13 (((sepInPowerset) =>
% 102.48/17.13 (((sepSubset) =>
% 102.48/17.13 (((binunionIL) =>
% 102.48/17.13 (((upairset2IR) =>
% 102.48/17.13 (((binunionIR) =>
% 102.48/17.13 (((binunionEcases) =>
% 102.48/17.13 (((binunionE) =>
% 102.48/17.13 (((binunionLsub) =>
% 102.48/17.13 (((binunionRsub) =>
% 102.48/17.13 (((binintersectI) =>
% 102.48/17.13 (((binintersectSubset5) =>
% 102.48/17.13 (((binintersectEL) =>
% 102.48/17.13 (((binintersectLsub) =>
% 102.48/17.13 (((binintersectSubset2) =>
% 102.48/17.13 (((binintersectSubset3) =>
% 102.48/17.13 (((binintersectER) =>
% 102.48/17.13 (((disjointsetsI1) =>
% 102.48/17.13 (((binintersectRsub) =>
% 102.48/17.13 (((binintersectSubset4) =>
% 102.48/17.13 (((binintersectSubset1) =>
% 102.48/17.13 (((bs114d) =>
% 102.48/17.13 (((setminusI) =>
% 102.48/17.13 (((setminusEL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusER) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusERneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusELneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusILneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusIRneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusLsub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffE) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI2) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg2) =>
% 102.48/17.13 ((
% 102.48/17.13 (secondinupair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairiskpair) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairp) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowerset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairset2E) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairsubunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairinpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem3) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair1) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionE2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton1) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I2) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsuniq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (theprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstin) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR11) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR12) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR1) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairequniteq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemEL) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemER) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempaircEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrI) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrSub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrERa) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrER) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcImageSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (apProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (app) =>
% 102.48/17.13 ((
% 102.48/17.13 (infuncsetfunc) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcinfuncset) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall1) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp3) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcextLem) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp4) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq2) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2lamEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifp) =>
% 102.48/17.13 ((
% 102.48/17.13 (theeq) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrue) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueorfalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setextT) =>
% 102.48/17.13 ((
% 102.48/17.13 (subsetTI) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTELcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTERcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT1) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT2) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT3) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub2) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTnotintersectT) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementImpComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementSubsetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementInPowersetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (contraSubsetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTcontraSubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTILcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTIRcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion2) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (intersectInPowersetIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpNotIn1) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpInComplement1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTE) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTEcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementUnionInPowersetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule0) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_5) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all2) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1SetBreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (choice2fnsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all1) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compEex) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionEcases) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionCommutes) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2W) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2A) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2B) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex1) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Equiv) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1E) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncInInjFuncSet) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncInj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (leftInvIsSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjCantorThm) =>
% 102.48/17.13 ((
% 102.48/17.13 (foundation2) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself2) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSp) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSclos) =>
% 102.48/17.13 ((
% 102.48/17.13 (peano0notS) =>
% 102.48/17.13 ((
% 102.48/17.13 (peanoSinj) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (ordinalMinLem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y0 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (ordinal @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y1 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y2 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (in @
% 102.48/17.13 Y2 @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @
% 102.48/17.13 Y2) =>
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl843])).
% 102.48/17.13 thf(zip_derived_cl857, plain,
% 102.48/17.13 (~ (((setextsub) =>
% 102.48/17.13 (((subsetemptysetimpeq) =>
% 102.48/17.13 (((powersetI1) =>
% 102.48/17.13 (((powersetE1) =>
% 102.48/17.13 (((inPowerset) =>
% 102.48/17.13 (((powersetsubset) =>
% 102.48/17.13 (((sepInPowerset) =>
% 102.48/17.13 (((sepSubset) =>
% 102.48/17.13 (((binunionIL) =>
% 102.48/17.13 (((upairset2IR) =>
% 102.48/17.13 (((binunionIR) =>
% 102.48/17.13 (((binunionEcases) =>
% 102.48/17.13 (((binunionE) =>
% 102.48/17.13 (((binunionLsub) =>
% 102.48/17.13 (((binunionRsub) =>
% 102.48/17.13 (((binintersectI) =>
% 102.48/17.13 (((binintersectSubset5) =>
% 102.48/17.13 (((binintersectEL) =>
% 102.48/17.13 (((binintersectLsub) =>
% 102.48/17.13 (((binintersectSubset2) =>
% 102.48/17.13 (((binintersectSubset3) =>
% 102.48/17.13 (((binintersectER) =>
% 102.48/17.13 (((disjointsetsI1) =>
% 102.48/17.13 (((binintersectRsub) =>
% 102.48/17.13 (((binintersectSubset4) =>
% 102.48/17.13 (((binintersectSubset1) =>
% 102.48/17.13 (((bs114d) =>
% 102.48/17.13 (((setminusI) =>
% 102.48/17.13 (((setminusEL) =>
% 102.48/17.13 (((setminusER) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusERneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusELneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusILneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusIRneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusLsub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffE) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI2) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg2) =>
% 102.48/17.13 ((
% 102.48/17.13 (secondinupair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairiskpair) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairp) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowerset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairset2E) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairsubunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairinpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem3) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair1) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionE2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton1) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I2) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsuniq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (theprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstin) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR11) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR12) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR1) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairequniteq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemEL) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemER) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempaircEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrI) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrSub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrERa) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrEL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (dpsetconstrER) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcImageSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (apProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (app) =>
% 102.48/17.13 ((
% 102.48/17.13 (infuncsetfunc) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcinfuncset) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamProp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lamp) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2p) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall1) =>
% 102.48/17.13 ((
% 102.48/17.13 (brelnall2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp3) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcextLem) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcGraphProp4) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext) =>
% 102.48/17.13 ((
% 102.48/17.13 (funcext2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ap2apEq2) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta1) =>
% 102.48/17.13 ((
% 102.48/17.13 (lam2lamEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (beta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (eta2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalseProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueProp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifSingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ifp) =>
% 102.48/17.13 ((
% 102.48/17.13 (theeq) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrue) =>
% 102.48/17.13 ((
% 102.48/17.13 (iffalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (iftrueorfalse) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementT_lem) =>
% 102.48/17.13 ((
% 102.48/17.13 (setextT) =>
% 102.48/17.13 ((
% 102.48/17.13 (subsetTI) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (powersetTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTELcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintersectTERcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT1) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT2) =>
% 102.48/17.13 ((
% 102.48/17.13 (contrasubsetT3) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementE1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub1) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementSub2) =>
% 102.48/17.13 ((
% 102.48/17.13 (doubleComplementEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTnotintersectT) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementImpComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementSubsetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementInPowersetComplementIntersect) =>
% 102.48/17.13 ((
% 102.48/17.13 (contraSubsetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementTcontraSubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTILcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTIRcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInUnion2) =>
% 102.48/17.13 ((
% 102.48/17.13 (inIntersectImpInIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (intersectInPowersetIntersectUnions) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpNotIn1) =>
% 102.48/17.13 ((
% 102.48/17.13 (inComplementUnionImpInComplement1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTE) =>
% 102.48/17.13 ((
% 102.48/17.13 (binunionTEcontra) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a1) =>
% 102.48/17.13 ((
% 102.48/17.13 (complementUnionInPowersetComplement) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan1) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2a) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b2) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2b) =>
% 102.48/17.13 ((
% 102.48/17.13 (demorgan2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule0) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz13rule4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_1) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_2) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_3) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_4) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz1_5) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all2) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1SetBreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (choice2fnsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (setOfPairsIsBReln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1all1) =>
% 102.48/17.13 ((
% 102.48/17.13 (subbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (eqbreln1) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1invE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1compEex) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionI) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionE) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionEcases) =>
% 102.48/17.13 ((
% 102.48/17.13 (breln1unionCommutes) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2W) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2A) =>
% 102.48/17.13 ((
% 102.48/17.13 (woz2B) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Ex1) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1Equiv) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1E) =>
% 102.48/17.13 ((
% 102.48/17.13 (image1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncInInjFuncSet) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (injFuncSetFuncInj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncIn) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjFuncSetFuncSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (leftInvIsSurj) =>
% 102.48/17.13 ((
% 102.48/17.13 (surjCantorThm) =>
% 102.48/17.13 ((
% 102.48/17.13 (foundation2) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself) =>
% 102.48/17.13 ((
% 102.48/17.13 (notinself2) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSp) =>
% 102.48/17.13 ((
% 102.48/17.13 (omegaSclos) =>
% 102.48/17.13 ((
% 102.48/17.13 (peano0notS) =>
% 102.48/17.13 ((
% 102.48/17.13 (peanoSinj) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp1) =>
% 102.48/17.13 ((
% 102.48/17.13 (binintTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (transitivesetOp2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionTransitive) =>
% 102.48/17.13 ((
% 102.48/17.13 (ordinalMinLem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y0 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (ordinal @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y1 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (!!) @ (
% 102.48/17.13 ^[Y2 : $i]:
% 102.48/17.13 ((
% 102.48/17.13 (in @
% 102.48/17.13 Y2 @
% 102.48/17.13 Y0) =>
% 102.48/17.13 ((
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @
% 102.48/17.13 Y2) =>
% 102.48/17.13 (in @
% 102.48/17.13 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl851])).
% 102.48/17.13 thf(zip_derived_cl864, plain,
% 102.48/17.13 (~ (((subsetemptysetimpeq) =>
% 102.48/17.13 (((powersetI1) =>
% 102.48/17.13 (((powersetE1) =>
% 102.48/17.13 (((inPowerset) =>
% 102.48/17.13 (((powersetsubset) =>
% 102.48/17.13 (((sepInPowerset) =>
% 102.48/17.13 (((sepSubset) =>
% 102.48/17.13 (((binunionIL) =>
% 102.48/17.13 (((upairset2IR) =>
% 102.48/17.13 (((binunionIR) =>
% 102.48/17.13 (((binunionEcases) =>
% 102.48/17.13 (((binunionE) =>
% 102.48/17.13 (((binunionLsub) =>
% 102.48/17.13 (((binunionRsub) =>
% 102.48/17.13 (((binintersectI) =>
% 102.48/17.13 (((binintersectSubset5) =>
% 102.48/17.13 (((binintersectEL) =>
% 102.48/17.13 (((binintersectLsub) =>
% 102.48/17.13 (((binintersectSubset2) =>
% 102.48/17.13 (((binintersectSubset3) =>
% 102.48/17.13 (((binintersectER) =>
% 102.48/17.13 (((disjointsetsI1) =>
% 102.48/17.13 (((binintersectRsub) =>
% 102.48/17.13 (((binintersectSubset4) =>
% 102.48/17.13 (((binintersectSubset1) =>
% 102.48/17.13 (((bs114d) =>
% 102.48/17.13 (((setminusI) =>
% 102.48/17.13 (((setminusEL) =>
% 102.48/17.13 (((setminusER) =>
% 102.48/17.13 (((setminusSubset2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusERneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusELneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusILneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusIRneg) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusLsub) =>
% 102.48/17.13 ((
% 102.48/17.13 (setminusSubset1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffE) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffI2) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg1) =>
% 102.48/17.13 ((
% 102.48/17.13 (symdiffIneg2) =>
% 102.48/17.13 ((
% 102.48/17.13 (secondinupair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairIR) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairiskpair) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairp) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsubset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowerset) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletoninpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairset2E) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairsubunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairinpowunion) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem2) =>
% 102.48/17.13 ((
% 102.48/17.13 (ubforcartprodlem3) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair1) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempair) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionE2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton1) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setunionsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1E1) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I) =>
% 102.48/17.13 ((
% 102.48/17.13 (ex1I2) =>
% 102.48/17.13 ((
% 102.48/17.13 (singletonsuniq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL1) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (theprop) =>
% 102.48/17.13 ((
% 102.48/17.13 (kfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstin) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjL) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR11) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR12) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR1) =>
% 102.48/17.13 ((
% 102.48/17.13 (upairequniteq) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR2) =>
% 102.48/17.13 ((
% 102.48/17.13 (setukpairinjR) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndsingleton) =>
% 102.48/17.13 ((
% 102.48/17.13 (ksndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (kpairsurjEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndin) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemEL) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodpairmemER) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodmempaircEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodfstpairEq) =>
% 102.48/17.13 ((
% 102.48/17.13 (cartprodsndpairEq) =>
% 102.48/17.13 ((
% 102.48/17.14 (cartprodpairsurjEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrI) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrSub) =>
% 102.48/17.14 ((
% 102.48/17.14 (setOfPairsIsBReln) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrERa) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrEL1) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrEL2) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrER) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcImageSingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (apProp) =>
% 102.48/17.14 ((
% 102.48/17.14 (app) =>
% 102.48/17.14 ((
% 102.48/17.14 (infuncsetfunc) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2p) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcinfuncset) =>
% 102.48/17.14 ((
% 102.48/17.14 (lamProp) =>
% 102.48/17.14 ((
% 102.48/17.14 (lamp) =>
% 102.48/17.14 ((
% 102.48/17.14 (lam2p) =>
% 102.48/17.14 ((
% 102.48/17.14 (brelnall1) =>
% 102.48/17.14 ((
% 102.48/17.14 (brelnall2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1E2) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp3) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcextLem) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp4) =>
% 102.48/17.14 ((
% 102.48/17.14 (subbreln) =>
% 102.48/17.14 ((
% 102.48/17.14 (eqbreln) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcext) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcext2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2apEq1) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2apEq2) =>
% 102.48/17.14 ((
% 102.48/17.14 (beta1) =>
% 102.48/17.14 ((
% 102.48/17.14 (eta1) =>
% 102.48/17.14 ((
% 102.48/17.14 (lam2lamEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (beta2) =>
% 102.48/17.14 ((
% 102.48/17.14 (eta2) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalseProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalseProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ifSingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (ifp) =>
% 102.48/17.14 ((
% 102.48/17.14 (theeq) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrue) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalse) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueorfalse) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (setextT) =>
% 102.48/17.14 ((
% 102.48/17.14 (subsetTI) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetTI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetTE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectTELcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectTERcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT1) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT2) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT3) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementSub1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementSub2) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTnotintersectT) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementImpComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementSubsetComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementInPowersetComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (contraSubsetComplement) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTcontraSubset) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTILcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTIRcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInUnion) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInUnion2) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInIntersectUnions) =>
% 102.48/17.14 ((
% 102.48/17.14 (intersectInPowersetIntersectUnions) =>
% 102.48/17.14 ((
% 102.48/17.14 (inComplementUnionImpNotIn1) =>
% 102.48/17.14 ((
% 102.48/17.14 (inComplementUnionImpInComplement1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTE) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTEcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2a1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementUnionInPowersetComplement) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2a2) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan1a) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan1b) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan1) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2a) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2b2) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2b) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule0) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule1) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule2) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule3) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule4) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_1) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_2) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_3) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_4) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_5) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1all2) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1SetBreln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (choice2fnsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (setOfPairsIsBReln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1all1) =>
% 102.48/17.14 ((
% 102.48/17.14 (subbreln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (eqbreln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1invprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1invI) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1invE) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compI) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compE) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compEex) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionIL) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionIR) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionI) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionE) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionEcases) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionCommutes) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2Ex) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2W) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2A) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2B) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1Ex) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1Ex1) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1Equiv) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1E) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1I) =>
% 102.48/17.14 ((
% 102.48/17.14 (injFuncInInjFuncSet) =>
% 102.48/17.14 ((
% 102.48/17.14 (injFuncSetFuncIn) =>
% 102.48/17.14 ((
% 102.48/17.14 (injFuncSetFuncInj) =>
% 102.48/17.14 ((
% 102.48/17.14 (surjFuncSetFuncIn) =>
% 102.48/17.14 ((
% 102.48/17.14 (surjFuncSetFuncSurj) =>
% 102.48/17.14 ((
% 102.48/17.14 (leftInvIsSurj) =>
% 102.48/17.14 ((
% 102.48/17.14 (surjCantorThm) =>
% 102.48/17.14 ((
% 102.48/17.14 (foundation2) =>
% 102.48/17.14 ((
% 102.48/17.14 (notinself) =>
% 102.48/17.14 ((
% 102.48/17.14 (notinself2) =>
% 102.48/17.14 ((
% 102.48/17.14 (omegaSp) =>
% 102.48/17.14 ((
% 102.48/17.14 (omegaSclos) =>
% 102.48/17.14 ((
% 102.48/17.14 (peano0notS) =>
% 102.48/17.14 ((
% 102.48/17.14 (peanoSinj) =>
% 102.48/17.14 ((
% 102.48/17.14 (transitivesetOp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintTransitive) =>
% 102.48/17.14 ((
% 102.48/17.14 (transitivesetOp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionTransitive) =>
% 102.48/17.14 ((
% 102.48/17.14 (ordinalMinLem1) =>
% 102.48/17.14 ((
% 102.48/17.14 (!!) @ (
% 102.48/17.14 ^[Y0 : $i]:
% 102.48/17.14 ((
% 102.48/17.14 (ordinal @
% 102.48/17.14 Y0) =>
% 102.48/17.14 ((
% 102.48/17.14 (!!) @ (
% 102.48/17.14 ^[Y1 : $i]:
% 102.48/17.14 ((
% 102.48/17.14 (!!) @ (
% 102.48/17.14 ^[Y2 : $i]:
% 102.48/17.14 ((
% 102.48/17.14 (in @
% 102.48/17.14 Y2 @
% 102.48/17.14 Y0) =>
% 102.48/17.14 ((
% 102.48/17.14 (in @
% 102.48/17.14 Y1 @
% 102.48/17.14 Y2) =>
% 102.48/17.14 (in @
% 102.48/17.14 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl857])).
% 102.48/17.14 thf(zip_derived_cl872, plain,
% 102.48/17.14 (~ (((powersetI1) =>
% 102.48/17.14 (((powersetE1) =>
% 102.48/17.14 (((inPowerset) =>
% 102.48/17.14 (((powersetsubset) =>
% 102.48/17.14 (((sepInPowerset) =>
% 102.48/17.14 (((sepSubset) =>
% 102.48/17.14 (((binunionIL) =>
% 102.48/17.14 (((upairset2IR) =>
% 102.48/17.14 (((binunionIR) =>
% 102.48/17.14 (((binunionEcases) =>
% 102.48/17.14 (((binunionE) =>
% 102.48/17.14 (((binunionLsub) =>
% 102.48/17.14 (((binunionRsub) =>
% 102.48/17.14 (((binintersectI) =>
% 102.48/17.14 (((binintersectSubset5) =>
% 102.48/17.14 (((binintersectEL) =>
% 102.48/17.14 (((binintersectLsub) =>
% 102.48/17.14 (((binintersectSubset2) =>
% 102.48/17.14 (((binintersectSubset3) =>
% 102.48/17.14 (((binintersectER) =>
% 102.48/17.14 (((disjointsetsI1) =>
% 102.48/17.14 (((binintersectRsub) =>
% 102.48/17.14 (((binintersectSubset4) =>
% 102.48/17.14 (((binintersectSubset1) =>
% 102.48/17.14 (((bs114d) =>
% 102.48/17.14 (((setminusI) =>
% 102.48/17.14 (((setminusEL) =>
% 102.48/17.14 (((setminusER) =>
% 102.48/17.14 (((setminusSubset2) =>
% 102.48/17.14 (((setminusERneg) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusELneg) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusILneg) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusIRneg) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusLsub) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusSubset1) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffE) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffI2) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffIneg1) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffIneg2) =>
% 102.48/17.14 ((
% 102.48/17.14 (secondinupair) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairIL) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairIR) =>
% 102.48/17.14 ((
% 102.48/17.14 (kpairiskpair) =>
% 102.48/17.14 ((
% 102.48/17.14 (kpairp) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletonsubset) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletoninpowerset) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletoninpowunion) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairset2E) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairsubunion) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairinpowunion) =>
% 102.48/17.14 ((
% 102.48/17.14 (ubforcartprodlem1) =>
% 102.48/17.14 ((
% 102.48/17.14 (ubforcartprodlem2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ubforcartprodlem3) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairin) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodmempair1) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodmempair) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionE2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionsingleton1) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionsingleton2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletonprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1E1) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1I) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1I2) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletonsuniq) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjL1) =>
% 102.48/17.14 ((
% 102.48/17.14 (kfstsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (theprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (kfstpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodfstin) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjL2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjL) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR11) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR12) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR1) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairequniteq) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR) =>
% 102.48/17.14 ((
% 102.48/17.14 (ksndsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (ksndpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (kpairsurjEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodsndin) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairmemEL) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairmemER) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodmempaircEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodfstpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodsndpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairsurjEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrI) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrSub) =>
% 102.48/17.14 ((
% 102.48/17.14 (setOfPairsIsBReln) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrERa) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrEL1) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrEL2) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrER) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcImageSingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (apProp) =>
% 102.48/17.14 ((
% 102.48/17.14 (app) =>
% 102.48/17.14 ((
% 102.48/17.14 (infuncsetfunc) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2p) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcinfuncset) =>
% 102.48/17.14 ((
% 102.48/17.14 (lamProp) =>
% 102.48/17.14 ((
% 102.48/17.14 (lamp) =>
% 102.48/17.14 ((
% 102.48/17.14 (lam2p) =>
% 102.48/17.14 ((
% 102.48/17.14 (brelnall1) =>
% 102.48/17.14 ((
% 102.48/17.14 (brelnall2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1E2) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp3) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcextLem) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp4) =>
% 102.48/17.14 ((
% 102.48/17.14 (subbreln) =>
% 102.48/17.14 ((
% 102.48/17.14 (eqbreln) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcext) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcext2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2apEq1) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2apEq2) =>
% 102.48/17.14 ((
% 102.48/17.14 (beta1) =>
% 102.48/17.14 ((
% 102.48/17.14 (eta1) =>
% 102.48/17.14 ((
% 102.48/17.14 (lam2lamEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (beta2) =>
% 102.48/17.14 ((
% 102.48/17.14 (eta2) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalseProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalseProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ifSingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (ifp) =>
% 102.48/17.14 ((
% 102.48/17.14 (theeq) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrue) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalse) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueorfalse) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (setextT) =>
% 102.48/17.14 ((
% 102.48/17.14 (subsetTI) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetTI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetTE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectTELcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectTERcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT1) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT2) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT3) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementSub1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementSub2) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTnotintersectT) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementImpComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementSubsetComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementInPowersetComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (contraSubsetComplement) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTcontraSubset) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTILcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTIRcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInUnion) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInUnion2) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInIntersectUnions) =>
% 102.48/17.14 ((
% 102.48/17.14 (intersectInPowersetIntersectUnions) =>
% 102.48/17.14 ((
% 102.48/17.14 (inComplementUnionImpNotIn1) =>
% 102.48/17.14 ((
% 102.48/17.14 (inComplementUnionImpInComplement1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTE) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTEcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2a1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementUnionInPowersetComplement) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2a2) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan1a) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan1b) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan1) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2a) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2b2) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2b) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule0) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule1) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule2) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule3) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule4) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_1) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_2) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_3) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_4) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_5) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1all2) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1SetBreln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (choice2fnsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (setOfPairsIsBReln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1all1) =>
% 102.48/17.14 ((
% 102.48/17.14 (subbreln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (eqbreln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1invprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1invI) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1invE) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compI) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compE) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compEex) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionIL) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionIR) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionI) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionE) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionEcases) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionCommutes) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2Ex) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2W) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2A) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2B) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1Ex) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1Ex1) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1Equiv) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1E) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1I) =>
% 102.48/17.14 ((
% 102.48/17.14 (injFuncInInjFuncSet) =>
% 102.48/17.14 ((
% 102.48/17.14 (injFuncSetFuncIn) =>
% 102.48/17.14 ((
% 102.48/17.14 (injFuncSetFuncInj) =>
% 102.48/17.14 ((
% 102.48/17.14 (surjFuncSetFuncIn) =>
% 102.48/17.14 ((
% 102.48/17.14 (surjFuncSetFuncSurj) =>
% 102.48/17.14 ((
% 102.48/17.14 (leftInvIsSurj) =>
% 102.48/17.14 ((
% 102.48/17.14 (surjCantorThm) =>
% 102.48/17.14 ((
% 102.48/17.14 (foundation2) =>
% 102.48/17.14 ((
% 102.48/17.14 (notinself) =>
% 102.48/17.14 ((
% 102.48/17.14 (notinself2) =>
% 102.48/17.14 ((
% 102.48/17.14 (omegaSp) =>
% 102.48/17.14 ((
% 102.48/17.14 (omegaSclos) =>
% 102.48/17.14 ((
% 102.48/17.14 (peano0notS) =>
% 102.48/17.14 ((
% 102.48/17.14 (peanoSinj) =>
% 102.48/17.14 ((
% 102.48/17.14 (transitivesetOp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintTransitive) =>
% 102.48/17.14 ((
% 102.48/17.14 (transitivesetOp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionTransitive) =>
% 102.48/17.14 ((
% 102.48/17.14 (ordinalMinLem1) =>
% 102.48/17.14 ((
% 102.48/17.14 (!!) @ (
% 102.48/17.14 ^[Y0 : $i]:
% 102.48/17.14 ((
% 102.48/17.14 (ordinal @
% 102.48/17.14 Y0) =>
% 102.48/17.14 ((
% 102.48/17.14 (!!) @ (
% 102.48/17.14 ^[Y1 : $i]:
% 102.48/17.14 ((
% 102.48/17.14 (!!) @ (
% 102.48/17.14 ^[Y2 : $i]:
% 102.48/17.14 ((
% 102.48/17.14 (in @
% 102.48/17.14 Y2 @
% 102.48/17.14 Y0) =>
% 102.48/17.14 ((
% 102.48/17.14 (in @
% 102.48/17.14 Y1 @
% 102.48/17.14 Y2) =>
% 102.48/17.14 (in @
% 102.48/17.14 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl864])).
% 102.48/17.14 thf(zip_derived_cl879, plain,
% 102.48/17.14 (~ (((powersetE1) =>
% 102.48/17.14 (((inPowerset) =>
% 102.48/17.14 (((powersetsubset) =>
% 102.48/17.14 (((sepInPowerset) =>
% 102.48/17.14 (((sepSubset) =>
% 102.48/17.14 (((binunionIL) =>
% 102.48/17.14 (((upairset2IR) =>
% 102.48/17.14 (((binunionIR) =>
% 102.48/17.14 (((binunionEcases) =>
% 102.48/17.14 (((binunionE) =>
% 102.48/17.14 (((binunionLsub) =>
% 102.48/17.14 (((binunionRsub) =>
% 102.48/17.14 (((binintersectI) =>
% 102.48/17.14 (((binintersectSubset5) =>
% 102.48/17.14 (((binintersectEL) =>
% 102.48/17.14 (((binintersectLsub) =>
% 102.48/17.14 (((binintersectSubset2) =>
% 102.48/17.14 (((binintersectSubset3) =>
% 102.48/17.14 (((binintersectER) =>
% 102.48/17.14 (((disjointsetsI1) =>
% 102.48/17.14 (((binintersectRsub) =>
% 102.48/17.14 (((binintersectSubset4) =>
% 102.48/17.14 (((binintersectSubset1) =>
% 102.48/17.14 (((bs114d) =>
% 102.48/17.14 (((setminusI) =>
% 102.48/17.14 (((setminusEL) =>
% 102.48/17.14 (((setminusER) =>
% 102.48/17.14 (((setminusSubset2) =>
% 102.48/17.14 (((setminusERneg) =>
% 102.48/17.14 (((setminusELneg) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusILneg) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusIRneg) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusLsub) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusSubset1) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffE) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffI2) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffIneg1) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffIneg2) =>
% 102.48/17.14 ((
% 102.48/17.14 (secondinupair) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairIL) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairIR) =>
% 102.48/17.14 ((
% 102.48/17.14 (kpairiskpair) =>
% 102.48/17.14 ((
% 102.48/17.14 (kpairp) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletonsubset) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletoninpowerset) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletoninpowunion) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairset2E) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairsubunion) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairinpowunion) =>
% 102.48/17.14 ((
% 102.48/17.14 (ubforcartprodlem1) =>
% 102.48/17.14 ((
% 102.48/17.14 (ubforcartprodlem2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ubforcartprodlem3) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairin) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodmempair1) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodmempair) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionE2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionsingleton1) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionsingleton2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletonprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1E1) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1I) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1I2) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletonsuniq) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjL1) =>
% 102.48/17.14 ((
% 102.48/17.14 (kfstsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (theprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (kfstpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodfstin) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjL2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjL) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR11) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR12) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR1) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairequniteq) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR) =>
% 102.48/17.14 ((
% 102.48/17.14 (ksndsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (ksndpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (kpairsurjEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodsndin) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairmemEL) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairmemER) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodmempaircEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodfstpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodsndpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairsurjEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrI) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrSub) =>
% 102.48/17.14 ((
% 102.48/17.14 (setOfPairsIsBReln) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrERa) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrEL1) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrEL2) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrER) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcImageSingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (apProp) =>
% 102.48/17.14 ((
% 102.48/17.14 (app) =>
% 102.48/17.14 ((
% 102.48/17.14 (infuncsetfunc) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2p) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcinfuncset) =>
% 102.48/17.14 ((
% 102.48/17.14 (lamProp) =>
% 102.48/17.14 ((
% 102.48/17.14 (lamp) =>
% 102.48/17.14 ((
% 102.48/17.14 (lam2p) =>
% 102.48/17.14 ((
% 102.48/17.14 (brelnall1) =>
% 102.48/17.14 ((
% 102.48/17.14 (brelnall2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1E2) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp3) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcextLem) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp4) =>
% 102.48/17.14 ((
% 102.48/17.14 (subbreln) =>
% 102.48/17.14 ((
% 102.48/17.14 (eqbreln) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcext) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcext2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2apEq1) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2apEq2) =>
% 102.48/17.14 ((
% 102.48/17.14 (beta1) =>
% 102.48/17.14 ((
% 102.48/17.14 (eta1) =>
% 102.48/17.14 ((
% 102.48/17.14 (lam2lamEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (beta2) =>
% 102.48/17.14 ((
% 102.48/17.14 (eta2) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalseProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalseProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ifSingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (ifp) =>
% 102.48/17.14 ((
% 102.48/17.14 (theeq) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrue) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalse) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueorfalse) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (setextT) =>
% 102.48/17.14 ((
% 102.48/17.14 (subsetTI) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetTI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetTE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectTELcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectTERcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT1) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT2) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT3) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementSub1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementSub2) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTnotintersectT) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementImpComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementSubsetComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementInPowersetComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (contraSubsetComplement) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTcontraSubset) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTILcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTIRcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInUnion) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInUnion2) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInIntersectUnions) =>
% 102.48/17.14 ((
% 102.48/17.14 (intersectInPowersetIntersectUnions) =>
% 102.48/17.14 ((
% 102.48/17.14 (inComplementUnionImpNotIn1) =>
% 102.48/17.14 ((
% 102.48/17.14 (inComplementUnionImpInComplement1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTE) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTEcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2a1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementUnionInPowersetComplement) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2a2) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan1a) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan1b) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan1) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2a) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2b2) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2b) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule0) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule1) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule2) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule3) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule4) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_1) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_2) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_3) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_4) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_5) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1all2) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1SetBreln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (choice2fnsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (setOfPairsIsBReln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1all1) =>
% 102.48/17.14 ((
% 102.48/17.14 (subbreln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (eqbreln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1invprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1invI) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1invE) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compI) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compE) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compEex) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionIL) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionIR) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionI) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionE) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionEcases) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionCommutes) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2Ex) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2W) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2A) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2B) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1Ex) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1Ex1) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1Equiv) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1E) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1I) =>
% 102.48/17.14 ((
% 102.48/17.14 (injFuncInInjFuncSet) =>
% 102.48/17.14 ((
% 102.48/17.14 (injFuncSetFuncIn) =>
% 102.48/17.14 ((
% 102.48/17.14 (injFuncSetFuncInj) =>
% 102.48/17.14 ((
% 102.48/17.14 (surjFuncSetFuncIn) =>
% 102.48/17.14 ((
% 102.48/17.14 (surjFuncSetFuncSurj) =>
% 102.48/17.14 ((
% 102.48/17.14 (leftInvIsSurj) =>
% 102.48/17.14 ((
% 102.48/17.14 (surjCantorThm) =>
% 102.48/17.14 ((
% 102.48/17.14 (foundation2) =>
% 102.48/17.14 ((
% 102.48/17.14 (notinself) =>
% 102.48/17.14 ((
% 102.48/17.14 (notinself2) =>
% 102.48/17.14 ((
% 102.48/17.14 (omegaSp) =>
% 102.48/17.14 ((
% 102.48/17.14 (omegaSclos) =>
% 102.48/17.14 ((
% 102.48/17.14 (peano0notS) =>
% 102.48/17.14 ((
% 102.48/17.14 (peanoSinj) =>
% 102.48/17.14 ((
% 102.48/17.14 (transitivesetOp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintTransitive) =>
% 102.48/17.14 ((
% 102.48/17.14 (transitivesetOp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionTransitive) =>
% 102.48/17.14 ((
% 102.48/17.14 (ordinalMinLem1) =>
% 102.48/17.14 ((
% 102.48/17.14 (!!) @ (
% 102.48/17.14 ^[Y0 : $i]:
% 102.48/17.14 ((
% 102.48/17.14 (ordinal @
% 102.48/17.14 Y0) =>
% 102.48/17.14 ((
% 102.48/17.14 (!!) @ (
% 102.48/17.14 ^[Y1 : $i]:
% 102.48/17.14 ((
% 102.48/17.14 (!!) @ (
% 102.48/17.14 ^[Y2 : $i]:
% 102.48/17.14 ((
% 102.48/17.14 (in @
% 102.48/17.14 Y2 @
% 102.48/17.14 Y0) =>
% 102.48/17.14 ((
% 102.48/17.14 (in @
% 102.48/17.14 Y1 @
% 102.48/17.14 Y2) =>
% 102.48/17.14 (in @
% 102.48/17.14 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl872])).
% 102.48/17.14 thf(zip_derived_cl886, plain,
% 102.48/17.14 (~ (((inPowerset) =>
% 102.48/17.14 (((powersetsubset) =>
% 102.48/17.14 (((sepInPowerset) =>
% 102.48/17.14 (((sepSubset) =>
% 102.48/17.14 (((binunionIL) =>
% 102.48/17.14 (((upairset2IR) =>
% 102.48/17.14 (((binunionIR) =>
% 102.48/17.14 (((binunionEcases) =>
% 102.48/17.14 (((binunionE) =>
% 102.48/17.14 (((binunionLsub) =>
% 102.48/17.14 (((binunionRsub) =>
% 102.48/17.14 (((binintersectI) =>
% 102.48/17.14 (((binintersectSubset5) =>
% 102.48/17.14 (((binintersectEL) =>
% 102.48/17.14 (((binintersectLsub) =>
% 102.48/17.14 (((binintersectSubset2) =>
% 102.48/17.14 (((binintersectSubset3) =>
% 102.48/17.14 (((binintersectER) =>
% 102.48/17.14 (((disjointsetsI1) =>
% 102.48/17.14 (((binintersectRsub) =>
% 102.48/17.14 (((binintersectSubset4) =>
% 102.48/17.14 (((binintersectSubset1) =>
% 102.48/17.14 (((bs114d) =>
% 102.48/17.14 (((setminusI) =>
% 102.48/17.14 (((setminusEL) =>
% 102.48/17.14 (((setminusER) =>
% 102.48/17.14 (((setminusSubset2) =>
% 102.48/17.14 (((setminusERneg) =>
% 102.48/17.14 (((setminusELneg) =>
% 102.48/17.14 (((setminusILneg) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusIRneg) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusLsub) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusSubset1) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffE) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffI2) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffIneg1) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffIneg2) =>
% 102.48/17.14 ((
% 102.48/17.14 (secondinupair) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairIL) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairIR) =>
% 102.48/17.14 ((
% 102.48/17.14 (kpairiskpair) =>
% 102.48/17.14 ((
% 102.48/17.14 (kpairp) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletonsubset) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletoninpowerset) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletoninpowunion) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairset2E) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairsubunion) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairinpowunion) =>
% 102.48/17.14 ((
% 102.48/17.14 (ubforcartprodlem1) =>
% 102.48/17.14 ((
% 102.48/17.14 (ubforcartprodlem2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ubforcartprodlem3) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairin) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodmempair1) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodmempair) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionE2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionsingleton1) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionsingleton2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletonprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1E1) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1I) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1I2) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletonsuniq) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjL1) =>
% 102.48/17.14 ((
% 102.48/17.14 (kfstsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (theprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (kfstpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodfstin) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjL2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjL) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR11) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR12) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR1) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairequniteq) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR) =>
% 102.48/17.14 ((
% 102.48/17.14 (ksndsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (ksndpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (kpairsurjEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodsndin) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairmemEL) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairmemER) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodmempaircEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodfstpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodsndpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairsurjEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrI) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrSub) =>
% 102.48/17.14 ((
% 102.48/17.14 (setOfPairsIsBReln) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrERa) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrEL1) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrEL2) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrER) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcImageSingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (apProp) =>
% 102.48/17.14 ((
% 102.48/17.14 (app) =>
% 102.48/17.14 ((
% 102.48/17.14 (infuncsetfunc) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2p) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcinfuncset) =>
% 102.48/17.14 ((
% 102.48/17.14 (lamProp) =>
% 102.48/17.14 ((
% 102.48/17.14 (lamp) =>
% 102.48/17.14 ((
% 102.48/17.14 (lam2p) =>
% 102.48/17.14 ((
% 102.48/17.14 (brelnall1) =>
% 102.48/17.14 ((
% 102.48/17.14 (brelnall2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1E2) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp3) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcextLem) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp4) =>
% 102.48/17.14 ((
% 102.48/17.14 (subbreln) =>
% 102.48/17.14 ((
% 102.48/17.14 (eqbreln) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcext) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcext2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2apEq1) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2apEq2) =>
% 102.48/17.14 ((
% 102.48/17.14 (beta1) =>
% 102.48/17.14 ((
% 102.48/17.14 (eta1) =>
% 102.48/17.14 ((
% 102.48/17.14 (lam2lamEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (beta2) =>
% 102.48/17.14 ((
% 102.48/17.14 (eta2) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalseProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalseProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ifSingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (ifp) =>
% 102.48/17.14 ((
% 102.48/17.14 (theeq) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrue) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalse) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueorfalse) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (setextT) =>
% 102.48/17.14 ((
% 102.48/17.14 (subsetTI) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetTI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetTE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectTELcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectTERcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT1) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT2) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT3) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementSub1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementSub2) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTnotintersectT) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementImpComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementSubsetComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementInPowersetComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (contraSubsetComplement) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTcontraSubset) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTILcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTIRcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInUnion) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInUnion2) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInIntersectUnions) =>
% 102.48/17.14 ((
% 102.48/17.14 (intersectInPowersetIntersectUnions) =>
% 102.48/17.14 ((
% 102.48/17.14 (inComplementUnionImpNotIn1) =>
% 102.48/17.14 ((
% 102.48/17.14 (inComplementUnionImpInComplement1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTE) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTEcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2a1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementUnionInPowersetComplement) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2a2) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan1a) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan1b) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan1) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2a) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2b2) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2b) =>
% 102.48/17.14 ((
% 102.48/17.14 (demorgan2) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule0) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule1) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule2) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule3) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz13rule4) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_1) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_2) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_3) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_4) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz1_5) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1all2) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1SetBreln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (choice2fnsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (setOfPairsIsBReln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1all1) =>
% 102.48/17.14 ((
% 102.48/17.14 (subbreln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (eqbreln1) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1invprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1invI) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1invE) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compI) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compE) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1compEex) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionIL) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionIR) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionI) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionE) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionEcases) =>
% 102.48/17.14 ((
% 102.48/17.14 (breln1unionCommutes) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2Ex) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2W) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2A) =>
% 102.48/17.14 ((
% 102.48/17.14 (woz2B) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1Ex) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1Ex1) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1Equiv) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1E) =>
% 102.48/17.14 ((
% 102.48/17.14 (image1I) =>
% 102.48/17.14 ((
% 102.48/17.14 (injFuncInInjFuncSet) =>
% 102.48/17.14 ((
% 102.48/17.14 (injFuncSetFuncIn) =>
% 102.48/17.14 ((
% 102.48/17.14 (injFuncSetFuncInj) =>
% 102.48/17.14 ((
% 102.48/17.14 (surjFuncSetFuncIn) =>
% 102.48/17.14 ((
% 102.48/17.14 (surjFuncSetFuncSurj) =>
% 102.48/17.14 ((
% 102.48/17.14 (leftInvIsSurj) =>
% 102.48/17.14 ((
% 102.48/17.14 (surjCantorThm) =>
% 102.48/17.14 ((
% 102.48/17.14 (foundation2) =>
% 102.48/17.14 ((
% 102.48/17.14 (notinself) =>
% 102.48/17.14 ((
% 102.48/17.14 (notinself2) =>
% 102.48/17.14 ((
% 102.48/17.14 (omegaSp) =>
% 102.48/17.14 ((
% 102.48/17.14 (omegaSclos) =>
% 102.48/17.14 ((
% 102.48/17.14 (peano0notS) =>
% 102.48/17.14 ((
% 102.48/17.14 (peanoSinj) =>
% 102.48/17.14 ((
% 102.48/17.14 (transitivesetOp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintTransitive) =>
% 102.48/17.14 ((
% 102.48/17.14 (transitivesetOp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionTransitive) =>
% 102.48/17.14 ((
% 102.48/17.14 (ordinalMinLem1) =>
% 102.48/17.14 ((
% 102.48/17.14 (!!) @ (
% 102.48/17.14 ^[Y0 : $i]:
% 102.48/17.14 ((
% 102.48/17.14 (ordinal @
% 102.48/17.14 Y0) =>
% 102.48/17.14 ((
% 102.48/17.14 (!!) @ (
% 102.48/17.14 ^[Y1 : $i]:
% 102.48/17.14 ((
% 102.48/17.14 (!!) @ (
% 102.48/17.14 ^[Y2 : $i]:
% 102.48/17.14 ((
% 102.48/17.14 (in @
% 102.48/17.14 Y2 @
% 102.48/17.14 Y0) =>
% 102.48/17.14 ((
% 102.48/17.14 (in @
% 102.48/17.14 Y1 @
% 102.48/17.14 Y2) =>
% 102.48/17.14 (in @
% 102.48/17.14 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.48/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl879])).
% 102.48/17.14 thf(zip_derived_cl892, plain,
% 102.48/17.14 (~ (((powersetsubset) =>
% 102.48/17.14 (((sepInPowerset) =>
% 102.48/17.14 (((sepSubset) =>
% 102.48/17.14 (((binunionIL) =>
% 102.48/17.14 (((upairset2IR) =>
% 102.48/17.14 (((binunionIR) =>
% 102.48/17.14 (((binunionEcases) =>
% 102.48/17.14 (((binunionE) =>
% 102.48/17.14 (((binunionLsub) =>
% 102.48/17.14 (((binunionRsub) =>
% 102.48/17.14 (((binintersectI) =>
% 102.48/17.14 (((binintersectSubset5) =>
% 102.48/17.14 (((binintersectEL) =>
% 102.48/17.14 (((binintersectLsub) =>
% 102.48/17.14 (((binintersectSubset2) =>
% 102.48/17.14 (((binintersectSubset3) =>
% 102.48/17.14 (((binintersectER) =>
% 102.48/17.14 (((disjointsetsI1) =>
% 102.48/17.14 (((binintersectRsub) =>
% 102.48/17.14 (((binintersectSubset4) =>
% 102.48/17.14 (((binintersectSubset1) =>
% 102.48/17.14 (((bs114d) =>
% 102.48/17.14 (((setminusI) =>
% 102.48/17.14 (((setminusEL) =>
% 102.48/17.14 (((setminusER) =>
% 102.48/17.14 (((setminusSubset2) =>
% 102.48/17.14 (((setminusERneg) =>
% 102.48/17.14 (((setminusELneg) =>
% 102.48/17.14 (((setminusILneg) =>
% 102.48/17.14 (((setminusIRneg) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusLsub) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusSubset1) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffE) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffI2) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffIneg1) =>
% 102.48/17.14 ((
% 102.48/17.14 (symdiffIneg2) =>
% 102.48/17.14 ((
% 102.48/17.14 (secondinupair) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairIL) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairIR) =>
% 102.48/17.14 ((
% 102.48/17.14 (kpairiskpair) =>
% 102.48/17.14 ((
% 102.48/17.14 (kpairp) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletonsubset) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletoninpowerset) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletoninpowunion) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairset2E) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairsubunion) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairinpowunion) =>
% 102.48/17.14 ((
% 102.48/17.14 (ubforcartprodlem1) =>
% 102.48/17.14 ((
% 102.48/17.14 (ubforcartprodlem2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ubforcartprodlem3) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairin) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodmempair1) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodmempair) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionE2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionsingleton1) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionsingleton2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setunionsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletonprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1E1) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1I) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1I2) =>
% 102.48/17.14 ((
% 102.48/17.14 (singletonsuniq) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjL1) =>
% 102.48/17.14 ((
% 102.48/17.14 (kfstsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (theprop) =>
% 102.48/17.14 ((
% 102.48/17.14 (kfstpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodfstin) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjL2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjL) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR11) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR12) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR1) =>
% 102.48/17.14 ((
% 102.48/17.14 (upairequniteq) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR2) =>
% 102.48/17.14 ((
% 102.48/17.14 (setukpairinjR) =>
% 102.48/17.14 ((
% 102.48/17.14 (ksndsingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (ksndpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (kpairsurjEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodsndin) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairmemEL) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairmemER) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodmempaircEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodfstpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodsndpairEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (cartprodpairsurjEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrI) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrSub) =>
% 102.48/17.14 ((
% 102.48/17.14 (setOfPairsIsBReln) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrERa) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrEL1) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrEL2) =>
% 102.48/17.14 ((
% 102.48/17.14 (dpsetconstrER) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcImageSingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (apProp) =>
% 102.48/17.14 ((
% 102.48/17.14 (app) =>
% 102.48/17.14 ((
% 102.48/17.14 (infuncsetfunc) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2p) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcinfuncset) =>
% 102.48/17.14 ((
% 102.48/17.14 (lamProp) =>
% 102.48/17.14 ((
% 102.48/17.14 (lamp) =>
% 102.48/17.14 ((
% 102.48/17.14 (lam2p) =>
% 102.48/17.14 ((
% 102.48/17.14 (brelnall1) =>
% 102.48/17.14 ((
% 102.48/17.14 (brelnall2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ex1E2) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp3) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcextLem) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcGraphProp4) =>
% 102.48/17.14 ((
% 102.48/17.14 (subbreln) =>
% 102.48/17.14 ((
% 102.48/17.14 (eqbreln) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcext) =>
% 102.48/17.14 ((
% 102.48/17.14 (funcext2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2apEq1) =>
% 102.48/17.14 ((
% 102.48/17.14 (ap2apEq2) =>
% 102.48/17.14 ((
% 102.48/17.14 (beta1) =>
% 102.48/17.14 ((
% 102.48/17.14 (eta1) =>
% 102.48/17.14 ((
% 102.48/17.14 (lam2lamEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (beta2) =>
% 102.48/17.14 ((
% 102.48/17.14 (eta2) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalseProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalseProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueProp1) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueProp2) =>
% 102.48/17.14 ((
% 102.48/17.14 (ifSingleton) =>
% 102.48/17.14 ((
% 102.48/17.14 (ifp) =>
% 102.48/17.14 ((
% 102.48/17.14 (theeq) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrue) =>
% 102.48/17.14 ((
% 102.48/17.14 (iffalse) =>
% 102.48/17.14 ((
% 102.48/17.14 (iftrueorfalse) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (setminusT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementT_lem) =>
% 102.48/17.14 ((
% 102.48/17.14 (setextT) =>
% 102.48/17.14 ((
% 102.48/17.14 (subsetTI) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetTI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (powersetTE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectTELcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (binintersectTERcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT1) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT2) =>
% 102.48/17.14 ((
% 102.48/17.14 (contrasubsetT3) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementI1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementE1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementSub1) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementSub2) =>
% 102.48/17.14 ((
% 102.48/17.14 (doubleComplementEq) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTnotintersectT) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementImpComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementSubsetComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementInPowersetComplementIntersect) =>
% 102.48/17.14 ((
% 102.48/17.14 (contraSubsetComplement) =>
% 102.48/17.14 ((
% 102.48/17.14 (complementTcontraSubset) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTILcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTIRcontra) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInUnion) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInUnion2) =>
% 102.48/17.14 ((
% 102.48/17.14 (inIntersectImpInIntersectUnions) =>
% 102.48/17.14 ((
% 102.48/17.14 (intersectInPowersetIntersectUnions) =>
% 102.48/17.14 ((
% 102.48/17.14 (inComplementUnionImpNotIn1) =>
% 102.48/17.14 ((
% 102.48/17.14 (inComplementUnionImpInComplement1) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTE) =>
% 102.48/17.14 ((
% 102.48/17.14 (binunionTEcontra) =>
% 102.48/17.14 ((
% 102.63/17.14 (demorgan2a1) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementUnionInPowersetComplement) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2a2) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan1a) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan1b) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan1) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2a) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2b2) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2b) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule0) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule1) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule2) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule3) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule4) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_1) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_2) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_3) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_4) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_5) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1all2) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1SetBreln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (choice2fnsingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (setOfPairsIsBReln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1all1) =>
% 102.63/17.14 ((
% 102.63/17.14 (subbreln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (eqbreln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1invprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1invI) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1invE) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1compprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1compI) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1compE) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1compEex) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionIL) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionIR) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionI) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionE) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionEcases) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionCommutes) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz2Ex) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz2W) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz2A) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz2B) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1Ex) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1Ex1) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1Equiv) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1E) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1I) =>
% 102.63/17.14 ((
% 102.63/17.14 (injFuncInInjFuncSet) =>
% 102.63/17.14 ((
% 102.63/17.14 (injFuncSetFuncIn) =>
% 102.63/17.14 ((
% 102.63/17.14 (injFuncSetFuncInj) =>
% 102.63/17.14 ((
% 102.63/17.14 (surjFuncSetFuncIn) =>
% 102.63/17.14 ((
% 102.63/17.14 (surjFuncSetFuncSurj) =>
% 102.63/17.14 ((
% 102.63/17.14 (leftInvIsSurj) =>
% 102.63/17.14 ((
% 102.63/17.14 (surjCantorThm) =>
% 102.63/17.14 ((
% 102.63/17.14 (foundation2) =>
% 102.63/17.14 ((
% 102.63/17.14 (notinself) =>
% 102.63/17.14 ((
% 102.63/17.14 (notinself2) =>
% 102.63/17.14 ((
% 102.63/17.14 (omegaSp) =>
% 102.63/17.14 ((
% 102.63/17.14 (omegaSclos) =>
% 102.63/17.14 ((
% 102.63/17.14 (peano0notS) =>
% 102.63/17.14 ((
% 102.63/17.14 (peanoSinj) =>
% 102.63/17.14 ((
% 102.63/17.14 (transitivesetOp1) =>
% 102.63/17.14 ((
% 102.63/17.14 (binintTransitive) =>
% 102.63/17.14 ((
% 102.63/17.14 (transitivesetOp2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionTransitive) =>
% 102.63/17.14 ((
% 102.63/17.14 (ordinalMinLem1) =>
% 102.63/17.14 ((
% 102.63/17.14 (!!) @ (
% 102.63/17.14 ^[Y0 : $i]:
% 102.63/17.14 ((
% 102.63/17.14 (ordinal @
% 102.63/17.14 Y0) =>
% 102.63/17.14 ((
% 102.63/17.14 (!!) @ (
% 102.63/17.14 ^[Y1 : $i]:
% 102.63/17.14 ((
% 102.63/17.14 (!!) @ (
% 102.63/17.14 ^[Y2 : $i]:
% 102.63/17.14 ((
% 102.63/17.14 (in @
% 102.63/17.14 Y2 @
% 102.63/17.14 Y0) =>
% 102.63/17.14 ((
% 102.63/17.14 (in @
% 102.63/17.14 Y1 @
% 102.63/17.14 Y2) =>
% 102.63/17.14 (in @
% 102.63/17.14 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl886])).
% 102.63/17.14 thf(zip_derived_cl899, plain,
% 102.63/17.14 (~ (((sepInPowerset) =>
% 102.63/17.14 (((sepSubset) =>
% 102.63/17.14 (((binunionIL) =>
% 102.63/17.14 (((upairset2IR) =>
% 102.63/17.14 (((binunionIR) =>
% 102.63/17.14 (((binunionEcases) =>
% 102.63/17.14 (((binunionE) =>
% 102.63/17.14 (((binunionLsub) =>
% 102.63/17.14 (((binunionRsub) =>
% 102.63/17.14 (((binintersectI) =>
% 102.63/17.14 (((binintersectSubset5) =>
% 102.63/17.14 (((binintersectEL) =>
% 102.63/17.14 (((binintersectLsub) =>
% 102.63/17.14 (((binintersectSubset2) =>
% 102.63/17.14 (((binintersectSubset3) =>
% 102.63/17.14 (((binintersectER) =>
% 102.63/17.14 (((disjointsetsI1) =>
% 102.63/17.14 (((binintersectRsub) =>
% 102.63/17.14 (((binintersectSubset4) =>
% 102.63/17.14 (((binintersectSubset1) =>
% 102.63/17.14 (((bs114d) =>
% 102.63/17.14 (((setminusI) =>
% 102.63/17.14 (((setminusEL) =>
% 102.63/17.14 (((setminusER) =>
% 102.63/17.14 (((setminusSubset2) =>
% 102.63/17.14 (((setminusERneg) =>
% 102.63/17.14 (((setminusELneg) =>
% 102.63/17.14 (((setminusILneg) =>
% 102.63/17.14 (((setminusIRneg) =>
% 102.63/17.14 (((setminusLsub) =>
% 102.63/17.14 ((
% 102.63/17.14 (setminusSubset1) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffE) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffI1) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffI2) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffIneg1) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffIneg2) =>
% 102.63/17.14 ((
% 102.63/17.14 (secondinupair) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairIL) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairIR) =>
% 102.63/17.14 ((
% 102.63/17.14 (kpairiskpair) =>
% 102.63/17.14 ((
% 102.63/17.14 (kpairp) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletonsubset) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletoninpowerset) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletoninpowunion) =>
% 102.63/17.14 ((
% 102.63/17.14 (upairset2E) =>
% 102.63/17.14 ((
% 102.63/17.14 (upairsubunion) =>
% 102.63/17.14 ((
% 102.63/17.14 (upairinpowunion) =>
% 102.63/17.14 ((
% 102.63/17.14 (ubforcartprodlem1) =>
% 102.63/17.14 ((
% 102.63/17.14 (ubforcartprodlem2) =>
% 102.63/17.14 ((
% 102.63/17.14 (ubforcartprodlem3) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodpairin) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodmempair1) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodmempair) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionE2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionsingleton1) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionsingleton2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionsingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletonprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (ex1E1) =>
% 102.63/17.14 ((
% 102.63/17.14 (ex1I) =>
% 102.63/17.14 ((
% 102.63/17.14 (ex1I2) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletonsuniq) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjL1) =>
% 102.63/17.14 ((
% 102.63/17.14 (kfstsingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (theprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (kfstpairEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodfstin) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjL2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjL) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR11) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR12) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR1) =>
% 102.63/17.14 ((
% 102.63/17.14 (upairequniteq) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR) =>
% 102.63/17.14 ((
% 102.63/17.14 (ksndsingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (ksndpairEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (kpairsurjEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodsndin) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodpairmemEL) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodpairmemER) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodmempaircEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodfstpairEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodsndpairEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodpairsurjEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrI) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrSub) =>
% 102.63/17.14 ((
% 102.63/17.14 (setOfPairsIsBReln) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrERa) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrEL1) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrEL2) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrER) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcImageSingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (apProp) =>
% 102.63/17.14 ((
% 102.63/17.14 (app) =>
% 102.63/17.14 ((
% 102.63/17.14 (infuncsetfunc) =>
% 102.63/17.14 ((
% 102.63/17.14 (ap2p) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcinfuncset) =>
% 102.63/17.14 ((
% 102.63/17.14 (lamProp) =>
% 102.63/17.14 ((
% 102.63/17.14 (lamp) =>
% 102.63/17.14 ((
% 102.63/17.14 (lam2p) =>
% 102.63/17.14 ((
% 102.63/17.14 (brelnall1) =>
% 102.63/17.14 ((
% 102.63/17.14 (brelnall2) =>
% 102.63/17.14 ((
% 102.63/17.14 (ex1E2) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcGraphProp1) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcGraphProp3) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcGraphProp2) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcextLem) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcGraphProp4) =>
% 102.63/17.14 ((
% 102.63/17.14 (subbreln) =>
% 102.63/17.14 ((
% 102.63/17.14 (eqbreln) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcext) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcext2) =>
% 102.63/17.14 ((
% 102.63/17.14 (ap2apEq1) =>
% 102.63/17.14 ((
% 102.63/17.14 (ap2apEq2) =>
% 102.63/17.14 ((
% 102.63/17.14 (beta1) =>
% 102.63/17.14 ((
% 102.63/17.14 (eta1) =>
% 102.63/17.14 ((
% 102.63/17.14 (lam2lamEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (beta2) =>
% 102.63/17.14 ((
% 102.63/17.14 (eta2) =>
% 102.63/17.14 ((
% 102.63/17.14 (iffalseProp1) =>
% 102.63/17.14 ((
% 102.63/17.14 (iffalseProp2) =>
% 102.63/17.14 ((
% 102.63/17.14 (iftrueProp1) =>
% 102.63/17.14 ((
% 102.63/17.14 (iftrueProp2) =>
% 102.63/17.14 ((
% 102.63/17.14 (ifSingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (ifp) =>
% 102.63/17.14 ((
% 102.63/17.14 (theeq) =>
% 102.63/17.14 ((
% 102.63/17.14 (iftrue) =>
% 102.63/17.14 ((
% 102.63/17.14 (iffalse) =>
% 102.63/17.14 ((
% 102.63/17.14 (iftrueorfalse) =>
% 102.63/17.14 ((
% 102.63/17.14 (binintersectT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (powersetT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (setminusT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (setextT) =>
% 102.63/17.14 ((
% 102.63/17.14 (subsetTI) =>
% 102.63/17.14 ((
% 102.63/17.14 (powersetTI1) =>
% 102.63/17.14 ((
% 102.63/17.14 (powersetTE1) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementTI1) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementTE1) =>
% 102.63/17.14 ((
% 102.63/17.14 (binintersectTELcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (binintersectTERcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (contrasubsetT) =>
% 102.63/17.14 ((
% 102.63/17.14 (contrasubsetT1) =>
% 102.63/17.14 ((
% 102.63/17.14 (contrasubsetT2) =>
% 102.63/17.14 ((
% 102.63/17.14 (contrasubsetT3) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementI1) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementE1) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementSub1) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementSub2) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementTnotintersectT) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementImpComplementIntersect) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementSubsetComplementIntersect) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementInPowersetComplementIntersect) =>
% 102.63/17.14 ((
% 102.63/17.14 (contraSubsetComplement) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementTcontraSubset) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionTILcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionTIRcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (inIntersectImpInUnion) =>
% 102.63/17.14 ((
% 102.63/17.14 (inIntersectImpInUnion2) =>
% 102.63/17.14 ((
% 102.63/17.14 (inIntersectImpInIntersectUnions) =>
% 102.63/17.14 ((
% 102.63/17.14 (intersectInPowersetIntersectUnions) =>
% 102.63/17.14 ((
% 102.63/17.14 (inComplementUnionImpNotIn1) =>
% 102.63/17.14 ((
% 102.63/17.14 (inComplementUnionImpInComplement1) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionTE) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionTEcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2a1) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementUnionInPowersetComplement) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2a2) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan1a) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan1b) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan1) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2a) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2b2) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2b) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule0) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule1) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule2) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule3) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule4) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_1) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_2) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_3) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_4) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_5) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1all2) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1SetBreln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (choice2fnsingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (setOfPairsIsBReln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1all1) =>
% 102.63/17.14 ((
% 102.63/17.14 (subbreln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (eqbreln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1invprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1invI) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1invE) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1compprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1compI) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1compE) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1compEex) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionIL) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionIR) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionI) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionE) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionEcases) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionCommutes) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz2Ex) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz2W) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz2A) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz2B) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1Ex) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1Ex1) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1Equiv) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1E) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1I) =>
% 102.63/17.14 ((
% 102.63/17.14 (injFuncInInjFuncSet) =>
% 102.63/17.14 ((
% 102.63/17.14 (injFuncSetFuncIn) =>
% 102.63/17.14 ((
% 102.63/17.14 (injFuncSetFuncInj) =>
% 102.63/17.14 ((
% 102.63/17.14 (surjFuncSetFuncIn) =>
% 102.63/17.14 ((
% 102.63/17.14 (surjFuncSetFuncSurj) =>
% 102.63/17.14 ((
% 102.63/17.14 (leftInvIsSurj) =>
% 102.63/17.14 ((
% 102.63/17.14 (surjCantorThm) =>
% 102.63/17.14 ((
% 102.63/17.14 (foundation2) =>
% 102.63/17.14 ((
% 102.63/17.14 (notinself) =>
% 102.63/17.14 ((
% 102.63/17.14 (notinself2) =>
% 102.63/17.14 ((
% 102.63/17.14 (omegaSp) =>
% 102.63/17.14 ((
% 102.63/17.14 (omegaSclos) =>
% 102.63/17.14 ((
% 102.63/17.14 (peano0notS) =>
% 102.63/17.14 ((
% 102.63/17.14 (peanoSinj) =>
% 102.63/17.14 ((
% 102.63/17.14 (transitivesetOp1) =>
% 102.63/17.14 ((
% 102.63/17.14 (binintTransitive) =>
% 102.63/17.14 ((
% 102.63/17.14 (transitivesetOp2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionTransitive) =>
% 102.63/17.14 ((
% 102.63/17.14 (ordinalMinLem1) =>
% 102.63/17.14 ((
% 102.63/17.14 (!!) @ (
% 102.63/17.14 ^[Y0 : $i]:
% 102.63/17.14 ((
% 102.63/17.14 (ordinal @
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% 102.63/17.14 ((
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% 102.63/17.14 ^[Y2 : $i]:
% 102.63/17.14 ((
% 102.63/17.14 (in @
% 102.63/17.14 Y2 @
% 102.63/17.14 Y0) =>
% 102.63/17.14 ((
% 102.63/17.14 (in @
% 102.63/17.14 Y1 @
% 102.63/17.14 Y2) =>
% 102.63/17.14 (in @
% 102.63/17.14 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl892])).
% 102.63/17.14 thf(zip_derived_cl906, plain,
% 102.63/17.14 (~ (((sepSubset) =>
% 102.63/17.14 (((binunionIL) =>
% 102.63/17.14 (((upairset2IR) =>
% 102.63/17.14 (((binunionIR) =>
% 102.63/17.14 (((binunionEcases) =>
% 102.63/17.14 (((binunionE) =>
% 102.63/17.14 (((binunionLsub) =>
% 102.63/17.14 (((binunionRsub) =>
% 102.63/17.14 (((binintersectI) =>
% 102.63/17.14 (((binintersectSubset5) =>
% 102.63/17.14 (((binintersectEL) =>
% 102.63/17.14 (((binintersectLsub) =>
% 102.63/17.14 (((binintersectSubset2) =>
% 102.63/17.14 (((binintersectSubset3) =>
% 102.63/17.14 (((binintersectER) =>
% 102.63/17.14 (((disjointsetsI1) =>
% 102.63/17.14 (((binintersectRsub) =>
% 102.63/17.14 (((binintersectSubset4) =>
% 102.63/17.14 (((binintersectSubset1) =>
% 102.63/17.14 (((bs114d) =>
% 102.63/17.14 (((setminusI) =>
% 102.63/17.14 (((setminusEL) =>
% 102.63/17.14 (((setminusER) =>
% 102.63/17.14 (((setminusSubset2) =>
% 102.63/17.14 (((setminusERneg) =>
% 102.63/17.14 (((setminusELneg) =>
% 102.63/17.14 (((setminusILneg) =>
% 102.63/17.14 (((setminusIRneg) =>
% 102.63/17.14 (((setminusLsub) =>
% 102.63/17.14 (((setminusSubset1) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffE) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffI1) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffI2) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffIneg1) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffIneg2) =>
% 102.63/17.14 ((
% 102.63/17.14 (secondinupair) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairIL) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairIR) =>
% 102.63/17.14 ((
% 102.63/17.14 (kpairiskpair) =>
% 102.63/17.14 ((
% 102.63/17.14 (kpairp) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletonsubset) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletoninpowerset) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletoninpowunion) =>
% 102.63/17.14 ((
% 102.63/17.14 (upairset2E) =>
% 102.63/17.14 ((
% 102.63/17.14 (upairsubunion) =>
% 102.63/17.14 ((
% 102.63/17.14 (upairinpowunion) =>
% 102.63/17.14 ((
% 102.63/17.14 (ubforcartprodlem1) =>
% 102.63/17.14 ((
% 102.63/17.14 (ubforcartprodlem2) =>
% 102.63/17.14 ((
% 102.63/17.14 (ubforcartprodlem3) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodpairin) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodmempair1) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodmempair) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionE2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionsingleton1) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionsingleton2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionsingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletonprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (ex1E1) =>
% 102.63/17.14 ((
% 102.63/17.14 (ex1I) =>
% 102.63/17.14 ((
% 102.63/17.14 (ex1I2) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletonsuniq) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjL1) =>
% 102.63/17.14 ((
% 102.63/17.14 (kfstsingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (theprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (kfstpairEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodfstin) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjL2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjL) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR11) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR12) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR1) =>
% 102.63/17.14 ((
% 102.63/17.14 (upairequniteq) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR) =>
% 102.63/17.14 ((
% 102.63/17.14 (ksndsingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (ksndpairEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (kpairsurjEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodsndin) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodpairmemEL) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodpairmemER) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodmempaircEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodfstpairEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodsndpairEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodpairsurjEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrI) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrSub) =>
% 102.63/17.14 ((
% 102.63/17.14 (setOfPairsIsBReln) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrERa) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrEL1) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrEL2) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrER) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcImageSingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (apProp) =>
% 102.63/17.14 ((
% 102.63/17.14 (app) =>
% 102.63/17.14 ((
% 102.63/17.14 (infuncsetfunc) =>
% 102.63/17.14 ((
% 102.63/17.14 (ap2p) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcinfuncset) =>
% 102.63/17.14 ((
% 102.63/17.14 (lamProp) =>
% 102.63/17.14 ((
% 102.63/17.14 (lamp) =>
% 102.63/17.14 ((
% 102.63/17.14 (lam2p) =>
% 102.63/17.14 ((
% 102.63/17.14 (brelnall1) =>
% 102.63/17.14 ((
% 102.63/17.14 (brelnall2) =>
% 102.63/17.14 ((
% 102.63/17.14 (ex1E2) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcGraphProp1) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcGraphProp3) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcGraphProp2) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcextLem) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcGraphProp4) =>
% 102.63/17.14 ((
% 102.63/17.14 (subbreln) =>
% 102.63/17.14 ((
% 102.63/17.14 (eqbreln) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcext) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcext2) =>
% 102.63/17.14 ((
% 102.63/17.14 (ap2apEq1) =>
% 102.63/17.14 ((
% 102.63/17.14 (ap2apEq2) =>
% 102.63/17.14 ((
% 102.63/17.14 (beta1) =>
% 102.63/17.14 ((
% 102.63/17.14 (eta1) =>
% 102.63/17.14 ((
% 102.63/17.14 (lam2lamEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (beta2) =>
% 102.63/17.14 ((
% 102.63/17.14 (eta2) =>
% 102.63/17.14 ((
% 102.63/17.14 (iffalseProp1) =>
% 102.63/17.14 ((
% 102.63/17.14 (iffalseProp2) =>
% 102.63/17.14 ((
% 102.63/17.14 (iftrueProp1) =>
% 102.63/17.14 ((
% 102.63/17.14 (iftrueProp2) =>
% 102.63/17.14 ((
% 102.63/17.14 (ifSingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (ifp) =>
% 102.63/17.14 ((
% 102.63/17.14 (theeq) =>
% 102.63/17.14 ((
% 102.63/17.14 (iftrue) =>
% 102.63/17.14 ((
% 102.63/17.14 (iffalse) =>
% 102.63/17.14 ((
% 102.63/17.14 (iftrueorfalse) =>
% 102.63/17.14 ((
% 102.63/17.14 (binintersectT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (powersetT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (setminusT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (setextT) =>
% 102.63/17.14 ((
% 102.63/17.14 (subsetTI) =>
% 102.63/17.14 ((
% 102.63/17.14 (powersetTI1) =>
% 102.63/17.14 ((
% 102.63/17.14 (powersetTE1) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementTI1) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementTE1) =>
% 102.63/17.14 ((
% 102.63/17.14 (binintersectTELcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (binintersectTERcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (contrasubsetT) =>
% 102.63/17.14 ((
% 102.63/17.14 (contrasubsetT1) =>
% 102.63/17.14 ((
% 102.63/17.14 (contrasubsetT2) =>
% 102.63/17.14 ((
% 102.63/17.14 (contrasubsetT3) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementI1) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementE1) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementSub1) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementSub2) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementTnotintersectT) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementImpComplementIntersect) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementSubsetComplementIntersect) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementInPowersetComplementIntersect) =>
% 102.63/17.14 ((
% 102.63/17.14 (contraSubsetComplement) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementTcontraSubset) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionTILcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionTIRcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (inIntersectImpInUnion) =>
% 102.63/17.14 ((
% 102.63/17.14 (inIntersectImpInUnion2) =>
% 102.63/17.14 ((
% 102.63/17.14 (inIntersectImpInIntersectUnions) =>
% 102.63/17.14 ((
% 102.63/17.14 (intersectInPowersetIntersectUnions) =>
% 102.63/17.14 ((
% 102.63/17.14 (inComplementUnionImpNotIn1) =>
% 102.63/17.14 ((
% 102.63/17.14 (inComplementUnionImpInComplement1) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionTE) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionTEcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2a1) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementUnionInPowersetComplement) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2a2) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan1a) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan1b) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan1) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2a) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2b2) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2b) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule0) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule1) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule2) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule3) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule4) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_1) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_2) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_3) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_4) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_5) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1all2) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1SetBreln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (choice2fnsingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (setOfPairsIsBReln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1all1) =>
% 102.63/17.14 ((
% 102.63/17.14 (subbreln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (eqbreln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1invprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1invI) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1invE) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1compprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1compI) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1compE) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1compEex) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionIL) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionIR) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionI) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionE) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionEcases) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1unionCommutes) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz2Ex) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz2W) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz2A) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz2B) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1Ex) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1Ex1) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1Equiv) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1E) =>
% 102.63/17.14 ((
% 102.63/17.14 (image1I) =>
% 102.63/17.14 ((
% 102.63/17.14 (injFuncInInjFuncSet) =>
% 102.63/17.14 ((
% 102.63/17.14 (injFuncSetFuncIn) =>
% 102.63/17.14 ((
% 102.63/17.14 (injFuncSetFuncInj) =>
% 102.63/17.14 ((
% 102.63/17.14 (surjFuncSetFuncIn) =>
% 102.63/17.14 ((
% 102.63/17.14 (surjFuncSetFuncSurj) =>
% 102.63/17.14 ((
% 102.63/17.14 (leftInvIsSurj) =>
% 102.63/17.14 ((
% 102.63/17.14 (surjCantorThm) =>
% 102.63/17.14 ((
% 102.63/17.14 (foundation2) =>
% 102.63/17.14 ((
% 102.63/17.14 (notinself) =>
% 102.63/17.14 ((
% 102.63/17.14 (notinself2) =>
% 102.63/17.14 ((
% 102.63/17.14 (omegaSp) =>
% 102.63/17.14 ((
% 102.63/17.14 (omegaSclos) =>
% 102.63/17.14 ((
% 102.63/17.14 (peano0notS) =>
% 102.63/17.14 ((
% 102.63/17.14 (peanoSinj) =>
% 102.63/17.14 ((
% 102.63/17.14 (transitivesetOp1) =>
% 102.63/17.14 ((
% 102.63/17.14 (binintTransitive) =>
% 102.63/17.14 ((
% 102.63/17.14 (transitivesetOp2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionTransitive) =>
% 102.63/17.14 ((
% 102.63/17.14 (ordinalMinLem1) =>
% 102.63/17.14 ((
% 102.63/17.14 (!!) @ (
% 102.63/17.14 ^[Y0 : $i]:
% 102.63/17.14 ((
% 102.63/17.14 (ordinal @
% 102.63/17.14 Y0) =>
% 102.63/17.14 ((
% 102.63/17.14 (!!) @ (
% 102.63/17.14 ^[Y1 : $i]:
% 102.63/17.14 ((
% 102.63/17.14 (!!) @ (
% 102.63/17.14 ^[Y2 : $i]:
% 102.63/17.14 ((
% 102.63/17.14 (in @
% 102.63/17.14 Y2 @
% 102.63/17.14 Y0) =>
% 102.63/17.14 ((
% 102.63/17.14 (in @
% 102.63/17.14 Y1 @
% 102.63/17.14 Y2) =>
% 102.63/17.14 (in @
% 102.63/17.14 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl899])).
% 102.63/17.14 thf(zip_derived_cl911, plain,
% 102.63/17.14 (~ (((binunionIL) =>
% 102.63/17.14 (((upairset2IR) =>
% 102.63/17.14 (((binunionIR) =>
% 102.63/17.14 (((binunionEcases) =>
% 102.63/17.14 (((binunionE) =>
% 102.63/17.14 (((binunionLsub) =>
% 102.63/17.14 (((binunionRsub) =>
% 102.63/17.14 (((binintersectI) =>
% 102.63/17.14 (((binintersectSubset5) =>
% 102.63/17.14 (((binintersectEL) =>
% 102.63/17.14 (((binintersectLsub) =>
% 102.63/17.14 (((binintersectSubset2) =>
% 102.63/17.14 (((binintersectSubset3) =>
% 102.63/17.14 (((binintersectER) =>
% 102.63/17.14 (((disjointsetsI1) =>
% 102.63/17.14 (((binintersectRsub) =>
% 102.63/17.14 (((binintersectSubset4) =>
% 102.63/17.14 (((binintersectSubset1) =>
% 102.63/17.14 (((bs114d) =>
% 102.63/17.14 (((setminusI) =>
% 102.63/17.14 (((setminusEL) =>
% 102.63/17.14 (((setminusER) =>
% 102.63/17.14 (((setminusSubset2) =>
% 102.63/17.14 (((setminusERneg) =>
% 102.63/17.14 (((setminusELneg) =>
% 102.63/17.14 (((setminusILneg) =>
% 102.63/17.14 (((setminusIRneg) =>
% 102.63/17.14 (((setminusLsub) =>
% 102.63/17.14 (((setminusSubset1) =>
% 102.63/17.14 (((symdiffE) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffI1) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffI2) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffIneg1) =>
% 102.63/17.14 ((
% 102.63/17.14 (symdiffIneg2) =>
% 102.63/17.14 ((
% 102.63/17.14 (secondinupair) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairIL) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairIR) =>
% 102.63/17.14 ((
% 102.63/17.14 (kpairiskpair) =>
% 102.63/17.14 ((
% 102.63/17.14 (kpairp) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletonsubset) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletoninpowerset) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletoninpowunion) =>
% 102.63/17.14 ((
% 102.63/17.14 (upairset2E) =>
% 102.63/17.14 ((
% 102.63/17.14 (upairsubunion) =>
% 102.63/17.14 ((
% 102.63/17.14 (upairinpowunion) =>
% 102.63/17.14 ((
% 102.63/17.14 (ubforcartprodlem1) =>
% 102.63/17.14 ((
% 102.63/17.14 (ubforcartprodlem2) =>
% 102.63/17.14 ((
% 102.63/17.14 (ubforcartprodlem3) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodpairin) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodmempair1) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodmempair) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionE2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionsingleton1) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionsingleton2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setunionsingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletonprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (ex1E1) =>
% 102.63/17.14 ((
% 102.63/17.14 (ex1I) =>
% 102.63/17.14 ((
% 102.63/17.14 (ex1I2) =>
% 102.63/17.14 ((
% 102.63/17.14 (singletonsuniq) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjL1) =>
% 102.63/17.14 ((
% 102.63/17.14 (kfstsingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (theprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (kfstpairEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodfstin) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjL2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjL) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR11) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR12) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR1) =>
% 102.63/17.14 ((
% 102.63/17.14 (upairequniteq) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR2) =>
% 102.63/17.14 ((
% 102.63/17.14 (setukpairinjR) =>
% 102.63/17.14 ((
% 102.63/17.14 (ksndsingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (ksndpairEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (kpairsurjEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodsndin) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodpairmemEL) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodpairmemER) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodmempaircEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodfstpairEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodsndpairEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (cartprodpairsurjEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrI) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrSub) =>
% 102.63/17.14 ((
% 102.63/17.14 (setOfPairsIsBReln) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrERa) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrEL1) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrEL2) =>
% 102.63/17.14 ((
% 102.63/17.14 (dpsetconstrER) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcImageSingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (apProp) =>
% 102.63/17.14 ((
% 102.63/17.14 (app) =>
% 102.63/17.14 ((
% 102.63/17.14 (infuncsetfunc) =>
% 102.63/17.14 ((
% 102.63/17.14 (ap2p) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcinfuncset) =>
% 102.63/17.14 ((
% 102.63/17.14 (lamProp) =>
% 102.63/17.14 ((
% 102.63/17.14 (lamp) =>
% 102.63/17.14 ((
% 102.63/17.14 (lam2p) =>
% 102.63/17.14 ((
% 102.63/17.14 (brelnall1) =>
% 102.63/17.14 ((
% 102.63/17.14 (brelnall2) =>
% 102.63/17.14 ((
% 102.63/17.14 (ex1E2) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcGraphProp1) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcGraphProp3) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcGraphProp2) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcextLem) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcGraphProp4) =>
% 102.63/17.14 ((
% 102.63/17.14 (subbreln) =>
% 102.63/17.14 ((
% 102.63/17.14 (eqbreln) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcext) =>
% 102.63/17.14 ((
% 102.63/17.14 (funcext2) =>
% 102.63/17.14 ((
% 102.63/17.14 (ap2apEq1) =>
% 102.63/17.14 ((
% 102.63/17.14 (ap2apEq2) =>
% 102.63/17.14 ((
% 102.63/17.14 (beta1) =>
% 102.63/17.14 ((
% 102.63/17.14 (eta1) =>
% 102.63/17.14 ((
% 102.63/17.14 (lam2lamEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (beta2) =>
% 102.63/17.14 ((
% 102.63/17.14 (eta2) =>
% 102.63/17.14 ((
% 102.63/17.14 (iffalseProp1) =>
% 102.63/17.14 ((
% 102.63/17.14 (iffalseProp2) =>
% 102.63/17.14 ((
% 102.63/17.14 (iftrueProp1) =>
% 102.63/17.14 ((
% 102.63/17.14 (iftrueProp2) =>
% 102.63/17.14 ((
% 102.63/17.14 (ifSingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (ifp) =>
% 102.63/17.14 ((
% 102.63/17.14 (theeq) =>
% 102.63/17.14 ((
% 102.63/17.14 (iftrue) =>
% 102.63/17.14 ((
% 102.63/17.14 (iffalse) =>
% 102.63/17.14 ((
% 102.63/17.14 (iftrueorfalse) =>
% 102.63/17.14 ((
% 102.63/17.14 (binintersectT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (powersetT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (setminusT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementT_lem) =>
% 102.63/17.14 ((
% 102.63/17.14 (setextT) =>
% 102.63/17.14 ((
% 102.63/17.14 (subsetTI) =>
% 102.63/17.14 ((
% 102.63/17.14 (powersetTI1) =>
% 102.63/17.14 ((
% 102.63/17.14 (powersetTE1) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementTI1) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementTE1) =>
% 102.63/17.14 ((
% 102.63/17.14 (binintersectTELcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (binintersectTERcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (contrasubsetT) =>
% 102.63/17.14 ((
% 102.63/17.14 (contrasubsetT1) =>
% 102.63/17.14 ((
% 102.63/17.14 (contrasubsetT2) =>
% 102.63/17.14 ((
% 102.63/17.14 (contrasubsetT3) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementI1) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementE1) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementSub1) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementSub2) =>
% 102.63/17.14 ((
% 102.63/17.14 (doubleComplementEq) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementTnotintersectT) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementImpComplementIntersect) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementSubsetComplementIntersect) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementInPowersetComplementIntersect) =>
% 102.63/17.14 ((
% 102.63/17.14 (contraSubsetComplement) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementTcontraSubset) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionTILcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionTIRcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (inIntersectImpInUnion) =>
% 102.63/17.14 ((
% 102.63/17.14 (inIntersectImpInUnion2) =>
% 102.63/17.14 ((
% 102.63/17.14 (inIntersectImpInIntersectUnions) =>
% 102.63/17.14 ((
% 102.63/17.14 (intersectInPowersetIntersectUnions) =>
% 102.63/17.14 ((
% 102.63/17.14 (inComplementUnionImpNotIn1) =>
% 102.63/17.14 ((
% 102.63/17.14 (inComplementUnionImpInComplement1) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionTE) =>
% 102.63/17.14 ((
% 102.63/17.14 (binunionTEcontra) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2a1) =>
% 102.63/17.14 ((
% 102.63/17.14 (complementUnionInPowersetComplement) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2a2) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan1a) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan1b) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan1) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2a) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2b2) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2b) =>
% 102.63/17.14 ((
% 102.63/17.14 (demorgan2) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule0) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule1) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule2) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule3) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz13rule4) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_1) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_2) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_3) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_4) =>
% 102.63/17.14 ((
% 102.63/17.14 (woz1_5) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1all2) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1SetBreln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (choice2fnsingleton) =>
% 102.63/17.14 ((
% 102.63/17.14 (setOfPairsIsBReln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1all1) =>
% 102.63/17.14 ((
% 102.63/17.14 (subbreln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (eqbreln1) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1invprop) =>
% 102.63/17.14 ((
% 102.63/17.14 (breln1invI) =>
% 102.63/17.14 ((
% 102.63/17.15 (breln1invE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compEex) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIL) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionEcases) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionCommutes) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2Ex) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2W) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2A) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2B) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Ex) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Ex1) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Equiv) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1E) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncInInjFuncSet) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncInj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (leftInvIsSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjCantorThm) =>
% 102.63/17.15 ((
% 102.63/17.15 (foundation2) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself2) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSp) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSclos) =>
% 102.63/17.15 ((
% 102.63/17.15 (peano0notS) =>
% 102.63/17.15 ((
% 102.63/17.15 (peanoSinj) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (ordinalMinLem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y0 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (ordinal @
% 102.63/17.15 Y0) =>
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y1 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y2 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y2 @
% 102.63/17.15 Y0) =>
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @
% 102.63/17.15 Y2) =>
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl906])).
% 102.63/17.15 thf(zip_derived_cl917, plain,
% 102.63/17.15 (~ (((upairset2IR) =>
% 102.63/17.15 (((binunionIR) =>
% 102.63/17.15 (((binunionEcases) =>
% 102.63/17.15 (((binunionE) =>
% 102.63/17.15 (((binunionLsub) =>
% 102.63/17.15 (((binunionRsub) =>
% 102.63/17.15 (((binintersectI) =>
% 102.63/17.15 (((binintersectSubset5) =>
% 102.63/17.15 (((binintersectEL) =>
% 102.63/17.15 (((binintersectLsub) =>
% 102.63/17.15 (((binintersectSubset2) =>
% 102.63/17.15 (((binintersectSubset3) =>
% 102.63/17.15 (((binintersectER) =>
% 102.63/17.15 (((disjointsetsI1) =>
% 102.63/17.15 (((binintersectRsub) =>
% 102.63/17.15 (((binintersectSubset4) =>
% 102.63/17.15 (((binintersectSubset1) =>
% 102.63/17.15 (((bs114d) =>
% 102.63/17.15 (((setminusI) =>
% 102.63/17.15 (((setminusEL) =>
% 102.63/17.15 (((setminusER) =>
% 102.63/17.15 (((setminusSubset2) =>
% 102.63/17.15 (((setminusERneg) =>
% 102.63/17.15 (((setminusELneg) =>
% 102.63/17.15 (((setminusILneg) =>
% 102.63/17.15 (((setminusIRneg) =>
% 102.63/17.15 (((setminusLsub) =>
% 102.63/17.15 (((setminusSubset1) =>
% 102.63/17.15 (((symdiffE) =>
% 102.63/17.15 (((symdiffI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (symdiffI2) =>
% 102.63/17.15 ((
% 102.63/17.15 (symdiffIneg1) =>
% 102.63/17.15 ((
% 102.63/17.15 (symdiffIneg2) =>
% 102.63/17.15 ((
% 102.63/17.15 (secondinupair) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairIL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairiskpair) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairp) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowerset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairset2E) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairsubunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairinpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem3) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair1) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionE2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton1) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I2) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsuniq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (theprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstin) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR11) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR12) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR1) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairequniteq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemEL) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemER) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempaircEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrI) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrSub) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrERa) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrER) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcImageSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (apProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (app) =>
% 102.63/17.15 ((
% 102.63/17.15 (infuncsetfunc) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcinfuncset) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall1) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp3) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcextLem) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp4) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq2) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2lamEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifp) =>
% 102.63/17.15 ((
% 102.63/17.15 (theeq) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrue) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueorfalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setminusT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setextT) =>
% 102.63/17.15 ((
% 102.63/17.15 (subsetTI) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetTI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTELcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTERcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT1) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT2) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT3) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub2) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTnotintersectT) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementImpComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementSubsetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementInPowersetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (contraSubsetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTcontraSubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTILcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTIRcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion2) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (intersectInPowersetIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpNotIn1) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpInComplement1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTE) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTEcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementUnionInPowersetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1a) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2b2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule0) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule1) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule3) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule4) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_1) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_3) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_4) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_5) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1all2) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1SetBreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (choice2fnsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1all1) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compEex) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIL) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionEcases) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionCommutes) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2Ex) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2W) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2A) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2B) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Ex) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Ex1) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Equiv) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1E) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncInInjFuncSet) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncInj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (leftInvIsSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjCantorThm) =>
% 102.63/17.15 ((
% 102.63/17.15 (foundation2) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself2) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSp) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSclos) =>
% 102.63/17.15 ((
% 102.63/17.15 (peano0notS) =>
% 102.63/17.15 ((
% 102.63/17.15 (peanoSinj) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (ordinalMinLem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y0 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (ordinal @
% 102.63/17.15 Y0) =>
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y1 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y2 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y2 @
% 102.63/17.15 Y0) =>
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @
% 102.63/17.15 Y2) =>
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl911])).
% 102.63/17.15 thf(zip_derived_cl924, plain,
% 102.63/17.15 (~ (((binunionIR) =>
% 102.63/17.15 (((binunionEcases) =>
% 102.63/17.15 (((binunionE) =>
% 102.63/17.15 (((binunionLsub) =>
% 102.63/17.15 (((binunionRsub) =>
% 102.63/17.15 (((binintersectI) =>
% 102.63/17.15 (((binintersectSubset5) =>
% 102.63/17.15 (((binintersectEL) =>
% 102.63/17.15 (((binintersectLsub) =>
% 102.63/17.15 (((binintersectSubset2) =>
% 102.63/17.15 (((binintersectSubset3) =>
% 102.63/17.15 (((binintersectER) =>
% 102.63/17.15 (((disjointsetsI1) =>
% 102.63/17.15 (((binintersectRsub) =>
% 102.63/17.15 (((binintersectSubset4) =>
% 102.63/17.15 (((binintersectSubset1) =>
% 102.63/17.15 (((bs114d) =>
% 102.63/17.15 (((setminusI) =>
% 102.63/17.15 (((setminusEL) =>
% 102.63/17.15 (((setminusER) =>
% 102.63/17.15 (((setminusSubset2) =>
% 102.63/17.15 (((setminusERneg) =>
% 102.63/17.15 (((setminusELneg) =>
% 102.63/17.15 (((setminusILneg) =>
% 102.63/17.15 (((setminusIRneg) =>
% 102.63/17.15 (((setminusLsub) =>
% 102.63/17.15 (((setminusSubset1) =>
% 102.63/17.15 (((symdiffE) =>
% 102.63/17.15 (((symdiffI1) =>
% 102.63/17.15 (((symdiffI2) =>
% 102.63/17.15 ((
% 102.63/17.15 (symdiffIneg1) =>
% 102.63/17.15 ((
% 102.63/17.15 (symdiffIneg2) =>
% 102.63/17.15 ((
% 102.63/17.15 (secondinupair) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairIL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairiskpair) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairp) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowerset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairset2E) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairsubunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairinpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem3) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair1) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionE2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton1) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I2) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsuniq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (theprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstin) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR11) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR12) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR1) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairequniteq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemEL) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemER) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempaircEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrI) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrSub) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrERa) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrER) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcImageSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (apProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (app) =>
% 102.63/17.15 ((
% 102.63/17.15 (infuncsetfunc) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcinfuncset) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall1) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp3) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcextLem) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp4) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq2) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2lamEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifp) =>
% 102.63/17.15 ((
% 102.63/17.15 (theeq) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrue) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueorfalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setminusT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setextT) =>
% 102.63/17.15 ((
% 102.63/17.15 (subsetTI) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetTI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTELcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTERcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT1) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT2) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT3) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub2) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTnotintersectT) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementImpComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementSubsetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementInPowersetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (contraSubsetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTcontraSubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTILcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTIRcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion2) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (intersectInPowersetIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpNotIn1) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpInComplement1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTE) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTEcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementUnionInPowersetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1a) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2b2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule0) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule1) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule3) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule4) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_1) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_3) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_4) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_5) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1all2) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1SetBreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (choice2fnsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1all1) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compEex) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIL) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionEcases) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionCommutes) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2Ex) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2W) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2A) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2B) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Ex) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Ex1) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Equiv) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1E) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncInInjFuncSet) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncInj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (leftInvIsSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjCantorThm) =>
% 102.63/17.15 ((
% 102.63/17.15 (foundation2) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself2) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSp) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSclos) =>
% 102.63/17.15 ((
% 102.63/17.15 (peano0notS) =>
% 102.63/17.15 ((
% 102.63/17.15 (peanoSinj) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (ordinalMinLem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y0 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (ordinal @
% 102.63/17.15 Y0) =>
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y1 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y2 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y2 @
% 102.63/17.15 Y0) =>
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @
% 102.63/17.15 Y2) =>
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl917])).
% 102.63/17.15 thf(zip_derived_cl929, plain,
% 102.63/17.15 (~ (((binunionEcases) =>
% 102.63/17.15 (((binunionE) =>
% 102.63/17.15 (((binunionLsub) =>
% 102.63/17.15 (((binunionRsub) =>
% 102.63/17.15 (((binintersectI) =>
% 102.63/17.15 (((binintersectSubset5) =>
% 102.63/17.15 (((binintersectEL) =>
% 102.63/17.15 (((binintersectLsub) =>
% 102.63/17.15 (((binintersectSubset2) =>
% 102.63/17.15 (((binintersectSubset3) =>
% 102.63/17.15 (((binintersectER) =>
% 102.63/17.15 (((disjointsetsI1) =>
% 102.63/17.15 (((binintersectRsub) =>
% 102.63/17.15 (((binintersectSubset4) =>
% 102.63/17.15 (((binintersectSubset1) =>
% 102.63/17.15 (((bs114d) =>
% 102.63/17.15 (((setminusI) =>
% 102.63/17.15 (((setminusEL) =>
% 102.63/17.15 (((setminusER) =>
% 102.63/17.15 (((setminusSubset2) =>
% 102.63/17.15 (((setminusERneg) =>
% 102.63/17.15 (((setminusELneg) =>
% 102.63/17.15 (((setminusILneg) =>
% 102.63/17.15 (((setminusIRneg) =>
% 102.63/17.15 (((setminusLsub) =>
% 102.63/17.15 (((setminusSubset1) =>
% 102.63/17.15 (((symdiffE) =>
% 102.63/17.15 (((symdiffI1) =>
% 102.63/17.15 (((symdiffI2) =>
% 102.63/17.15 (((symdiffIneg1) =>
% 102.63/17.15 ((
% 102.63/17.15 (symdiffIneg2) =>
% 102.63/17.15 ((
% 102.63/17.15 (secondinupair) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairIL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairiskpair) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairp) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowerset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairset2E) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairsubunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairinpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem3) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair1) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionE2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton1) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I2) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsuniq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (theprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstin) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR11) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR12) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR1) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairequniteq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemEL) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemER) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempaircEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrI) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrSub) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrERa) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrER) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcImageSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (apProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (app) =>
% 102.63/17.15 ((
% 102.63/17.15 (infuncsetfunc) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcinfuncset) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall1) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp3) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcextLem) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp4) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq2) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2lamEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifp) =>
% 102.63/17.15 ((
% 102.63/17.15 (theeq) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrue) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueorfalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setminusT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setextT) =>
% 102.63/17.15 ((
% 102.63/17.15 (subsetTI) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetTI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTELcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTERcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT1) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT2) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT3) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub2) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTnotintersectT) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementImpComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementSubsetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementInPowersetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (contraSubsetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTcontraSubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTILcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTIRcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion2) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (intersectInPowersetIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpNotIn1) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpInComplement1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTE) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTEcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementUnionInPowersetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1a) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2b2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule0) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule1) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule3) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule4) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_1) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_3) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_4) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_5) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1all2) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1SetBreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (choice2fnsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1all1) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compEex) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIL) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionEcases) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionCommutes) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2Ex) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2W) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2A) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2B) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Ex) =>
% 102.63/17.15 ((
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% 102.63/17.15 ((
% 102.63/17.15 (image1Equiv) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1E) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncInInjFuncSet) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncInj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (leftInvIsSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjCantorThm) =>
% 102.63/17.15 ((
% 102.63/17.15 (foundation2) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself2) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSp) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSclos) =>
% 102.63/17.15 ((
% 102.63/17.15 (peano0notS) =>
% 102.63/17.15 ((
% 102.63/17.15 (peanoSinj) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (ordinalMinLem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y0 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (ordinal @
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% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y1 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y2 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (in @
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% 102.63/17.15 Y0) =>
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @
% 102.63/17.15 Y2) =>
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl924])).
% 102.63/17.15 thf(zip_derived_cl934, plain,
% 102.63/17.15 (~ (((binunionE) =>
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% 102.63/17.15 (((binunionRsub) =>
% 102.63/17.15 (((binintersectI) =>
% 102.63/17.15 (((binintersectSubset5) =>
% 102.63/17.15 (((binintersectEL) =>
% 102.63/17.15 (((binintersectLsub) =>
% 102.63/17.15 (((binintersectSubset2) =>
% 102.63/17.15 (((binintersectSubset3) =>
% 102.63/17.15 (((binintersectER) =>
% 102.63/17.15 (((disjointsetsI1) =>
% 102.63/17.15 (((binintersectRsub) =>
% 102.63/17.15 (((binintersectSubset4) =>
% 102.63/17.15 (((binintersectSubset1) =>
% 102.63/17.15 (((bs114d) =>
% 102.63/17.15 (((setminusI) =>
% 102.63/17.15 (((setminusEL) =>
% 102.63/17.15 (((setminusER) =>
% 102.63/17.15 (((setminusSubset2) =>
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% 102.63/17.15 (((setminusELneg) =>
% 102.63/17.15 (((setminusILneg) =>
% 102.63/17.15 (((setminusIRneg) =>
% 102.63/17.15 (((setminusLsub) =>
% 102.63/17.15 (((setminusSubset1) =>
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% 102.63/17.15 (((symdiffI1) =>
% 102.63/17.15 (((symdiffI2) =>
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% 102.63/17.15 (((symdiffIneg2) =>
% 102.63/17.15 ((
% 102.63/17.15 (secondinupair) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairIL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairiskpair) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairp) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowerset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairset2E) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairsubunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairinpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem3) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair1) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionE2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton1) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton2) =>
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% 102.63/17.15 (setunionsingleton) =>
% 102.63/17.15 ((
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% 102.63/17.15 (ex1E1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I2) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsuniq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (theprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstin) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR11) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR12) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR1) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairequniteq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemEL) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemER) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempaircEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrI) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrSub) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrERa) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrER) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcImageSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (apProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (app) =>
% 102.63/17.15 ((
% 102.63/17.15 (infuncsetfunc) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcinfuncset) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall1) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp3) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcextLem) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp4) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq2) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2lamEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifp) =>
% 102.63/17.15 ((
% 102.63/17.15 (theeq) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrue) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueorfalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setminusT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setextT) =>
% 102.63/17.15 ((
% 102.63/17.15 (subsetTI) =>
% 102.63/17.15 ((
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% 102.63/17.15 ((
% 102.63/17.15 (powersetTE1) =>
% 102.63/17.15 ((
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% 102.63/17.15 ((
% 102.63/17.15 (complementTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTELcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTERcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT1) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT2) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT3) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub2) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTnotintersectT) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementImpComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementSubsetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementInPowersetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (contraSubsetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTcontraSubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTILcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTIRcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion2) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (intersectInPowersetIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpNotIn1) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpInComplement1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTE) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTEcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementUnionInPowersetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1a) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1) =>
% 102.63/17.15 ((
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% 102.63/17.15 (demorgan2b2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule0) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule1) =>
% 102.63/17.15 ((
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% 102.63/17.15 ((
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% 102.63/17.15 ((
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% 102.63/17.15 ((
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% 102.63/17.15 ((
% 102.63/17.15 (breln1all2) =>
% 102.63/17.15 ((
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% 102.63/17.15 ((
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% 102.63/17.15 ((
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% 102.63/17.15 ((
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% 102.63/17.15 ((
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% 102.63/17.15 ((
% 102.63/17.15 (breln1unionI) =>
% 102.63/17.15 ((
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% 102.63/17.15 ((
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% 102.63/17.15 ((
% 102.63/17.15 (image1E) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncInInjFuncSet) =>
% 102.63/17.15 ((
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% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncInj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (leftInvIsSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjCantorThm) =>
% 102.63/17.15 ((
% 102.63/17.15 (foundation2) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself2) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSp) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSclos) =>
% 102.63/17.15 ((
% 102.63/17.15 (peano0notS) =>
% 102.63/17.15 ((
% 102.63/17.15 (peanoSinj) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (ordinalMinLem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y0 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (ordinal @
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% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y1 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y2 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y2 @
% 102.63/17.15 Y0) =>
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @
% 102.63/17.15 Y2) =>
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl929])).
% 102.63/17.15 thf(zip_derived_cl940, plain,
% 102.63/17.15 (~ (((binunionLsub) =>
% 102.63/17.15 (((binunionRsub) =>
% 102.63/17.15 (((binintersectI) =>
% 102.63/17.15 (((binintersectSubset5) =>
% 102.63/17.15 (((binintersectEL) =>
% 102.63/17.15 (((binintersectLsub) =>
% 102.63/17.15 (((binintersectSubset2) =>
% 102.63/17.15 (((binintersectSubset3) =>
% 102.63/17.15 (((binintersectER) =>
% 102.63/17.15 (((disjointsetsI1) =>
% 102.63/17.15 (((binintersectRsub) =>
% 102.63/17.15 (((binintersectSubset4) =>
% 102.63/17.15 (((binintersectSubset1) =>
% 102.63/17.15 (((bs114d) =>
% 102.63/17.15 (((setminusI) =>
% 102.63/17.15 (((setminusEL) =>
% 102.63/17.15 (((setminusER) =>
% 102.63/17.15 (((setminusSubset2) =>
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% 102.63/17.15 (((setminusELneg) =>
% 102.63/17.15 (((setminusILneg) =>
% 102.63/17.15 (((setminusIRneg) =>
% 102.63/17.15 (((setminusLsub) =>
% 102.63/17.15 (((setminusSubset1) =>
% 102.63/17.15 (((symdiffE) =>
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% 102.63/17.15 (((secondinupair) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairIL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairiskpair) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairp) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowerset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairset2E) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairsubunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairinpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem3) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair1) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionE2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton1) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I2) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsuniq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (theprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstin) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR11) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR12) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR1) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairequniteq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemEL) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemER) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempaircEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrI) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrSub) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrERa) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrER) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcImageSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (apProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (app) =>
% 102.63/17.15 ((
% 102.63/17.15 (infuncsetfunc) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcinfuncset) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall1) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp3) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcextLem) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp4) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq2) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2lamEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifp) =>
% 102.63/17.15 ((
% 102.63/17.15 (theeq) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrue) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueorfalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setminusT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setextT) =>
% 102.63/17.15 ((
% 102.63/17.15 (subsetTI) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetTI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTELcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTERcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT1) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT2) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT3) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub2) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTnotintersectT) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementImpComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementSubsetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementInPowersetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (contraSubsetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTcontraSubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTILcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTIRcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion2) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (intersectInPowersetIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpNotIn1) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpInComplement1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTE) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTEcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementUnionInPowersetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1a) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2b2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule0) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule1) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule3) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule4) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_1) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_3) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_4) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_5) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1all2) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1SetBreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (choice2fnsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1all1) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compEex) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIL) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionEcases) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionCommutes) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2Ex) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2W) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2A) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2B) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Ex) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Ex1) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Equiv) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1E) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncInInjFuncSet) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncInj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (leftInvIsSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjCantorThm) =>
% 102.63/17.15 ((
% 102.63/17.15 (foundation2) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself2) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSp) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSclos) =>
% 102.63/17.15 ((
% 102.63/17.15 (peano0notS) =>
% 102.63/17.15 ((
% 102.63/17.15 (peanoSinj) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (ordinalMinLem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y0 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (ordinal @
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% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y1 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y2 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y2 @
% 102.63/17.15 Y0) =>
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @
% 102.63/17.15 Y2) =>
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl934])).
% 102.63/17.15 thf(zip_derived_cl945, plain,
% 102.63/17.15 (~ (((binunionRsub) =>
% 102.63/17.15 (((binintersectI) =>
% 102.63/17.15 (((binintersectSubset5) =>
% 102.63/17.15 (((binintersectEL) =>
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% 102.63/17.15 (((binintersectSubset3) =>
% 102.63/17.15 (((binintersectER) =>
% 102.63/17.15 (((disjointsetsI1) =>
% 102.63/17.15 (((binintersectRsub) =>
% 102.63/17.15 (((binintersectSubset4) =>
% 102.63/17.15 (((binintersectSubset1) =>
% 102.63/17.15 (((bs114d) =>
% 102.63/17.15 (((setminusI) =>
% 102.63/17.15 (((setminusEL) =>
% 102.63/17.15 (((setminusER) =>
% 102.63/17.15 (((setminusSubset2) =>
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% 102.63/17.15 (((setminusELneg) =>
% 102.63/17.15 (((setminusILneg) =>
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% 102.63/17.15 (((setminusSubset1) =>
% 102.63/17.15 (((symdiffE) =>
% 102.63/17.15 (((symdiffI1) =>
% 102.63/17.15 (((symdiffI2) =>
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% 102.63/17.15 (((symdiffIneg2) =>
% 102.63/17.15 (((secondinupair) =>
% 102.63/17.15 (((setukpairIL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairiskpair) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairp) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowerset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairset2E) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairsubunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairinpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem3) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair1) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionE2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton1) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton) =>
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% 102.63/17.15 (ex1E1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I2) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsuniq) =>
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% 102.63/17.15 (setukpairinjL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (theprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstin) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR11) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR12) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR1) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairequniteq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemEL) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemER) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempaircEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrI) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrSub) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrERa) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrER) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcImageSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (apProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (app) =>
% 102.63/17.15 ((
% 102.63/17.15 (infuncsetfunc) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcinfuncset) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall1) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp3) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcextLem) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp4) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq2) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2lamEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifp) =>
% 102.63/17.15 ((
% 102.63/17.15 (theeq) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrue) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueorfalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setminusT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setextT) =>
% 102.63/17.15 ((
% 102.63/17.15 (subsetTI) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetTI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTELcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTERcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT1) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT2) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT3) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub2) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTnotintersectT) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementImpComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementSubsetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementInPowersetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (contraSubsetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTcontraSubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTILcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTIRcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion2) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (intersectInPowersetIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpNotIn1) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpInComplement1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTE) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTEcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementUnionInPowersetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1a) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2b2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule0) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule1) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule3) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule4) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_1) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_3) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_4) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_5) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1all2) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1SetBreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (choice2fnsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1all1) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compEex) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIL) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionEcases) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionCommutes) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2Ex) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2W) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2A) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2B) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Ex) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Ex1) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Equiv) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1E) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncInInjFuncSet) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncInj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (leftInvIsSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjCantorThm) =>
% 102.63/17.15 ((
% 102.63/17.15 (foundation2) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself2) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSp) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSclos) =>
% 102.63/17.15 ((
% 102.63/17.15 (peano0notS) =>
% 102.63/17.15 ((
% 102.63/17.15 (peanoSinj) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (ordinalMinLem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y0 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (ordinal @
% 102.63/17.15 Y0) =>
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y1 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y2 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y2 @
% 102.63/17.15 Y0) =>
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @
% 102.63/17.15 Y2) =>
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl940])).
% 102.63/17.15 thf(zip_derived_cl951, plain,
% 102.63/17.15 (~ (((binintersectI) =>
% 102.63/17.15 (((binintersectSubset5) =>
% 102.63/17.15 (((binintersectEL) =>
% 102.63/17.15 (((binintersectLsub) =>
% 102.63/17.15 (((binintersectSubset2) =>
% 102.63/17.15 (((binintersectSubset3) =>
% 102.63/17.15 (((binintersectER) =>
% 102.63/17.15 (((disjointsetsI1) =>
% 102.63/17.15 (((binintersectRsub) =>
% 102.63/17.15 (((binintersectSubset4) =>
% 102.63/17.15 (((binintersectSubset1) =>
% 102.63/17.15 (((bs114d) =>
% 102.63/17.15 (((setminusI) =>
% 102.63/17.15 (((setminusEL) =>
% 102.63/17.15 (((setminusER) =>
% 102.63/17.15 (((setminusSubset2) =>
% 102.63/17.15 (((setminusERneg) =>
% 102.63/17.15 (((setminusELneg) =>
% 102.63/17.15 (((setminusILneg) =>
% 102.63/17.15 (((setminusIRneg) =>
% 102.63/17.15 (((setminusLsub) =>
% 102.63/17.15 (((setminusSubset1) =>
% 102.63/17.15 (((symdiffE) =>
% 102.63/17.15 (((symdiffI1) =>
% 102.63/17.15 (((symdiffI2) =>
% 102.63/17.15 (((symdiffIneg1) =>
% 102.63/17.15 (((symdiffIneg2) =>
% 102.63/17.15 (((secondinupair) =>
% 102.63/17.15 (((setukpairIL) =>
% 102.63/17.15 (((setukpairIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairiskpair) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairp) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowerset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairset2E) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairsubunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairinpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem3) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair1) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionE2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton1) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I2) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsuniq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (theprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstin) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR11) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR12) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR1) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairequniteq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemEL) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemER) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempaircEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrI) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrSub) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrERa) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrER) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcImageSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (apProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (app) =>
% 102.63/17.15 ((
% 102.63/17.15 (infuncsetfunc) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcinfuncset) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall1) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp3) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcextLem) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp4) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq2) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2lamEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifp) =>
% 102.63/17.15 ((
% 102.63/17.15 (theeq) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrue) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueorfalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setminusT_lem) =>
% 102.63/17.15 ((
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% 102.63/17.15 ((
% 102.63/17.15 (setextT) =>
% 102.63/17.15 ((
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% 102.63/17.15 ((
% 102.63/17.15 (powersetTI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetTE1) =>
% 102.63/17.15 ((
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% 102.63/17.15 ((
% 102.63/17.15 (complementTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTELcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTERcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT1) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT2) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT3) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub2) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTnotintersectT) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementImpComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementSubsetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementInPowersetComplementIntersect) =>
% 102.63/17.15 ((
% 102.63/17.15 (contraSubsetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTcontraSubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTILcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTIRcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInUnion2) =>
% 102.63/17.15 ((
% 102.63/17.15 (inIntersectImpInIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (intersectInPowersetIntersectUnions) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpNotIn1) =>
% 102.63/17.15 ((
% 102.63/17.15 (inComplementUnionImpInComplement1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTE) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionTEcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementUnionInPowersetComplement) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1a) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan1) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2a) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2b2) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2b) =>
% 102.63/17.15 ((
% 102.63/17.15 (demorgan2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule0) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule1) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule3) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz13rule4) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_1) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_2) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_3) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_4) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz1_5) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1all2) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1SetBreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (choice2fnsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1all1) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln1) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1invE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1compEex) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIL) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionIR) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionI) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionE) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionEcases) =>
% 102.63/17.15 ((
% 102.63/17.15 (breln1unionCommutes) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2Ex) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2W) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2A) =>
% 102.63/17.15 ((
% 102.63/17.15 (woz2B) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Ex) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Ex1) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1Equiv) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1E) =>
% 102.63/17.15 ((
% 102.63/17.15 (image1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncInInjFuncSet) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (injFuncSetFuncInj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncIn) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjFuncSetFuncSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (leftInvIsSurj) =>
% 102.63/17.15 ((
% 102.63/17.15 (surjCantorThm) =>
% 102.63/17.15 ((
% 102.63/17.15 (foundation2) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself) =>
% 102.63/17.15 ((
% 102.63/17.15 (notinself2) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSp) =>
% 102.63/17.15 ((
% 102.63/17.15 (omegaSclos) =>
% 102.63/17.15 ((
% 102.63/17.15 (peano0notS) =>
% 102.63/17.15 ((
% 102.63/17.15 (peanoSinj) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (transitivesetOp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionTransitive) =>
% 102.63/17.15 ((
% 102.63/17.15 (ordinalMinLem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y0 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (ordinal @
% 102.63/17.15 Y0) =>
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y1 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (!!) @ (
% 102.63/17.15 ^[Y2 : $i]:
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y2 @
% 102.63/17.15 Y0) =>
% 102.63/17.15 ((
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @
% 102.63/17.15 Y2) =>
% 102.63/17.15 (in @
% 102.63/17.15 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl945])).
% 102.63/17.15 thf(zip_derived_cl957, plain,
% 102.63/17.15 (~ (((binintersectSubset5) =>
% 102.63/17.15 (((binintersectEL) =>
% 102.63/17.15 (((binintersectLsub) =>
% 102.63/17.15 (((binintersectSubset2) =>
% 102.63/17.15 (((binintersectSubset3) =>
% 102.63/17.15 (((binintersectER) =>
% 102.63/17.15 (((disjointsetsI1) =>
% 102.63/17.15 (((binintersectRsub) =>
% 102.63/17.15 (((binintersectSubset4) =>
% 102.63/17.15 (((binintersectSubset1) =>
% 102.63/17.15 (((bs114d) =>
% 102.63/17.15 (((setminusI) =>
% 102.63/17.15 (((setminusEL) =>
% 102.63/17.15 (((setminusER) =>
% 102.63/17.15 (((setminusSubset2) =>
% 102.63/17.15 (((setminusERneg) =>
% 102.63/17.15 (((setminusELneg) =>
% 102.63/17.15 (((setminusILneg) =>
% 102.63/17.15 (((setminusIRneg) =>
% 102.63/17.15 (((setminusLsub) =>
% 102.63/17.15 (((setminusSubset1) =>
% 102.63/17.15 (((symdiffE) =>
% 102.63/17.15 (((symdiffI1) =>
% 102.63/17.15 (((symdiffI2) =>
% 102.63/17.15 (((symdiffIneg1) =>
% 102.63/17.15 (((symdiffIneg2) =>
% 102.63/17.15 (((secondinupair) =>
% 102.63/17.15 (((setukpairIL) =>
% 102.63/17.15 (((setukpairIR) =>
% 102.63/17.15 (((kpairiskpair) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairp) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsubset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowerset) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletoninpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairset2E) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairsubunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairinpowunion) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ubforcartprodlem3) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair1) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempair) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionE2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton1) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setunionsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1I2) =>
% 102.63/17.15 ((
% 102.63/17.15 (singletonsuniq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (theprop) =>
% 102.63/17.15 ((
% 102.63/17.15 (kfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstin) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjL) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR11) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR12) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR1) =>
% 102.63/17.15 ((
% 102.63/17.15 (upairequniteq) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR2) =>
% 102.63/17.15 ((
% 102.63/17.15 (setukpairinjR) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndsingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ksndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (kpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndin) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemEL) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairmemER) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodmempaircEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodfstpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodsndpairEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (cartprodpairsurjEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrI) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrSub) =>
% 102.63/17.15 ((
% 102.63/17.15 (setOfPairsIsBReln) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrERa) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL1) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrEL2) =>
% 102.63/17.15 ((
% 102.63/17.15 (dpsetconstrER) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcImageSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (apProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (app) =>
% 102.63/17.15 ((
% 102.63/17.15 (infuncsetfunc) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcinfuncset) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamProp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lamp) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2p) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall1) =>
% 102.63/17.15 ((
% 102.63/17.15 (brelnall2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ex1E2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp3) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcextLem) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcGraphProp4) =>
% 102.63/17.15 ((
% 102.63/17.15 (subbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (eqbreln) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext) =>
% 102.63/17.15 ((
% 102.63/17.15 (funcext2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq1) =>
% 102.63/17.15 ((
% 102.63/17.15 (ap2apEq2) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta1) =>
% 102.63/17.15 ((
% 102.63/17.15 (lam2lamEq) =>
% 102.63/17.15 ((
% 102.63/17.15 (beta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (eta2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalseProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp1) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueProp2) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifSingleton) =>
% 102.63/17.15 ((
% 102.63/17.15 (ifp) =>
% 102.63/17.15 ((
% 102.63/17.15 (theeq) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrue) =>
% 102.63/17.15 ((
% 102.63/17.15 (iffalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (iftrueorfalse) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (binunionT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setminusT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementT_lem) =>
% 102.63/17.15 ((
% 102.63/17.15 (setextT) =>
% 102.63/17.15 ((
% 102.63/17.15 (subsetTI) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetTI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (powersetTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (complementTE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTELcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (binintersectTERcontra) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT1) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT2) =>
% 102.63/17.15 ((
% 102.63/17.15 (contrasubsetT3) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementI1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementE1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub1) =>
% 102.63/17.15 ((
% 102.63/17.15 (doubleComplementSub2) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTnotintersectT) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementImpComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementSubsetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementInPowersetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (contraSubsetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTcontraSubset) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTILcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTIRcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion2) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (intersectInPowersetIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpNotIn1) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpInComplement1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTE) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTEcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementUnionInPowersetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a2) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1b) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2b2) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2b) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule0) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule1) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule3) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule4) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_1) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_3) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_4) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_5) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1all2) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1SetBreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (choice2fnsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1all1) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compEex) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionIL) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionIR) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionEcases) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionCommutes) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2Ex) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2W) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2A) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2B) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Ex) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Ex1) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Equiv) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1E) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1I) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncInInjFuncSet) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncInj) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncSurj) =>
% 102.63/17.16 ((
% 102.63/17.16 (leftInvIsSurj) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjCantorThm) =>
% 102.63/17.16 ((
% 102.63/17.16 (foundation2) =>
% 102.63/17.16 ((
% 102.63/17.16 (notinself) =>
% 102.63/17.16 ((
% 102.63/17.16 (notinself2) =>
% 102.63/17.16 ((
% 102.63/17.16 (omegaSp) =>
% 102.63/17.16 ((
% 102.63/17.16 (omegaSclos) =>
% 102.63/17.16 ((
% 102.63/17.16 (peano0notS) =>
% 102.63/17.16 ((
% 102.63/17.16 (peanoSinj) =>
% 102.63/17.16 ((
% 102.63/17.16 (transitivesetOp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintTransitive) =>
% 102.63/17.16 ((
% 102.63/17.16 (transitivesetOp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionTransitive) =>
% 102.63/17.16 ((
% 102.63/17.16 (ordinalMinLem1) =>
% 102.63/17.16 ((
% 102.63/17.16 (!!) @ (
% 102.63/17.16 ^[Y0 : $i]:
% 102.63/17.16 ((
% 102.63/17.16 (ordinal @
% 102.63/17.16 Y0) =>
% 102.63/17.16 ((
% 102.63/17.16 (!!) @ (
% 102.63/17.16 ^[Y1 : $i]:
% 102.63/17.16 ((
% 102.63/17.16 (!!) @ (
% 102.63/17.16 ^[Y2 : $i]:
% 102.63/17.16 ((
% 102.63/17.16 (in @
% 102.63/17.16 Y2 @
% 102.63/17.16 Y0) =>
% 102.63/17.16 ((
% 102.63/17.16 (in @
% 102.63/17.16 Y1 @
% 102.63/17.16 Y2) =>
% 102.63/17.16 (in @
% 102.63/17.16 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl951])).
% 102.63/17.16 thf(zip_derived_cl964, plain,
% 102.63/17.16 (~ (((binintersectEL) =>
% 102.63/17.16 (((binintersectLsub) =>
% 102.63/17.16 (((binintersectSubset2) =>
% 102.63/17.16 (((binintersectSubset3) =>
% 102.63/17.16 (((binintersectER) =>
% 102.63/17.16 (((disjointsetsI1) =>
% 102.63/17.16 (((binintersectRsub) =>
% 102.63/17.16 (((binintersectSubset4) =>
% 102.63/17.16 (((binintersectSubset1) =>
% 102.63/17.16 (((bs114d) =>
% 102.63/17.16 (((setminusI) =>
% 102.63/17.16 (((setminusEL) =>
% 102.63/17.16 (((setminusER) =>
% 102.63/17.16 (((setminusSubset2) =>
% 102.63/17.16 (((setminusERneg) =>
% 102.63/17.16 (((setminusELneg) =>
% 102.63/17.16 (((setminusILneg) =>
% 102.63/17.16 (((setminusIRneg) =>
% 102.63/17.16 (((setminusLsub) =>
% 102.63/17.16 (((setminusSubset1) =>
% 102.63/17.16 (((symdiffE) =>
% 102.63/17.16 (((symdiffI1) =>
% 102.63/17.16 (((symdiffI2) =>
% 102.63/17.16 (((symdiffIneg1) =>
% 102.63/17.16 (((symdiffIneg2) =>
% 102.63/17.16 (((secondinupair) =>
% 102.63/17.16 (((setukpairIL) =>
% 102.63/17.16 (((setukpairIR) =>
% 102.63/17.16 (((kpairiskpair) =>
% 102.63/17.16 (((kpairp) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonsubset) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletoninpowerset) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletoninpowunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairset2E) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairsubunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairinpowunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem3) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair1) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionE2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton1) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I2) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonsuniq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (theprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstin) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR11) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR12) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR1) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairequniteq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (kpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemEL) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemER) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempaircEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrI) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrSub) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrERa) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrER) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcImageSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (apProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (app) =>
% 102.63/17.16 ((
% 102.63/17.16 (infuncsetfunc) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcinfuncset) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall1) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp3) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcextLem) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp4) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq2) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2lamEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifp) =>
% 102.63/17.16 ((
% 102.63/17.16 (theeq) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrue) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueorfalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setminusT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setextT) =>
% 102.63/17.16 ((
% 102.63/17.16 (subsetTI) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTELcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTERcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT1) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT2) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT3) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub2) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTnotintersectT) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementImpComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementSubsetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementInPowersetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (contraSubsetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTcontraSubset) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTILcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTIRcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion2) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (intersectInPowersetIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpNotIn1) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpInComplement1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTE) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTEcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementUnionInPowersetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a2) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1b) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2b2) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2b) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule0) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule1) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule3) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule4) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_1) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_3) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_4) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_5) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1all2) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1SetBreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (choice2fnsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1all1) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compEex) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionIL) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionIR) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionEcases) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionCommutes) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2Ex) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2W) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (image1E) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1I) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncInInjFuncSet) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncInj) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncSurj) =>
% 102.63/17.16 ((
% 102.63/17.16 (leftInvIsSurj) =>
% 102.63/17.16 ((
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% 102.63/17.16 (foundation2) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (notinself2) =>
% 102.63/17.16 ((
% 102.63/17.16 (omegaSp) =>
% 102.63/17.16 ((
% 102.63/17.16 (omegaSclos) =>
% 102.63/17.16 ((
% 102.63/17.16 (peano0notS) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 (in @
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% 102.63/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl957])).
% 102.63/17.16 thf(zip_derived_cl971, plain,
% 102.63/17.16 (~ (((binintersectLsub) =>
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% 102.63/17.16 (((setminusILneg) =>
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% 102.63/17.16 ((
% 102.63/17.16 (singletoninpowunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairset2E) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairsubunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairinpowunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem3) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair1) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionE2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton1) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton) =>
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% 102.63/17.16 (theprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstin) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR11) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR12) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR1) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairequniteq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (kpairsurjEq) =>
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% 102.63/17.16 (cartprodsndin) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemER) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempaircEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrI) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrSub) =>
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% 102.63/17.16 (setOfPairsIsBReln) =>
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% 102.63/17.16 (dpsetconstrERa) =>
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% 102.63/17.16 (dpsetconstrEL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrER) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcImageSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (apProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (app) =>
% 102.63/17.16 ((
% 102.63/17.16 (infuncsetfunc) =>
% 102.63/17.16 ((
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% 102.63/17.16 (funcinfuncset) =>
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% 102.63/17.16 ((
% 102.63/17.16 (lamp) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (brelnall1) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E2) =>
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% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp3) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcextLem) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp4) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq2) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (eta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2lamEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifp) =>
% 102.63/17.16 ((
% 102.63/17.16 (theeq) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrue) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueorfalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setminusT_lem) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (setextT) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (powersetTE1) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (complementTE1) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (binintersectTERcontra) =>
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% 102.63/17.16 (contrasubsetT2) =>
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% 102.63/17.16 (contrasubsetT3) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub2) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTnotintersectT) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementImpComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementSubsetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementInPowersetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (contraSubsetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTcontraSubset) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTILcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTIRcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion2) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInIntersectUnions) =>
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% 102.63/17.16 (intersectInPowersetIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpNotIn1) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpInComplement1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTE) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTEcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementUnionInPowersetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a2) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 (breln1unionCommutes) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncInj) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (notinself2) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (omegaSclos) =>
% 102.63/17.16 ((
% 102.63/17.16 (peano0notS) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 Y2) =>
% 102.63/17.16 (in @
% 102.63/17.16 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl964])).
% 102.63/17.16 thf(zip_derived_cl978, plain,
% 102.63/17.16 (~ (((binintersectSubset2) =>
% 102.63/17.16 (((binintersectSubset3) =>
% 102.63/17.16 (((binintersectER) =>
% 102.63/17.16 (((disjointsetsI1) =>
% 102.63/17.16 (((binintersectRsub) =>
% 102.63/17.16 (((binintersectSubset4) =>
% 102.63/17.16 (((binintersectSubset1) =>
% 102.63/17.16 (((bs114d) =>
% 102.63/17.16 (((setminusI) =>
% 102.63/17.16 (((setminusEL) =>
% 102.63/17.16 (((setminusER) =>
% 102.63/17.16 (((setminusSubset2) =>
% 102.63/17.16 (((setminusERneg) =>
% 102.63/17.16 (((setminusELneg) =>
% 102.63/17.16 (((setminusILneg) =>
% 102.63/17.16 (((setminusIRneg) =>
% 102.63/17.16 (((setminusLsub) =>
% 102.63/17.16 (((setminusSubset1) =>
% 102.63/17.16 (((symdiffE) =>
% 102.63/17.16 (((symdiffI1) =>
% 102.63/17.16 (((symdiffI2) =>
% 102.63/17.16 (((symdiffIneg1) =>
% 102.63/17.16 (((symdiffIneg2) =>
% 102.63/17.16 (((secondinupair) =>
% 102.63/17.16 (((setukpairIL) =>
% 102.63/17.16 (((setukpairIR) =>
% 102.63/17.16 (((kpairiskpair) =>
% 102.63/17.16 (((kpairp) =>
% 102.63/17.16 (((singletonsubset) =>
% 102.63/17.16 (((singletoninpowerset) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletoninpowunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairset2E) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairsubunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairinpowunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem3) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair1) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionE2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton1) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I2) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonsuniq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (theprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstin) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR11) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR12) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR1) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairequniteq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (kpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemEL) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemER) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempaircEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrI) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrSub) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrERa) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrER) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcImageSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (apProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (app) =>
% 102.63/17.16 ((
% 102.63/17.16 (infuncsetfunc) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcinfuncset) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall1) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp3) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcextLem) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp4) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq2) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2lamEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifp) =>
% 102.63/17.16 ((
% 102.63/17.16 (theeq) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrue) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueorfalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setminusT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setextT) =>
% 102.63/17.16 ((
% 102.63/17.16 (subsetTI) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTELcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTERcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT1) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT2) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT3) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub2) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTnotintersectT) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementImpComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementSubsetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementInPowersetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (contraSubsetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTcontraSubset) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTILcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTIRcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion2) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (intersectInPowersetIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpNotIn1) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpInComplement1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTE) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTEcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementUnionInPowersetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a2) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1b) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2b2) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2b) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule0) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule1) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule3) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule4) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_1) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_3) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_4) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_5) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1all2) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1SetBreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (choice2fnsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1all1) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compEex) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionIL) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionIR) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionEcases) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionCommutes) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2Ex) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2W) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2A) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2B) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Ex) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Ex1) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Equiv) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1E) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1I) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncInInjFuncSet) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncInj) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncSurj) =>
% 102.63/17.16 ((
% 102.63/17.16 (leftInvIsSurj) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjCantorThm) =>
% 102.63/17.16 ((
% 102.63/17.16 (foundation2) =>
% 102.63/17.16 ((
% 102.63/17.16 (notinself) =>
% 102.63/17.16 ((
% 102.63/17.16 (notinself2) =>
% 102.63/17.16 ((
% 102.63/17.16 (omegaSp) =>
% 102.63/17.16 ((
% 102.63/17.16 (omegaSclos) =>
% 102.63/17.16 ((
% 102.63/17.16 (peano0notS) =>
% 102.63/17.16 ((
% 102.63/17.16 (peanoSinj) =>
% 102.63/17.16 ((
% 102.63/17.16 (transitivesetOp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintTransitive) =>
% 102.63/17.16 ((
% 102.63/17.16 (transitivesetOp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionTransitive) =>
% 102.63/17.16 ((
% 102.63/17.16 (ordinalMinLem1) =>
% 102.63/17.16 ((
% 102.63/17.16 (!!) @ (
% 102.63/17.16 ^[Y0 : $i]:
% 102.63/17.16 ((
% 102.63/17.16 (ordinal @
% 102.63/17.16 Y0) =>
% 102.63/17.16 ((
% 102.63/17.16 (!!) @ (
% 102.63/17.16 ^[Y1 : $i]:
% 102.63/17.16 ((
% 102.63/17.16 (!!) @ (
% 102.63/17.16 ^[Y2 : $i]:
% 102.63/17.16 ((
% 102.63/17.16 (in @
% 102.63/17.16 Y2 @
% 102.63/17.16 Y0) =>
% 102.63/17.16 ((
% 102.63/17.16 (in @
% 102.63/17.16 Y1 @
% 102.63/17.16 Y2) =>
% 102.63/17.16 (in @
% 102.63/17.16 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl971])).
% 102.63/17.16 thf(zip_derived_cl985, plain,
% 102.63/17.16 (~ (((binintersectSubset3) =>
% 102.63/17.16 (((binintersectER) =>
% 102.63/17.16 (((disjointsetsI1) =>
% 102.63/17.16 (((binintersectRsub) =>
% 102.63/17.16 (((binintersectSubset4) =>
% 102.63/17.16 (((binintersectSubset1) =>
% 102.63/17.16 (((bs114d) =>
% 102.63/17.16 (((setminusI) =>
% 102.63/17.16 (((setminusEL) =>
% 102.63/17.16 (((setminusER) =>
% 102.63/17.16 (((setminusSubset2) =>
% 102.63/17.16 (((setminusERneg) =>
% 102.63/17.16 (((setminusELneg) =>
% 102.63/17.16 (((setminusILneg) =>
% 102.63/17.16 (((setminusIRneg) =>
% 102.63/17.16 (((setminusLsub) =>
% 102.63/17.16 (((setminusSubset1) =>
% 102.63/17.16 (((symdiffE) =>
% 102.63/17.16 (((symdiffI1) =>
% 102.63/17.16 (((symdiffI2) =>
% 102.63/17.16 (((symdiffIneg1) =>
% 102.63/17.16 (((symdiffIneg2) =>
% 102.63/17.16 (((secondinupair) =>
% 102.63/17.16 (((setukpairIL) =>
% 102.63/17.16 (((setukpairIR) =>
% 102.63/17.16 (((kpairiskpair) =>
% 102.63/17.16 (((kpairp) =>
% 102.63/17.16 (((singletonsubset) =>
% 102.63/17.16 (((singletoninpowerset) =>
% 102.63/17.16 (((singletoninpowunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairset2E) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairsubunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairinpowunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem3) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair1) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionE2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton1) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I2) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonsuniq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (theprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstin) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR11) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR12) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR1) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairequniteq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (kpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemEL) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemER) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempaircEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrI) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrSub) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrERa) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrER) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcImageSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (apProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (app) =>
% 102.63/17.16 ((
% 102.63/17.16 (infuncsetfunc) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcinfuncset) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall1) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp3) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcextLem) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp4) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq2) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2lamEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifp) =>
% 102.63/17.16 ((
% 102.63/17.16 (theeq) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrue) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueorfalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setminusT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setextT) =>
% 102.63/17.16 ((
% 102.63/17.16 (subsetTI) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTELcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTERcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT1) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT2) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT3) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub2) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTnotintersectT) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementImpComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementSubsetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementInPowersetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (contraSubsetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTcontraSubset) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTILcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTIRcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion2) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (intersectInPowersetIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpNotIn1) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpInComplement1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTE) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTEcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementUnionInPowersetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a2) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1b) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2b2) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2b) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule0) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule1) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule3) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule4) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_1) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_3) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_4) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_5) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1all2) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1SetBreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (choice2fnsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1all1) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compEex) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionIL) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionIR) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionEcases) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionCommutes) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2Ex) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2W) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2A) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2B) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Ex) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Ex1) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Equiv) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1E) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1I) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncInInjFuncSet) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncInj) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncSurj) =>
% 102.63/17.16 ((
% 102.63/17.16 (leftInvIsSurj) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjCantorThm) =>
% 102.63/17.16 ((
% 102.63/17.16 (foundation2) =>
% 102.63/17.16 ((
% 102.63/17.16 (notinself) =>
% 102.63/17.16 ((
% 102.63/17.16 (notinself2) =>
% 102.63/17.16 ((
% 102.63/17.16 (omegaSp) =>
% 102.63/17.16 ((
% 102.63/17.16 (omegaSclos) =>
% 102.63/17.16 ((
% 102.63/17.16 (peano0notS) =>
% 102.63/17.16 ((
% 102.63/17.16 (peanoSinj) =>
% 102.63/17.16 ((
% 102.63/17.16 (transitivesetOp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintTransitive) =>
% 102.63/17.16 ((
% 102.63/17.16 (transitivesetOp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionTransitive) =>
% 102.63/17.16 ((
% 102.63/17.16 (ordinalMinLem1) =>
% 102.63/17.16 ((
% 102.63/17.16 (!!) @ (
% 102.63/17.16 ^[Y0 : $i]:
% 102.63/17.16 ((
% 102.63/17.16 (ordinal @
% 102.63/17.16 Y0) =>
% 102.63/17.16 ((
% 102.63/17.16 (!!) @ (
% 102.63/17.16 ^[Y1 : $i]:
% 102.63/17.16 ((
% 102.63/17.16 (!!) @ (
% 102.63/17.16 ^[Y2 : $i]:
% 102.63/17.16 ((
% 102.63/17.16 (in @
% 102.63/17.16 Y2 @
% 102.63/17.16 Y0) =>
% 102.63/17.16 ((
% 102.63/17.16 (in @
% 102.63/17.16 Y1 @
% 102.63/17.16 Y2) =>
% 102.63/17.16 (in @
% 102.63/17.16 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl978])).
% 102.63/17.16 thf(zip_derived_cl994, plain,
% 102.63/17.16 (~ (((binintersectER) =>
% 102.63/17.16 (((disjointsetsI1) =>
% 102.63/17.16 (((binintersectRsub) =>
% 102.63/17.16 (((binintersectSubset4) =>
% 102.63/17.16 (((binintersectSubset1) =>
% 102.63/17.16 (((bs114d) =>
% 102.63/17.16 (((setminusI) =>
% 102.63/17.16 (((setminusEL) =>
% 102.63/17.16 (((setminusER) =>
% 102.63/17.16 (((setminusSubset2) =>
% 102.63/17.16 (((setminusERneg) =>
% 102.63/17.16 (((setminusELneg) =>
% 102.63/17.16 (((setminusILneg) =>
% 102.63/17.16 (((setminusIRneg) =>
% 102.63/17.16 (((setminusLsub) =>
% 102.63/17.16 (((setminusSubset1) =>
% 102.63/17.16 (((symdiffE) =>
% 102.63/17.16 (((symdiffI1) =>
% 102.63/17.16 (((symdiffI2) =>
% 102.63/17.16 (((symdiffIneg1) =>
% 102.63/17.16 (((symdiffIneg2) =>
% 102.63/17.16 (((secondinupair) =>
% 102.63/17.16 (((setukpairIL) =>
% 102.63/17.16 (((setukpairIR) =>
% 102.63/17.16 (((kpairiskpair) =>
% 102.63/17.16 (((kpairp) =>
% 102.63/17.16 (((singletonsubset) =>
% 102.63/17.16 (((singletoninpowerset) =>
% 102.63/17.16 (((singletoninpowunion) =>
% 102.63/17.16 (((upairset2E) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairsubunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairinpowunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem3) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair1) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionE2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton1) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I2) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonsuniq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (theprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstin) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR11) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR12) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR1) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairequniteq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (kpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemEL) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemER) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempaircEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrI) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrSub) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrERa) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrER) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcImageSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (apProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (app) =>
% 102.63/17.16 ((
% 102.63/17.16 (infuncsetfunc) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcinfuncset) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall1) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp3) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcextLem) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp4) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq2) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2lamEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifp) =>
% 102.63/17.16 ((
% 102.63/17.16 (theeq) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrue) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueorfalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setminusT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setextT) =>
% 102.63/17.16 ((
% 102.63/17.16 (subsetTI) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTELcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTERcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT1) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT2) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT3) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub2) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTnotintersectT) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementImpComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementSubsetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementInPowersetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (contraSubsetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTcontraSubset) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTILcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTIRcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion2) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (intersectInPowersetIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpNotIn1) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpInComplement1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTE) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTEcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementUnionInPowersetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a2) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1b) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2b2) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2b) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule0) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule1) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule3) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule4) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_1) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_3) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_4) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_5) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1all2) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1SetBreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (choice2fnsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1all1) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compEex) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionIL) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionIR) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionEcases) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionCommutes) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2Ex) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2W) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2A) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2B) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Ex) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Ex1) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Equiv) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1E) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1I) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncInInjFuncSet) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncInj) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncSurj) =>
% 102.63/17.16 ((
% 102.63/17.16 (leftInvIsSurj) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjCantorThm) =>
% 102.63/17.16 ((
% 102.63/17.16 (foundation2) =>
% 102.63/17.16 ((
% 102.63/17.16 (notinself) =>
% 102.63/17.16 ((
% 102.63/17.16 (notinself2) =>
% 102.63/17.16 ((
% 102.63/17.16 (omegaSp) =>
% 102.63/17.16 ((
% 102.63/17.16 (omegaSclos) =>
% 102.63/17.16 ((
% 102.63/17.16 (peano0notS) =>
% 102.63/17.16 ((
% 102.63/17.16 (peanoSinj) =>
% 102.63/17.16 ((
% 102.63/17.16 (transitivesetOp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintTransitive) =>
% 102.63/17.16 ((
% 102.63/17.16 (transitivesetOp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionTransitive) =>
% 102.63/17.16 ((
% 102.63/17.16 (ordinalMinLem1) =>
% 102.63/17.16 ((
% 102.63/17.16 (!!) @ (
% 102.63/17.16 ^[Y0 : $i]:
% 102.63/17.16 ((
% 102.63/17.16 (ordinal @
% 102.63/17.16 Y0) =>
% 102.63/17.16 ((
% 102.63/17.16 (!!) @ (
% 102.63/17.16 ^[Y1 : $i]:
% 102.63/17.16 ((
% 102.63/17.16 (!!) @ (
% 102.63/17.16 ^[Y2 : $i]:
% 102.63/17.16 ((
% 102.63/17.16 (in @
% 102.63/17.16 Y2 @
% 102.63/17.16 Y0) =>
% 102.63/17.16 ((
% 102.63/17.16 (in @
% 102.63/17.16 Y1 @
% 102.63/17.16 Y2) =>
% 102.63/17.16 (in @
% 102.63/17.16 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl985])).
% 102.63/17.16 thf(zip_derived_cl1002, plain,
% 102.63/17.16 (~ (((disjointsetsI1) =>
% 102.63/17.16 (((binintersectRsub) =>
% 102.63/17.16 (((binintersectSubset4) =>
% 102.63/17.16 (((binintersectSubset1) =>
% 102.63/17.16 (((bs114d) =>
% 102.63/17.16 (((setminusI) =>
% 102.63/17.16 (((setminusEL) =>
% 102.63/17.16 (((setminusER) =>
% 102.63/17.16 (((setminusSubset2) =>
% 102.63/17.16 (((setminusERneg) =>
% 102.63/17.16 (((setminusELneg) =>
% 102.63/17.16 (((setminusILneg) =>
% 102.63/17.16 (((setminusIRneg) =>
% 102.63/17.16 (((setminusLsub) =>
% 102.63/17.16 (((setminusSubset1) =>
% 102.63/17.16 (((symdiffE) =>
% 102.63/17.16 (((symdiffI1) =>
% 102.63/17.16 (((symdiffI2) =>
% 102.63/17.16 (((symdiffIneg1) =>
% 102.63/17.16 (((symdiffIneg2) =>
% 102.63/17.16 (((secondinupair) =>
% 102.63/17.16 (((setukpairIL) =>
% 102.63/17.16 (((setukpairIR) =>
% 102.63/17.16 (((kpairiskpair) =>
% 102.63/17.16 (((kpairp) =>
% 102.63/17.16 (((singletonsubset) =>
% 102.63/17.16 (((singletoninpowerset) =>
% 102.63/17.16 (((singletoninpowunion) =>
% 102.63/17.16 (((upairset2E) =>
% 102.63/17.16 (((upairsubunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairinpowunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem3) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair1) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionE2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton1) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I2) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonsuniq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (theprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstin) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR11) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR12) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR1) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairequniteq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (kpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemEL) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemER) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempaircEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrI) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrSub) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrERa) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrER) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcImageSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (apProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (app) =>
% 102.63/17.16 ((
% 102.63/17.16 (infuncsetfunc) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcinfuncset) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall1) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp3) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcextLem) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp4) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq2) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2lamEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifp) =>
% 102.63/17.16 ((
% 102.63/17.16 (theeq) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrue) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueorfalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setminusT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setextT) =>
% 102.63/17.16 ((
% 102.63/17.16 (subsetTI) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTELcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTERcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT1) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT2) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT3) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub2) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTnotintersectT) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementImpComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementSubsetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementInPowersetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (contraSubsetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTcontraSubset) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTILcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTIRcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion2) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (intersectInPowersetIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpNotIn1) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpInComplement1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTE) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTEcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementUnionInPowersetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a2) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1b) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2b2) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2b) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule0) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule1) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule3) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule4) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_1) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_3) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_4) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz1_5) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1all2) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1SetBreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (choice2fnsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1all1) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1invE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1compEex) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionIL) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionIR) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionI) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionEcases) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionCommutes) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2Ex) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2W) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2A) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz2B) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Ex) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Ex1) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1Equiv) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1E) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1I) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncInInjFuncSet) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncInj) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncSurj) =>
% 102.63/17.16 ((
% 102.63/17.16 (leftInvIsSurj) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjCantorThm) =>
% 102.63/17.16 ((
% 102.63/17.16 (foundation2) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (notinself2) =>
% 102.63/17.16 ((
% 102.63/17.16 (omegaSp) =>
% 102.63/17.16 ((
% 102.63/17.16 (omegaSclos) =>
% 102.63/17.16 ((
% 102.63/17.16 (peano0notS) =>
% 102.63/17.16 ((
% 102.63/17.16 (peanoSinj) =>
% 102.63/17.16 ((
% 102.63/17.16 (transitivesetOp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintTransitive) =>
% 102.63/17.16 ((
% 102.63/17.16 (transitivesetOp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionTransitive) =>
% 102.63/17.16 ((
% 102.63/17.16 (ordinalMinLem1) =>
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% 102.63/17.16 ^[Y0 : $i]:
% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (!!) @ (
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% 102.63/17.16 ((
% 102.63/17.16 (in @
% 102.63/17.16 Y1 @
% 102.63/17.16 Y2) =>
% 102.63/17.16 (in @
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% 102.63/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl994])).
% 102.63/17.16 thf(zip_derived_cl1008, plain,
% 102.63/17.16 (~ (((binintersectRsub) =>
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% 102.63/17.16 (((binintersectSubset1) =>
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% 102.63/17.16 (((setminusI) =>
% 102.63/17.16 (((setminusEL) =>
% 102.63/17.16 (((setminusER) =>
% 102.63/17.16 (((setminusSubset2) =>
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% 102.63/17.16 (((setminusELneg) =>
% 102.63/17.16 (((setminusILneg) =>
% 102.63/17.16 (((setminusIRneg) =>
% 102.63/17.16 (((setminusLsub) =>
% 102.63/17.16 (((setminusSubset1) =>
% 102.63/17.16 (((symdiffE) =>
% 102.63/17.16 (((symdiffI1) =>
% 102.63/17.16 (((symdiffI2) =>
% 102.63/17.16 (((symdiffIneg1) =>
% 102.63/17.16 (((symdiffIneg2) =>
% 102.63/17.16 (((secondinupair) =>
% 102.63/17.16 (((setukpairIL) =>
% 102.63/17.16 (((setukpairIR) =>
% 102.63/17.16 (((kpairiskpair) =>
% 102.63/17.16 (((kpairp) =>
% 102.63/17.16 (((singletonsubset) =>
% 102.63/17.16 (((singletoninpowerset) =>
% 102.63/17.16 (((singletoninpowunion) =>
% 102.63/17.16 (((upairset2E) =>
% 102.63/17.16 (((upairsubunion) =>
% 102.63/17.16 (((upairinpowunion) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem3) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair1) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionE2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton1) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I2) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonsuniq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (theprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstin) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR11) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR12) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR1) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairequniteq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (kpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemEL) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemER) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempaircEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrI) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrSub) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrERa) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrER) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcImageSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (apProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (app) =>
% 102.63/17.16 ((
% 102.63/17.16 (infuncsetfunc) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcinfuncset) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall1) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp3) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcextLem) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp4) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq2) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2lamEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifp) =>
% 102.63/17.16 ((
% 102.63/17.16 (theeq) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrue) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueorfalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setminusT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setextT) =>
% 102.63/17.16 ((
% 102.63/17.16 (subsetTI) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTELcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTERcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT1) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT2) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT3) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub2) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTnotintersectT) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementImpComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementSubsetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementInPowersetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (contraSubsetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTcontraSubset) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTILcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTIRcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInUnion2) =>
% 102.63/17.16 ((
% 102.63/17.16 (inIntersectImpInIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (intersectInPowersetIntersectUnions) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpNotIn1) =>
% 102.63/17.16 ((
% 102.63/17.16 (inComplementUnionImpInComplement1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTE) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionTEcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementUnionInPowersetComplement) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a2) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1b) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan1) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2a) =>
% 102.63/17.16 ((
% 102.63/17.16 (demorgan2b2) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (demorgan2) =>
% 102.63/17.16 ((
% 102.63/17.16 (woz13rule0) =>
% 102.63/17.16 ((
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% 102.63/17.16 (woz13rule2) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (woz1_5) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1all2) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1SetBreln1) =>
% 102.63/17.16 ((
% 102.63/17.16 (choice2fnsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln1) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (breln1unionE) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionEcases) =>
% 102.63/17.16 ((
% 102.63/17.16 (breln1unionCommutes) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (image1E) =>
% 102.63/17.16 ((
% 102.63/17.16 (image1I) =>
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% 102.63/17.16 (injFuncInInjFuncSet) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (injFuncSetFuncInj) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncIn) =>
% 102.63/17.16 ((
% 102.63/17.16 (surjFuncSetFuncSurj) =>
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (omegaSclos) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (peanoSinj) =>
% 102.63/17.16 ((
% 102.63/17.16 (transitivesetOp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintTransitive) =>
% 102.63/17.16 ((
% 102.63/17.16 (transitivesetOp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionTransitive) =>
% 102.63/17.16 ((
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% 102.63/17.16 ((
% 102.63/17.16 (in @
% 102.63/17.16 Y2 @
% 102.63/17.16 Y0) =>
% 102.63/17.16 ((
% 102.63/17.16 (in @
% 102.63/17.16 Y1 @
% 102.63/17.16 Y2) =>
% 102.63/17.16 (in @
% 102.63/17.16 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1002])).
% 102.63/17.16 thf(zip_derived_cl1014, plain,
% 102.63/17.16 (~ (((binintersectSubset4) =>
% 102.63/17.16 (((binintersectSubset1) =>
% 102.63/17.16 (((bs114d) =>
% 102.63/17.16 (((setminusI) =>
% 102.63/17.16 (((setminusEL) =>
% 102.63/17.16 (((setminusER) =>
% 102.63/17.16 (((setminusSubset2) =>
% 102.63/17.16 (((setminusERneg) =>
% 102.63/17.16 (((setminusELneg) =>
% 102.63/17.16 (((setminusILneg) =>
% 102.63/17.16 (((setminusIRneg) =>
% 102.63/17.16 (((setminusLsub) =>
% 102.63/17.16 (((setminusSubset1) =>
% 102.63/17.16 (((symdiffE) =>
% 102.63/17.16 (((symdiffI1) =>
% 102.63/17.16 (((symdiffI2) =>
% 102.63/17.16 (((symdiffIneg1) =>
% 102.63/17.16 (((symdiffIneg2) =>
% 102.63/17.16 (((secondinupair) =>
% 102.63/17.16 (((setukpairIL) =>
% 102.63/17.16 (((setukpairIR) =>
% 102.63/17.16 (((kpairiskpair) =>
% 102.63/17.16 (((kpairp) =>
% 102.63/17.16 (((singletonsubset) =>
% 102.63/17.16 (((singletoninpowerset) =>
% 102.63/17.16 (((singletoninpowunion) =>
% 102.63/17.16 (((upairset2E) =>
% 102.63/17.16 (((upairsubunion) =>
% 102.63/17.16 (((upairinpowunion) =>
% 102.63/17.16 (((ubforcartprodlem1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ubforcartprodlem3) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair1) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempair) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionE2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton1) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setunionsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1I2) =>
% 102.63/17.16 ((
% 102.63/17.16 (singletonsuniq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (theprop) =>
% 102.63/17.16 ((
% 102.63/17.16 (kfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstin) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjL) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR11) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR12) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR1) =>
% 102.63/17.16 ((
% 102.63/17.16 (upairequniteq) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR2) =>
% 102.63/17.16 ((
% 102.63/17.16 (setukpairinjR) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndsingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ksndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (kpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndin) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemEL) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairmemER) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodmempaircEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodfstpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodsndpairEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (cartprodpairsurjEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrI) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrSub) =>
% 102.63/17.16 ((
% 102.63/17.16 (setOfPairsIsBReln) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrERa) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL1) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrEL2) =>
% 102.63/17.16 ((
% 102.63/17.16 (dpsetconstrER) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcImageSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (apProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (app) =>
% 102.63/17.16 ((
% 102.63/17.16 (infuncsetfunc) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcinfuncset) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamProp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lamp) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2p) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall1) =>
% 102.63/17.16 ((
% 102.63/17.16 (brelnall2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ex1E2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp3) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcextLem) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcGraphProp4) =>
% 102.63/17.16 ((
% 102.63/17.16 (subbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (eqbreln) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext) =>
% 102.63/17.16 ((
% 102.63/17.16 (funcext2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq1) =>
% 102.63/17.16 ((
% 102.63/17.16 (ap2apEq2) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta1) =>
% 102.63/17.16 ((
% 102.63/17.16 (lam2lamEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (beta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (eta2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalseProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp1) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueProp2) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifSingleton) =>
% 102.63/17.16 ((
% 102.63/17.16 (ifp) =>
% 102.63/17.16 ((
% 102.63/17.16 (theeq) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrue) =>
% 102.63/17.16 ((
% 102.63/17.16 (iffalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (iftrueorfalse) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (binunionT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setminusT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementT_lem) =>
% 102.63/17.16 ((
% 102.63/17.16 (setextT) =>
% 102.63/17.16 ((
% 102.63/17.16 (subsetTI) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (powersetTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTELcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (binintersectTERcontra) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT1) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT2) =>
% 102.63/17.16 ((
% 102.63/17.16 (contrasubsetT3) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementI1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementE1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub1) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementSub2) =>
% 102.63/17.16 ((
% 102.63/17.16 (doubleComplementEq) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementTnotintersectT) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementImpComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementSubsetComplementIntersect) =>
% 102.63/17.16 ((
% 102.63/17.16 (complementInPowersetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (contraSubsetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTcontraSubset) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTILcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTIRcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion2) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (intersectInPowersetIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpNotIn1) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpInComplement1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTE) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTEcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementUnionInPowersetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule0) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_5) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all2) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1SetBreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (choice2fnsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all1) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compEex) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIL) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIR) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionEcases) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionCommutes) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2Ex) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2W) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2A) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2B) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Ex) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Ex1) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Equiv) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1E) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncInInjFuncSet) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncInj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (leftInvIsSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjCantorThm) =>
% 102.63/17.17 ((
% 102.63/17.17 (foundation2) =>
% 102.63/17.17 ((
% 102.63/17.17 (notinself) =>
% 102.63/17.17 ((
% 102.63/17.17 (notinself2) =>
% 102.63/17.17 ((
% 102.63/17.17 (omegaSp) =>
% 102.63/17.17 ((
% 102.63/17.17 (omegaSclos) =>
% 102.63/17.17 ((
% 102.63/17.17 (peano0notS) =>
% 102.63/17.17 ((
% 102.63/17.17 (peanoSinj) =>
% 102.63/17.17 ((
% 102.63/17.17 (transitivesetOp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintTransitive) =>
% 102.63/17.17 ((
% 102.63/17.17 (transitivesetOp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionTransitive) =>
% 102.63/17.17 ((
% 102.63/17.17 (ordinalMinLem1) =>
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y0 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (ordinal @
% 102.63/17.17 Y0) =>
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y1 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y2 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (in @
% 102.63/17.17 Y2 @
% 102.63/17.17 Y0) =>
% 102.63/17.17 ((
% 102.63/17.17 (in @
% 102.63/17.17 Y1 @
% 102.63/17.17 Y2) =>
% 102.63/17.17 (in @
% 102.63/17.17 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1008])).
% 102.63/17.17 thf(zip_derived_cl1021, plain,
% 102.63/17.17 (~ (((binintersectSubset1) =>
% 102.63/17.17 (((bs114d) =>
% 102.63/17.17 (((setminusI) =>
% 102.63/17.17 (((setminusEL) =>
% 102.63/17.17 (((setminusER) =>
% 102.63/17.17 (((setminusSubset2) =>
% 102.63/17.17 (((setminusERneg) =>
% 102.63/17.17 (((setminusELneg) =>
% 102.63/17.17 (((setminusILneg) =>
% 102.63/17.17 (((setminusIRneg) =>
% 102.63/17.17 (((setminusLsub) =>
% 102.63/17.17 (((setminusSubset1) =>
% 102.63/17.17 (((symdiffE) =>
% 102.63/17.17 (((symdiffI1) =>
% 102.63/17.17 (((symdiffI2) =>
% 102.63/17.17 (((symdiffIneg1) =>
% 102.63/17.17 (((symdiffIneg2) =>
% 102.63/17.17 (((secondinupair) =>
% 102.63/17.17 (((setukpairIL) =>
% 102.63/17.17 (((setukpairIR) =>
% 102.63/17.17 (((kpairiskpair) =>
% 102.63/17.17 (((kpairp) =>
% 102.63/17.17 (((singletonsubset) =>
% 102.63/17.17 (((singletoninpowerset) =>
% 102.63/17.17 (((singletoninpowunion) =>
% 102.63/17.17 (((upairset2E) =>
% 102.63/17.17 (((upairsubunion) =>
% 102.63/17.17 (((upairinpowunion) =>
% 102.63/17.17 (((ubforcartprodlem1) =>
% 102.63/17.17 (((ubforcartprodlem2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ubforcartprodlem3) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairin) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempair1) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempair) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionE2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton1) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (singletonprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1E1) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1I2) =>
% 102.63/17.17 ((
% 102.63/17.17 (singletonsuniq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL1) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (theprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstin) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR11) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR12) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR1) =>
% 102.63/17.17 ((
% 102.63/17.17 (upairequniteq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (kpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndin) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemEL) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemER) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempaircEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrI) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrSub) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrERa) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrEL1) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrEL2) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrER) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcImageSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (apProp) =>
% 102.63/17.17 ((
% 102.63/17.17 (app) =>
% 102.63/17.17 ((
% 102.63/17.17 (infuncsetfunc) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcinfuncset) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamProp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall1) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1E2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp3) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcextLem) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp4) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq1) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq2) =>
% 102.63/17.17 ((
% 102.63/17.17 (beta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2lamEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (beta2) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta2) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifp) =>
% 102.63/17.17 ((
% 102.63/17.17 (theeq) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrue) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueorfalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setminusT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setextT) =>
% 102.63/17.17 ((
% 102.63/17.17 (subsetTI) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTELcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTERcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT1) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT2) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT3) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub2) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTnotintersectT) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementImpComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementSubsetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementInPowersetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (contraSubsetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTcontraSubset) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTILcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTIRcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion2) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (intersectInPowersetIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpNotIn1) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpInComplement1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTE) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTEcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementUnionInPowersetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule0) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_5) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all2) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1SetBreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (choice2fnsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all1) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compEex) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIL) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIR) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionEcases) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionCommutes) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2Ex) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2W) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2A) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2B) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Ex) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Ex1) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Equiv) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1E) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncInInjFuncSet) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncInj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (leftInvIsSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjCantorThm) =>
% 102.63/17.17 ((
% 102.63/17.17 (foundation2) =>
% 102.63/17.17 ((
% 102.63/17.17 (notinself) =>
% 102.63/17.17 ((
% 102.63/17.17 (notinself2) =>
% 102.63/17.17 ((
% 102.63/17.17 (omegaSp) =>
% 102.63/17.17 ((
% 102.63/17.17 (omegaSclos) =>
% 102.63/17.17 ((
% 102.63/17.17 (peano0notS) =>
% 102.63/17.17 ((
% 102.63/17.17 (peanoSinj) =>
% 102.63/17.17 ((
% 102.63/17.17 (transitivesetOp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintTransitive) =>
% 102.63/17.17 ((
% 102.63/17.17 (transitivesetOp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionTransitive) =>
% 102.63/17.17 ((
% 102.63/17.17 (ordinalMinLem1) =>
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y0 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (ordinal @
% 102.63/17.17 Y0) =>
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y1 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y2 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (in @
% 102.63/17.17 Y2 @
% 102.63/17.17 Y0) =>
% 102.63/17.17 ((
% 102.63/17.17 (in @
% 102.63/17.17 Y1 @
% 102.63/17.17 Y2) =>
% 102.63/17.17 (in @
% 102.63/17.17 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1014])).
% 102.63/17.17 thf(zip_derived_cl1028, plain,
% 102.63/17.17 (~ (((bs114d) =>
% 102.63/17.17 (((setminusI) =>
% 102.63/17.17 (((setminusEL) =>
% 102.63/17.17 (((setminusER) =>
% 102.63/17.17 (((setminusSubset2) =>
% 102.63/17.17 (((setminusERneg) =>
% 102.63/17.17 (((setminusELneg) =>
% 102.63/17.17 (((setminusILneg) =>
% 102.63/17.17 (((setminusIRneg) =>
% 102.63/17.17 (((setminusLsub) =>
% 102.63/17.17 (((setminusSubset1) =>
% 102.63/17.17 (((symdiffE) =>
% 102.63/17.17 (((symdiffI1) =>
% 102.63/17.17 (((symdiffI2) =>
% 102.63/17.17 (((symdiffIneg1) =>
% 102.63/17.17 (((symdiffIneg2) =>
% 102.63/17.17 (((secondinupair) =>
% 102.63/17.17 (((setukpairIL) =>
% 102.63/17.17 (((setukpairIR) =>
% 102.63/17.17 (((kpairiskpair) =>
% 102.63/17.17 (((kpairp) =>
% 102.63/17.17 (((singletonsubset) =>
% 102.63/17.17 (((singletoninpowerset) =>
% 102.63/17.17 (((singletoninpowunion) =>
% 102.63/17.17 (((upairset2E) =>
% 102.63/17.17 (((upairsubunion) =>
% 102.63/17.17 (((upairinpowunion) =>
% 102.63/17.17 (((ubforcartprodlem1) =>
% 102.63/17.17 (((ubforcartprodlem2) =>
% 102.63/17.17 (((ubforcartprodlem3) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairin) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempair1) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempair) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionE2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton1) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (singletonprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1E1) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1I2) =>
% 102.63/17.17 ((
% 102.63/17.17 (singletonsuniq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL1) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (theprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstin) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR11) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR12) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR1) =>
% 102.63/17.17 ((
% 102.63/17.17 (upairequniteq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (kpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndin) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemEL) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemER) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempaircEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrI) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrSub) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrERa) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrEL1) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrEL2) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrER) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcImageSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (apProp) =>
% 102.63/17.17 ((
% 102.63/17.17 (app) =>
% 102.63/17.17 ((
% 102.63/17.17 (infuncsetfunc) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcinfuncset) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamProp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall1) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1E2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp3) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcextLem) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp4) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq1) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq2) =>
% 102.63/17.17 ((
% 102.63/17.17 (beta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2lamEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (beta2) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta2) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifp) =>
% 102.63/17.17 ((
% 102.63/17.17 (theeq) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrue) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueorfalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setminusT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setextT) =>
% 102.63/17.17 ((
% 102.63/17.17 (subsetTI) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTELcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTERcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT1) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT2) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT3) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub2) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTnotintersectT) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementImpComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementSubsetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementInPowersetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (contraSubsetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTcontraSubset) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTILcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTIRcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion2) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (intersectInPowersetIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpNotIn1) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpInComplement1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTE) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTEcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementUnionInPowersetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule0) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_5) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all2) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1SetBreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (choice2fnsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all1) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compEex) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIL) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIR) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionEcases) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionCommutes) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2Ex) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2W) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2A) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2B) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Ex) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Ex1) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Equiv) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1E) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncInInjFuncSet) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncInj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (leftInvIsSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjCantorThm) =>
% 102.63/17.17 ((
% 102.63/17.17 (foundation2) =>
% 102.63/17.17 ((
% 102.63/17.17 (notinself) =>
% 102.63/17.17 ((
% 102.63/17.17 (notinself2) =>
% 102.63/17.17 ((
% 102.63/17.17 (omegaSp) =>
% 102.63/17.17 ((
% 102.63/17.17 (omegaSclos) =>
% 102.63/17.17 ((
% 102.63/17.17 (peano0notS) =>
% 102.63/17.17 ((
% 102.63/17.17 (peanoSinj) =>
% 102.63/17.17 ((
% 102.63/17.17 (transitivesetOp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintTransitive) =>
% 102.63/17.17 ((
% 102.63/17.17 (transitivesetOp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionTransitive) =>
% 102.63/17.17 ((
% 102.63/17.17 (ordinalMinLem1) =>
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y0 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (ordinal @
% 102.63/17.17 Y0) =>
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y1 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y2 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (in @
% 102.63/17.17 Y2 @
% 102.63/17.17 Y0) =>
% 102.63/17.17 ((
% 102.63/17.17 (in @
% 102.63/17.17 Y1 @
% 102.63/17.17 Y2) =>
% 102.63/17.17 (in @
% 102.63/17.17 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1021])).
% 102.63/17.17 thf(zip_derived_cl1034, plain,
% 102.63/17.17 (~ (((setminusI) =>
% 102.63/17.17 (((setminusEL) =>
% 102.63/17.17 (((setminusER) =>
% 102.63/17.17 (((setminusSubset2) =>
% 102.63/17.17 (((setminusERneg) =>
% 102.63/17.17 (((setminusELneg) =>
% 102.63/17.17 (((setminusILneg) =>
% 102.63/17.17 (((setminusIRneg) =>
% 102.63/17.17 (((setminusLsub) =>
% 102.63/17.17 (((setminusSubset1) =>
% 102.63/17.17 (((symdiffE) =>
% 102.63/17.17 (((symdiffI1) =>
% 102.63/17.17 (((symdiffI2) =>
% 102.63/17.17 (((symdiffIneg1) =>
% 102.63/17.17 (((symdiffIneg2) =>
% 102.63/17.17 (((secondinupair) =>
% 102.63/17.17 (((setukpairIL) =>
% 102.63/17.17 (((setukpairIR) =>
% 102.63/17.17 (((kpairiskpair) =>
% 102.63/17.17 (((kpairp) =>
% 102.63/17.17 (((singletonsubset) =>
% 102.63/17.17 (((singletoninpowerset) =>
% 102.63/17.17 (((singletoninpowunion) =>
% 102.63/17.17 (((upairset2E) =>
% 102.63/17.17 (((upairsubunion) =>
% 102.63/17.17 (((upairinpowunion) =>
% 102.63/17.17 (((ubforcartprodlem1) =>
% 102.63/17.17 (((ubforcartprodlem2) =>
% 102.63/17.17 (((ubforcartprodlem3) =>
% 102.63/17.17 (((cartprodpairin) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempair1) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempair) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionE2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton1) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (singletonprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1E1) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1I2) =>
% 102.63/17.17 ((
% 102.63/17.17 (singletonsuniq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL1) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (theprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstin) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR11) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR12) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR1) =>
% 102.63/17.17 ((
% 102.63/17.17 (upairequniteq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (kpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndin) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemEL) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemER) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempaircEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrI) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrSub) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrERa) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrEL1) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrEL2) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrER) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcImageSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (apProp) =>
% 102.63/17.17 ((
% 102.63/17.17 (app) =>
% 102.63/17.17 ((
% 102.63/17.17 (infuncsetfunc) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcinfuncset) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamProp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall1) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1E2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp3) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcextLem) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp4) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq1) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq2) =>
% 102.63/17.17 ((
% 102.63/17.17 (beta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2lamEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (beta2) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta2) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifp) =>
% 102.63/17.17 ((
% 102.63/17.17 (theeq) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrue) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueorfalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setminusT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setextT) =>
% 102.63/17.17 ((
% 102.63/17.17 (subsetTI) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTELcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTERcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT1) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT2) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT3) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub2) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTnotintersectT) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementImpComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementSubsetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementInPowersetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (contraSubsetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTcontraSubset) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTILcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTIRcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion2) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (intersectInPowersetIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpNotIn1) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpInComplement1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTE) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTEcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementUnionInPowersetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule0) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_5) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all2) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1SetBreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (choice2fnsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all1) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln1) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (breln1invI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compEex) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIL) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIR) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionEcases) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionCommutes) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2Ex) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (image1I) =>
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% 102.63/17.17 (injFuncInInjFuncSet) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncInj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (leftInvIsSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjCantorThm) =>
% 102.63/17.17 ((
% 102.63/17.17 (foundation2) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (omegaSclos) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (peanoSinj) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1028])).
% 102.63/17.17 thf(zip_derived_cl1041, plain,
% 102.63/17.17 (~ (((setminusEL) =>
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% 102.63/17.17 (((upairinpowunion) =>
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% 102.63/17.17 (((ubforcartprodlem3) =>
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% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempair) =>
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% 102.63/17.17 (setunionE2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton1) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton) =>
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% 102.63/17.17 (theprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstin) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL2) =>
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% 102.63/17.17 (setukpairinjL) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR11) =>
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% 102.63/17.17 (setukpairinjR12) =>
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% 102.63/17.17 (setukpairinjR1) =>
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% 102.63/17.17 (upairequniteq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (kpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndin) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemEL) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemER) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempaircEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairsurjEq) =>
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% 102.63/17.17 (dpsetconstrI) =>
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% 102.63/17.17 (dpsetconstrSub) =>
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% 102.63/17.17 (setOfPairsIsBReln) =>
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% 102.63/17.17 (dpsetconstrERa) =>
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% 102.63/17.17 (dpsetconstrEL2) =>
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% 102.63/17.17 (dpsetconstrER) =>
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% 102.63/17.17 (funcImageSingleton) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (lamp) =>
% 102.63/17.17 ((
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% 102.63/17.17 (brelnall2) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp3) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcextLem) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp4) =>
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% 102.63/17.17 (subbreln) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (funcext2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq1) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq2) =>
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% 102.63/17.17 ((
% 102.63/17.17 (eta1) =>
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% 102.63/17.17 (beta2) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp2) =>
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% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifp) =>
% 102.63/17.17 ((
% 102.63/17.17 (theeq) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (binunionT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setminusT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setextT) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (powersetTI1) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 (contrasubsetT2) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT3) =>
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% 102.63/17.17 (doubleComplementI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub2) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTnotintersectT) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementImpComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementSubsetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementInPowersetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (contraSubsetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTcontraSubset) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTILcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTIRcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion2) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (intersectInPowersetIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpNotIn1) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpInComplement1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTE) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTEcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementUnionInPowersetComplement) =>
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% 102.63/17.17 (demorgan2a2) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (woz1_3) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (woz1_5) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all2) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1SetBreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (choice2fnsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln1) =>
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% 102.63/17.17 (breln1all1) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln1) =>
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% 102.63/17.17 (breln1invprop) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (breln1invE) =>
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% 102.63/17.17 (breln1compI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compEex) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIL) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIR) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionEcases) =>
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% 102.63/17.17 (breln1unionCommutes) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2Ex) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (image1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncInInjFuncSet) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncInj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncSurj) =>
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% 102.63/17.17 (leftInvIsSurj) =>
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (peano0notS) =>
% 102.63/17.17 ((
% 102.63/17.17 (peanoSinj) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ^[Y0 : $i]:
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% 102.63/17.17 (in @
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% 102.63/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1034])).
% 102.63/17.17 thf(zip_derived_cl1047, plain,
% 102.63/17.17 (~ (((setminusER) =>
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% 102.63/17.17 (((setminusELneg) =>
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% 102.63/17.17 (((setminusIRneg) =>
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% 102.63/17.17 (((setminusSubset1) =>
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% 102.63/17.17 (((singletoninpowunion) =>
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% 102.63/17.17 (((ubforcartprodlem1) =>
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% 102.63/17.17 (((cartprodmempair) =>
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% 102.63/17.17 (setunionE2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton1) =>
% 102.63/17.17 ((
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% 102.63/17.17 (theprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstin) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL) =>
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% 102.63/17.17 (setukpairinjR11) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR12) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR1) =>
% 102.63/17.17 ((
% 102.63/17.17 (upairequniteq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR) =>
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% 102.63/17.17 (ksndsingleton) =>
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% 102.63/17.17 (ksndpairEq) =>
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% 102.63/17.17 (kpairsurjEq) =>
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% 102.63/17.17 (cartprodsndin) =>
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% 102.63/17.17 (cartprodpairmemEL) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemER) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempaircEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrI) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrSub) =>
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% 102.63/17.17 (dpsetconstrEL1) =>
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% 102.63/17.17 (dpsetconstrEL2) =>
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% 102.63/17.17 (dpsetconstrER) =>
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% 102.63/17.17 (funcImageSingleton) =>
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% 102.63/17.17 (apProp) =>
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% 102.63/17.17 (ap2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcinfuncset) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamProp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall1) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1E2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp3) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcextLem) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp4) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq1) =>
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% 102.63/17.17 (ap2apEq2) =>
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% 102.63/17.17 (beta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2lamEq) =>
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% 102.63/17.17 (beta2) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta2) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp2) =>
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% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifp) =>
% 102.63/17.17 ((
% 102.63/17.17 (theeq) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrue) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueorfalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setminusT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setextT) =>
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% 102.63/17.17 (subsetTI) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTELcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTERcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT1) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT2) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT3) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub2) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTnotintersectT) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementImpComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementSubsetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementInPowersetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (contraSubsetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTcontraSubset) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTILcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTIRcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion2) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (intersectInPowersetIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpNotIn1) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpInComplement1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTE) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTEcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementUnionInPowersetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule0) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_5) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all2) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1SetBreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (choice2fnsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all1) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compEex) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIL) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIR) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionEcases) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionCommutes) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2Ex) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2W) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2A) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2B) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Ex) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Ex1) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Equiv) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1E) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncInInjFuncSet) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncInj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (leftInvIsSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjCantorThm) =>
% 102.63/17.17 ((
% 102.63/17.17 (foundation2) =>
% 102.63/17.17 ((
% 102.63/17.17 (notinself) =>
% 102.63/17.17 ((
% 102.63/17.17 (notinself2) =>
% 102.63/17.17 ((
% 102.63/17.17 (omegaSp) =>
% 102.63/17.17 ((
% 102.63/17.17 (omegaSclos) =>
% 102.63/17.17 ((
% 102.63/17.17 (peano0notS) =>
% 102.63/17.17 ((
% 102.63/17.17 (peanoSinj) =>
% 102.63/17.17 ((
% 102.63/17.17 (transitivesetOp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintTransitive) =>
% 102.63/17.17 ((
% 102.63/17.17 (transitivesetOp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionTransitive) =>
% 102.63/17.17 ((
% 102.63/17.17 (ordinalMinLem1) =>
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y0 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (ordinal @
% 102.63/17.17 Y0) =>
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y1 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y2 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (in @
% 102.63/17.17 Y2 @
% 102.63/17.17 Y0) =>
% 102.63/17.17 ((
% 102.63/17.17 (in @
% 102.63/17.17 Y1 @
% 102.63/17.17 Y2) =>
% 102.63/17.17 (in @
% 102.63/17.17 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1041])).
% 102.63/17.17 thf(zip_derived_cl1054, plain,
% 102.63/17.17 (~ (((setminusSubset2) =>
% 102.63/17.17 (((setminusERneg) =>
% 102.63/17.17 (((setminusELneg) =>
% 102.63/17.17 (((setminusILneg) =>
% 102.63/17.17 (((setminusIRneg) =>
% 102.63/17.17 (((setminusLsub) =>
% 102.63/17.17 (((setminusSubset1) =>
% 102.63/17.17 (((symdiffE) =>
% 102.63/17.17 (((symdiffI1) =>
% 102.63/17.17 (((symdiffI2) =>
% 102.63/17.17 (((symdiffIneg1) =>
% 102.63/17.17 (((symdiffIneg2) =>
% 102.63/17.17 (((secondinupair) =>
% 102.63/17.17 (((setukpairIL) =>
% 102.63/17.17 (((setukpairIR) =>
% 102.63/17.17 (((kpairiskpair) =>
% 102.63/17.17 (((kpairp) =>
% 102.63/17.17 (((singletonsubset) =>
% 102.63/17.17 (((singletoninpowerset) =>
% 102.63/17.17 (((singletoninpowunion) =>
% 102.63/17.17 (((upairset2E) =>
% 102.63/17.17 (((upairsubunion) =>
% 102.63/17.17 (((upairinpowunion) =>
% 102.63/17.17 (((ubforcartprodlem1) =>
% 102.63/17.17 (((ubforcartprodlem2) =>
% 102.63/17.17 (((ubforcartprodlem3) =>
% 102.63/17.17 (((cartprodpairin) =>
% 102.63/17.17 (((cartprodmempair1) =>
% 102.63/17.17 (((cartprodmempair) =>
% 102.63/17.17 (((setunionE2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton1) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (singletonprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1E1) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1I2) =>
% 102.63/17.17 ((
% 102.63/17.17 (singletonsuniq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL1) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (theprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstin) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR11) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR12) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR1) =>
% 102.63/17.17 ((
% 102.63/17.17 (upairequniteq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (kpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndin) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemEL) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemER) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempaircEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrI) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrSub) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrERa) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrEL1) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrEL2) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrER) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcImageSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (apProp) =>
% 102.63/17.17 ((
% 102.63/17.17 (app) =>
% 102.63/17.17 ((
% 102.63/17.17 (infuncsetfunc) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcinfuncset) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamProp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall1) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1E2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp3) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcextLem) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp4) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq1) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq2) =>
% 102.63/17.17 ((
% 102.63/17.17 (beta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2lamEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (beta2) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta2) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifp) =>
% 102.63/17.17 ((
% 102.63/17.17 (theeq) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrue) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueorfalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setminusT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setextT) =>
% 102.63/17.17 ((
% 102.63/17.17 (subsetTI) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTELcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTERcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT1) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT2) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT3) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub2) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTnotintersectT) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementImpComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementSubsetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementInPowersetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (contraSubsetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTcontraSubset) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTILcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTIRcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion2) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (intersectInPowersetIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpNotIn1) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpInComplement1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTE) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTEcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementUnionInPowersetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule0) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_5) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all2) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1SetBreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (choice2fnsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all1) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compEex) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIL) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIR) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionEcases) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionCommutes) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2Ex) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2W) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2A) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2B) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Ex) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Ex1) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Equiv) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1E) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncInInjFuncSet) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncInj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (leftInvIsSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjCantorThm) =>
% 102.63/17.17 ((
% 102.63/17.17 (foundation2) =>
% 102.63/17.17 ((
% 102.63/17.17 (notinself) =>
% 102.63/17.17 ((
% 102.63/17.17 (notinself2) =>
% 102.63/17.17 ((
% 102.63/17.17 (omegaSp) =>
% 102.63/17.17 ((
% 102.63/17.17 (omegaSclos) =>
% 102.63/17.17 ((
% 102.63/17.17 (peano0notS) =>
% 102.63/17.17 ((
% 102.63/17.17 (peanoSinj) =>
% 102.63/17.17 ((
% 102.63/17.17 (transitivesetOp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintTransitive) =>
% 102.63/17.17 ((
% 102.63/17.17 (transitivesetOp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionTransitive) =>
% 102.63/17.17 ((
% 102.63/17.17 (ordinalMinLem1) =>
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y0 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (ordinal @
% 102.63/17.17 Y0) =>
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y1 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y2 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (in @
% 102.63/17.17 Y2 @
% 102.63/17.17 Y0) =>
% 102.63/17.17 ((
% 102.63/17.17 (in @
% 102.63/17.17 Y1 @
% 102.63/17.17 Y2) =>
% 102.63/17.17 (in @
% 102.63/17.17 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1047])).
% 102.63/17.17 thf(zip_derived_cl1061, plain,
% 102.63/17.17 (~ (((setminusERneg) =>
% 102.63/17.17 (((setminusELneg) =>
% 102.63/17.17 (((setminusILneg) =>
% 102.63/17.17 (((setminusIRneg) =>
% 102.63/17.17 (((setminusLsub) =>
% 102.63/17.17 (((setminusSubset1) =>
% 102.63/17.17 (((symdiffE) =>
% 102.63/17.17 (((symdiffI1) =>
% 102.63/17.17 (((symdiffI2) =>
% 102.63/17.17 (((symdiffIneg1) =>
% 102.63/17.17 (((symdiffIneg2) =>
% 102.63/17.17 (((secondinupair) =>
% 102.63/17.17 (((setukpairIL) =>
% 102.63/17.17 (((setukpairIR) =>
% 102.63/17.17 (((kpairiskpair) =>
% 102.63/17.17 (((kpairp) =>
% 102.63/17.17 (((singletonsubset) =>
% 102.63/17.17 (((singletoninpowerset) =>
% 102.63/17.17 (((singletoninpowunion) =>
% 102.63/17.17 (((upairset2E) =>
% 102.63/17.17 (((upairsubunion) =>
% 102.63/17.17 (((upairinpowunion) =>
% 102.63/17.17 (((ubforcartprodlem1) =>
% 102.63/17.17 (((ubforcartprodlem2) =>
% 102.63/17.17 (((ubforcartprodlem3) =>
% 102.63/17.17 (((cartprodpairin) =>
% 102.63/17.17 (((cartprodmempair1) =>
% 102.63/17.17 (((cartprodmempair) =>
% 102.63/17.17 (((setunionE2) =>
% 102.63/17.17 (((setunionsingleton1) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (singletonprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1E1) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1I2) =>
% 102.63/17.17 ((
% 102.63/17.17 (singletonsuniq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL1) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (theprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstin) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR11) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR12) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR1) =>
% 102.63/17.17 ((
% 102.63/17.17 (upairequniteq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (kpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndin) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemEL) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemER) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempaircEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrI) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrSub) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrERa) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrEL1) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrEL2) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrER) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcImageSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (apProp) =>
% 102.63/17.17 ((
% 102.63/17.17 (app) =>
% 102.63/17.17 ((
% 102.63/17.17 (infuncsetfunc) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcinfuncset) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamProp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall1) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1E2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp3) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcextLem) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp4) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq1) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq2) =>
% 102.63/17.17 ((
% 102.63/17.17 (beta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2lamEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (beta2) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta2) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifp) =>
% 102.63/17.17 ((
% 102.63/17.17 (theeq) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrue) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueorfalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setminusT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setextT) =>
% 102.63/17.17 ((
% 102.63/17.17 (subsetTI) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTELcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTERcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT1) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT2) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT3) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub2) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTnotintersectT) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementImpComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementSubsetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementInPowersetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (contraSubsetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTcontraSubset) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTILcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTIRcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion2) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (intersectInPowersetIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpNotIn1) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpInComplement1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTE) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTEcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementUnionInPowersetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule0) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_5) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all2) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1SetBreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (choice2fnsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all1) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compEex) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIL) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIR) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionEcases) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionCommutes) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2Ex) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2W) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2A) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2B) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Ex) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Ex1) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Equiv) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1E) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncInInjFuncSet) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncInj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (leftInvIsSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjCantorThm) =>
% 102.63/17.17 ((
% 102.63/17.17 (foundation2) =>
% 102.63/17.17 ((
% 102.63/17.17 (notinself) =>
% 102.63/17.17 ((
% 102.63/17.17 (notinself2) =>
% 102.63/17.17 ((
% 102.63/17.17 (omegaSp) =>
% 102.63/17.17 ((
% 102.63/17.17 (omegaSclos) =>
% 102.63/17.17 ((
% 102.63/17.17 (peano0notS) =>
% 102.63/17.17 ((
% 102.63/17.17 (peanoSinj) =>
% 102.63/17.17 ((
% 102.63/17.17 (transitivesetOp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintTransitive) =>
% 102.63/17.17 ((
% 102.63/17.17 (transitivesetOp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionTransitive) =>
% 102.63/17.17 ((
% 102.63/17.17 (ordinalMinLem1) =>
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y0 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (ordinal @
% 102.63/17.17 Y0) =>
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y1 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (!!) @ (
% 102.63/17.17 ^[Y2 : $i]:
% 102.63/17.17 ((
% 102.63/17.17 (in @
% 102.63/17.17 Y2 @
% 102.63/17.17 Y0) =>
% 102.63/17.17 ((
% 102.63/17.17 (in @
% 102.63/17.17 Y1 @
% 102.63/17.17 Y2) =>
% 102.63/17.17 (in @
% 102.63/17.17 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1054])).
% 102.63/17.17 thf(zip_derived_cl1068, plain,
% 102.63/17.17 (~ (((setminusELneg) =>
% 102.63/17.17 (((setminusILneg) =>
% 102.63/17.17 (((setminusIRneg) =>
% 102.63/17.17 (((setminusLsub) =>
% 102.63/17.17 (((setminusSubset1) =>
% 102.63/17.17 (((symdiffE) =>
% 102.63/17.17 (((symdiffI1) =>
% 102.63/17.17 (((symdiffI2) =>
% 102.63/17.17 (((symdiffIneg1) =>
% 102.63/17.17 (((symdiffIneg2) =>
% 102.63/17.17 (((secondinupair) =>
% 102.63/17.17 (((setukpairIL) =>
% 102.63/17.17 (((setukpairIR) =>
% 102.63/17.17 (((kpairiskpair) =>
% 102.63/17.17 (((kpairp) =>
% 102.63/17.17 (((singletonsubset) =>
% 102.63/17.17 (((singletoninpowerset) =>
% 102.63/17.17 (((singletoninpowunion) =>
% 102.63/17.17 (((upairset2E) =>
% 102.63/17.17 (((upairsubunion) =>
% 102.63/17.17 (((upairinpowunion) =>
% 102.63/17.17 (((ubforcartprodlem1) =>
% 102.63/17.17 (((ubforcartprodlem2) =>
% 102.63/17.17 (((ubforcartprodlem3) =>
% 102.63/17.17 (((cartprodpairin) =>
% 102.63/17.17 (((cartprodmempair1) =>
% 102.63/17.17 (((cartprodmempair) =>
% 102.63/17.17 (((setunionE2) =>
% 102.63/17.17 (((setunionsingleton1) =>
% 102.63/17.17 (((setunionsingleton2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setunionsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (singletonprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1E1) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1I2) =>
% 102.63/17.17 ((
% 102.63/17.17 (singletonsuniq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL1) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (theprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (kfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstin) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjL) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR11) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR12) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR1) =>
% 102.63/17.17 ((
% 102.63/17.17 (upairequniteq) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR2) =>
% 102.63/17.17 ((
% 102.63/17.17 (setukpairinjR) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ksndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (kpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndin) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemEL) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairmemER) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodmempaircEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodfstpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodsndpairEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (cartprodpairsurjEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrI) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrSub) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrERa) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrEL1) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrEL2) =>
% 102.63/17.17 ((
% 102.63/17.17 (dpsetconstrER) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcImageSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (apProp) =>
% 102.63/17.17 ((
% 102.63/17.17 (app) =>
% 102.63/17.17 ((
% 102.63/17.17 (infuncsetfunc) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcinfuncset) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamProp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lamp) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2p) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall1) =>
% 102.63/17.17 ((
% 102.63/17.17 (brelnall2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ex1E2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp3) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcextLem) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcGraphProp4) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext) =>
% 102.63/17.17 ((
% 102.63/17.17 (funcext2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq1) =>
% 102.63/17.17 ((
% 102.63/17.17 (ap2apEq2) =>
% 102.63/17.17 ((
% 102.63/17.17 (beta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta1) =>
% 102.63/17.17 ((
% 102.63/17.17 (lam2lamEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (beta2) =>
% 102.63/17.17 ((
% 102.63/17.17 (eta2) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalseProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp1) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueProp2) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifSingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (ifp) =>
% 102.63/17.17 ((
% 102.63/17.17 (theeq) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrue) =>
% 102.63/17.17 ((
% 102.63/17.17 (iffalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (iftrueorfalse) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setminusT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementT_lem) =>
% 102.63/17.17 ((
% 102.63/17.17 (setextT) =>
% 102.63/17.17 ((
% 102.63/17.17 (subsetTI) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (powersetTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTELcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binintersectTERcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT1) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT2) =>
% 102.63/17.17 ((
% 102.63/17.17 (contrasubsetT3) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementI1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementE1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub1) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementSub2) =>
% 102.63/17.17 ((
% 102.63/17.17 (doubleComplementEq) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTnotintersectT) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementImpComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementSubsetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementInPowersetComplementIntersect) =>
% 102.63/17.17 ((
% 102.63/17.17 (contraSubsetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementTcontraSubset) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTILcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTIRcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInUnion2) =>
% 102.63/17.17 ((
% 102.63/17.17 (inIntersectImpInIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (intersectInPowersetIntersectUnions) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpNotIn1) =>
% 102.63/17.17 ((
% 102.63/17.17 (inComplementUnionImpInComplement1) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTE) =>
% 102.63/17.17 ((
% 102.63/17.17 (binunionTEcontra) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a1) =>
% 102.63/17.17 ((
% 102.63/17.17 (complementUnionInPowersetComplement) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan1) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2a) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b2) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2b) =>
% 102.63/17.17 ((
% 102.63/17.17 (demorgan2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule0) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz13rule4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_1) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_2) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_3) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_4) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz1_5) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all2) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1SetBreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (choice2fnsingleton) =>
% 102.63/17.17 ((
% 102.63/17.17 (setOfPairsIsBReln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1all1) =>
% 102.63/17.17 ((
% 102.63/17.17 (subbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (eqbreln1) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1invE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1compEex) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionprop) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIL) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionIR) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionI) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionE) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionEcases) =>
% 102.63/17.17 ((
% 102.63/17.17 (breln1unionCommutes) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2Ex) =>
% 102.63/17.17 ((
% 102.63/17.17 (woz2W) =>
% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
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% 102.63/17.17 ((
% 102.63/17.17 (image1Ex1) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1Equiv) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1E) =>
% 102.63/17.17 ((
% 102.63/17.17 (image1I) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncInInjFuncSet) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (injFuncSetFuncInj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncIn) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjFuncSetFuncSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (leftInvIsSurj) =>
% 102.63/17.17 ((
% 102.63/17.17 (surjCantorThm) =>
% 102.63/17.17 ((
% 102.63/17.17 (foundation2) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself2) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSp) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSclos) =>
% 102.63/17.18 ((
% 102.63/17.18 (peano0notS) =>
% 102.63/17.18 ((
% 102.63/17.18 (peanoSinj) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (binintTransitive) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setunionTransitive) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 ^[Y0 : $i]:
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% 102.63/17.18 (ordinal @
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% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y2 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (in @
% 102.63/17.18 Y2 @
% 102.63/17.18 Y0) =>
% 102.63/17.18 ((
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @
% 102.63/17.18 Y2) =>
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1061])).
% 102.63/17.18 thf(zip_derived_cl1075, plain,
% 102.63/17.18 (~ (((setminusILneg) =>
% 102.63/17.18 (((setminusIRneg) =>
% 102.63/17.18 (((setminusLsub) =>
% 102.63/17.18 (((setminusSubset1) =>
% 102.63/17.18 (((symdiffE) =>
% 102.63/17.18 (((symdiffI1) =>
% 102.63/17.18 (((symdiffI2) =>
% 102.63/17.18 (((symdiffIneg1) =>
% 102.63/17.18 (((symdiffIneg2) =>
% 102.63/17.18 (((secondinupair) =>
% 102.63/17.18 (((setukpairIL) =>
% 102.63/17.18 (((setukpairIR) =>
% 102.63/17.18 (((kpairiskpair) =>
% 102.63/17.18 (((kpairp) =>
% 102.63/17.18 (((singletonsubset) =>
% 102.63/17.18 (((singletoninpowerset) =>
% 102.63/17.18 (((singletoninpowunion) =>
% 102.63/17.18 (((upairset2E) =>
% 102.63/17.18 (((upairsubunion) =>
% 102.63/17.18 (((upairinpowunion) =>
% 102.63/17.18 (((ubforcartprodlem1) =>
% 102.63/17.18 (((ubforcartprodlem2) =>
% 102.63/17.18 (((ubforcartprodlem3) =>
% 102.63/17.18 (((cartprodpairin) =>
% 102.63/17.18 (((cartprodmempair1) =>
% 102.63/17.18 (((cartprodmempair) =>
% 102.63/17.18 (((setunionE2) =>
% 102.63/17.18 (((setunionsingleton1) =>
% 102.63/17.18 (((setunionsingleton2) =>
% 102.63/17.18 (((setunionsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (singletonprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1E1) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1I) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1I2) =>
% 102.63/17.18 ((
% 102.63/17.18 (singletonsuniq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (theprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstin) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR11) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR12) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR1) =>
% 102.63/17.18 ((
% 102.63/17.18 (upairequniteq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (kpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndin) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemEL) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemER) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodmempaircEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrI) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrSub) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrERa) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrER) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcImageSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (apProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (app) =>
% 102.63/17.18 ((
% 102.63/17.18 (infuncsetfunc) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcinfuncset) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall1) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1E2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp3) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcextLem) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp4) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq1) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq2) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2lamEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifp) =>
% 102.63/17.18 ((
% 102.63/17.18 (theeq) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrue) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueorfalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setminusT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setextT) =>
% 102.63/17.18 ((
% 102.63/17.18 (subsetTI) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTELcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTERcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT1) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT2) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT3) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub2) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTnotintersectT) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementImpComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementSubsetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementInPowersetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (contraSubsetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTcontraSubset) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTILcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTIRcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion2) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (intersectInPowersetIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpNotIn1) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpInComplement1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTE) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTEcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementUnionInPowersetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule0) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule4) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_4) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_5) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all2) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1SetBreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (choice2fnsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all1) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compEex) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIL) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIR) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionEcases) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionCommutes) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2Ex) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2W) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2A) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2B) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Ex) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Ex1) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Equiv) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1E) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1I) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncInInjFuncSet) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncInj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (leftInvIsSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjCantorThm) =>
% 102.63/17.18 ((
% 102.63/17.18 (foundation2) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself2) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSp) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSclos) =>
% 102.63/17.18 ((
% 102.63/17.18 (peano0notS) =>
% 102.63/17.18 ((
% 102.63/17.18 (peanoSinj) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintTransitive) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setunionTransitive) =>
% 102.63/17.18 ((
% 102.63/17.18 (ordinalMinLem1) =>
% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y0 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (ordinal @
% 102.63/17.18 Y0) =>
% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y1 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y2 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (in @
% 102.63/17.18 Y2 @
% 102.63/17.18 Y0) =>
% 102.63/17.18 ((
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @
% 102.63/17.18 Y2) =>
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1068])).
% 102.63/17.18 thf(zip_derived_cl1082, plain,
% 102.63/17.18 (~ (((setminusIRneg) =>
% 102.63/17.18 (((setminusLsub) =>
% 102.63/17.18 (((setminusSubset1) =>
% 102.63/17.18 (((symdiffE) =>
% 102.63/17.18 (((symdiffI1) =>
% 102.63/17.18 (((symdiffI2) =>
% 102.63/17.18 (((symdiffIneg1) =>
% 102.63/17.18 (((symdiffIneg2) =>
% 102.63/17.18 (((secondinupair) =>
% 102.63/17.18 (((setukpairIL) =>
% 102.63/17.18 (((setukpairIR) =>
% 102.63/17.18 (((kpairiskpair) =>
% 102.63/17.18 (((kpairp) =>
% 102.63/17.18 (((singletonsubset) =>
% 102.63/17.18 (((singletoninpowerset) =>
% 102.63/17.18 (((singletoninpowunion) =>
% 102.63/17.18 (((upairset2E) =>
% 102.63/17.18 (((upairsubunion) =>
% 102.63/17.18 (((upairinpowunion) =>
% 102.63/17.18 (((ubforcartprodlem1) =>
% 102.63/17.18 (((ubforcartprodlem2) =>
% 102.63/17.18 (((ubforcartprodlem3) =>
% 102.63/17.18 (((cartprodpairin) =>
% 102.63/17.18 (((cartprodmempair1) =>
% 102.63/17.18 (((cartprodmempair) =>
% 102.63/17.18 (((setunionE2) =>
% 102.63/17.18 (((setunionsingleton1) =>
% 102.63/17.18 (((setunionsingleton2) =>
% 102.63/17.18 (((setunionsingleton) =>
% 102.63/17.18 (((singletonprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1E1) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1I) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1I2) =>
% 102.63/17.18 ((
% 102.63/17.18 (singletonsuniq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (theprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstin) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR11) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR12) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR1) =>
% 102.63/17.18 ((
% 102.63/17.18 (upairequniteq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (kpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndin) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemEL) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemER) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodmempaircEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrI) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrSub) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrERa) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrER) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcImageSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (apProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (app) =>
% 102.63/17.18 ((
% 102.63/17.18 (infuncsetfunc) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcinfuncset) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall1) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1E2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp3) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcextLem) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp4) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq1) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq2) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2lamEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifp) =>
% 102.63/17.18 ((
% 102.63/17.18 (theeq) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrue) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueorfalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setminusT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setextT) =>
% 102.63/17.18 ((
% 102.63/17.18 (subsetTI) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTELcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTERcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT1) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT2) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT3) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub2) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTnotintersectT) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementImpComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementSubsetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementInPowersetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (contraSubsetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTcontraSubset) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTILcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTIRcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion2) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (intersectInPowersetIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpNotIn1) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpInComplement1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTE) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTEcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementUnionInPowersetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule0) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule4) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_4) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_5) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all2) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1SetBreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (choice2fnsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all1) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compEex) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIL) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIR) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionEcases) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionCommutes) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2Ex) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2W) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2A) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2B) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Ex) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Ex1) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Equiv) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1E) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1I) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncInInjFuncSet) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncInj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (leftInvIsSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjCantorThm) =>
% 102.63/17.18 ((
% 102.63/17.18 (foundation2) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself2) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSp) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSclos) =>
% 102.63/17.18 ((
% 102.63/17.18 (peano0notS) =>
% 102.63/17.18 ((
% 102.63/17.18 (peanoSinj) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintTransitive) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setunionTransitive) =>
% 102.63/17.18 ((
% 102.63/17.18 (ordinalMinLem1) =>
% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y0 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (ordinal @
% 102.63/17.18 Y0) =>
% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y1 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y2 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (in @
% 102.63/17.18 Y2 @
% 102.63/17.18 Y0) =>
% 102.63/17.18 ((
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @
% 102.63/17.18 Y2) =>
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1075])).
% 102.63/17.18 thf(zip_derived_cl1089, plain,
% 102.63/17.18 (~ (((setminusLsub) =>
% 102.63/17.18 (((setminusSubset1) =>
% 102.63/17.18 (((symdiffE) =>
% 102.63/17.18 (((symdiffI1) =>
% 102.63/17.18 (((symdiffI2) =>
% 102.63/17.18 (((symdiffIneg1) =>
% 102.63/17.18 (((symdiffIneg2) =>
% 102.63/17.18 (((secondinupair) =>
% 102.63/17.18 (((setukpairIL) =>
% 102.63/17.18 (((setukpairIR) =>
% 102.63/17.18 (((kpairiskpair) =>
% 102.63/17.18 (((kpairp) =>
% 102.63/17.18 (((singletonsubset) =>
% 102.63/17.18 (((singletoninpowerset) =>
% 102.63/17.18 (((singletoninpowunion) =>
% 102.63/17.18 (((upairset2E) =>
% 102.63/17.18 (((upairsubunion) =>
% 102.63/17.18 (((upairinpowunion) =>
% 102.63/17.18 (((ubforcartprodlem1) =>
% 102.63/17.18 (((ubforcartprodlem2) =>
% 102.63/17.18 (((ubforcartprodlem3) =>
% 102.63/17.18 (((cartprodpairin) =>
% 102.63/17.18 (((cartprodmempair1) =>
% 102.63/17.18 (((cartprodmempair) =>
% 102.63/17.18 (((setunionE2) =>
% 102.63/17.18 (((setunionsingleton1) =>
% 102.63/17.18 (((setunionsingleton2) =>
% 102.63/17.18 (((setunionsingleton) =>
% 102.63/17.18 (((singletonprop) =>
% 102.63/17.18 (((ex1E1) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1I) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1I2) =>
% 102.63/17.18 ((
% 102.63/17.18 (singletonsuniq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (theprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstin) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR11) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR12) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR1) =>
% 102.63/17.18 ((
% 102.63/17.18 (upairequniteq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (kpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndin) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemEL) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemER) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodmempaircEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrI) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrSub) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrERa) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrER) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcImageSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (apProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (app) =>
% 102.63/17.18 ((
% 102.63/17.18 (infuncsetfunc) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcinfuncset) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall1) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1E2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp3) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcextLem) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp4) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq1) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq2) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2lamEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifp) =>
% 102.63/17.18 ((
% 102.63/17.18 (theeq) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrue) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueorfalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setminusT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setextT) =>
% 102.63/17.18 ((
% 102.63/17.18 (subsetTI) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTELcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTERcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT1) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT2) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT3) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub2) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTnotintersectT) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementImpComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementSubsetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementInPowersetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (contraSubsetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTcontraSubset) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTILcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTIRcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion2) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (intersectInPowersetIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpNotIn1) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpInComplement1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTE) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTEcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementUnionInPowersetComplement) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (demorgan1a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (woz13rule1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule4) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (woz1_2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_4) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_5) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all2) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1SetBreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (choice2fnsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all1) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln1) =>
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% 102.63/17.18 ((
% 102.63/17.18 (breln1invI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compEex) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIL) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIR) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionEcases) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionCommutes) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2Ex) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2W) =>
% 102.63/17.18 ((
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% 102.63/17.18 (woz2B) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (image1Ex1) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Equiv) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1E) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1I) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncInInjFuncSet) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncInj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (leftInvIsSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjCantorThm) =>
% 102.63/17.18 ((
% 102.63/17.18 (foundation2) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself2) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSp) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSclos) =>
% 102.63/17.18 ((
% 102.63/17.18 (peano0notS) =>
% 102.63/17.18 ((
% 102.63/17.18 (peanoSinj) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp1) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp2) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 ^[Y0 : $i]:
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% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
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% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 Y0) =>
% 102.63/17.18 ((
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% 102.63/17.18 Y1 @
% 102.63/17.18 Y2) =>
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])).
% 102.63/17.18 thf(zip_derived_cl1096, plain,
% 102.63/17.18 (~ (((setminusSubset1) =>
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% 102.63/17.18 (((symdiffI1) =>
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% 102.63/17.18 (((symdiffIneg2) =>
% 102.63/17.18 (((secondinupair) =>
% 102.63/17.18 (((setukpairIL) =>
% 102.63/17.18 (((setukpairIR) =>
% 102.63/17.18 (((kpairiskpair) =>
% 102.63/17.18 (((kpairp) =>
% 102.63/17.18 (((singletonsubset) =>
% 102.63/17.18 (((singletoninpowerset) =>
% 102.63/17.18 (((singletoninpowunion) =>
% 102.63/17.18 (((upairset2E) =>
% 102.63/17.18 (((upairsubunion) =>
% 102.63/17.18 (((upairinpowunion) =>
% 102.63/17.18 (((ubforcartprodlem1) =>
% 102.63/17.18 (((ubforcartprodlem2) =>
% 102.63/17.18 (((ubforcartprodlem3) =>
% 102.63/17.18 (((cartprodpairin) =>
% 102.63/17.18 (((cartprodmempair1) =>
% 102.63/17.18 (((cartprodmempair) =>
% 102.63/17.18 (((setunionE2) =>
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% 102.63/17.18 (singletonsuniq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (theprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstin) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR11) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR12) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR1) =>
% 102.63/17.18 ((
% 102.63/17.18 (upairequniteq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (kpairsurjEq) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemEL) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemER) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodmempaircEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrI) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrSub) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrERa) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrER) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcImageSingleton) =>
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% 102.63/17.18 (apProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (app) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (funcinfuncset) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall1) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall2) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp3) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcextLem) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp4) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq1) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq2) =>
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% 102.63/17.18 ((
% 102.63/17.18 (eta1) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (eta2) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp2) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp2) =>
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% 102.63/17.18 (ifSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifp) =>
% 102.63/17.18 ((
% 102.63/17.18 (theeq) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrue) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueorfalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setminusT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setextT) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (powersetTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTELcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTERcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT1) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT2) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT3) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub2) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTnotintersectT) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementImpComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementSubsetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementInPowersetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (contraSubsetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTcontraSubset) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTILcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTIRcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion2) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (intersectInPowersetIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpNotIn1) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpInComplement1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTE) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTEcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementUnionInPowersetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule0) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule4) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (woz1_2) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (woz1_5) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all2) =>
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% 102.63/17.18 (breln1compE) =>
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% 102.63/17.18 ((
% 102.63/17.18 (breln1unionprop) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 (breln1unionCommutes) =>
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% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncInj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncSurj) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 ^[Y0 : $i]:
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% 102.63/17.18 (ordinal @
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% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
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% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
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% 102.63/17.18 ((
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @
% 102.63/17.18 Y2) =>
% 102.63/17.18 (in @
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% 102.63/17.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1089])).
% 102.63/17.18 thf(zip_derived_cl1103, plain,
% 102.63/17.18 (~ (((symdiffE) =>
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% 102.63/17.18 (((symdiffI2) =>
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% 102.63/17.18 (((kpairp) =>
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% 102.63/17.18 (((singletoninpowunion) =>
% 102.63/17.18 (((upairset2E) =>
% 102.63/17.18 (((upairsubunion) =>
% 102.63/17.18 (((upairinpowunion) =>
% 102.63/17.18 (((ubforcartprodlem1) =>
% 102.63/17.18 (((ubforcartprodlem2) =>
% 102.63/17.18 (((ubforcartprodlem3) =>
% 102.63/17.18 (((cartprodpairin) =>
% 102.63/17.18 (((cartprodmempair1) =>
% 102.63/17.18 (((cartprodmempair) =>
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% 102.63/17.18 (((singletonprop) =>
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% 102.63/17.18 ((
% 102.63/17.18 (singletonsuniq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (theprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstin) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR11) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR12) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR1) =>
% 102.63/17.18 ((
% 102.63/17.18 (upairequniteq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (kpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndin) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemER) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodmempaircEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrI) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrSub) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrERa) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrER) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcImageSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (apProp) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (infuncsetfunc) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcinfuncset) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall1) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1E2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp3) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcextLem) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp4) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq1) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq2) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2lamEq) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp2) =>
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% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifp) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (iftrue) =>
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% 102.63/17.18 (iffalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueorfalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setminusT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setextT) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (powersetTI1) =>
% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (complementTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTELcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTERcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT1) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT2) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT3) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub2) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTnotintersectT) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementImpComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementSubsetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementInPowersetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (contraSubsetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTcontraSubset) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTILcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTIRcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion2) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (intersectInPowersetIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpNotIn1) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpInComplement1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTE) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTEcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementUnionInPowersetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule0) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule4) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_4) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_5) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all2) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1SetBreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (choice2fnsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all1) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compEex) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIL) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIR) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionEcases) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionCommutes) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2Ex) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2W) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2A) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2B) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Ex) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Ex1) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Equiv) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1E) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1I) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncInInjFuncSet) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncInj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (leftInvIsSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjCantorThm) =>
% 102.63/17.18 ((
% 102.63/17.18 (foundation2) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself2) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSp) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSclos) =>
% 102.63/17.18 ((
% 102.63/17.18 (peano0notS) =>
% 102.63/17.18 ((
% 102.63/17.18 (peanoSinj) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintTransitive) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setunionTransitive) =>
% 102.63/17.18 ((
% 102.63/17.18 (ordinalMinLem1) =>
% 102.63/17.18 ((
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% 102.63/17.18 ^[Y0 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (ordinal @
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% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y1 : $i]:
% 102.63/17.18 ((
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% 102.63/17.18 ((
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% 102.63/17.18 Y0) =>
% 102.63/17.18 ((
% 102.63/17.18 (in @
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% 102.63/17.18 Y2) =>
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])).
% 102.63/17.18 thf(zip_derived_cl1111, plain,
% 102.63/17.18 (~ (((symdiffI1) =>
% 102.63/17.18 (((symdiffI2) =>
% 102.63/17.18 (((symdiffIneg1) =>
% 102.63/17.18 (((symdiffIneg2) =>
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% 102.63/17.18 (((setukpairIL) =>
% 102.63/17.18 (((setukpairIR) =>
% 102.63/17.18 (((kpairiskpair) =>
% 102.63/17.18 (((kpairp) =>
% 102.63/17.18 (((singletonsubset) =>
% 102.63/17.18 (((singletoninpowerset) =>
% 102.63/17.18 (((singletoninpowunion) =>
% 102.63/17.18 (((upairset2E) =>
% 102.63/17.18 (((upairsubunion) =>
% 102.63/17.18 (((upairinpowunion) =>
% 102.63/17.18 (((ubforcartprodlem1) =>
% 102.63/17.18 (((ubforcartprodlem2) =>
% 102.63/17.18 (((ubforcartprodlem3) =>
% 102.63/17.18 (((cartprodpairin) =>
% 102.63/17.18 (((cartprodmempair1) =>
% 102.63/17.18 (((cartprodmempair) =>
% 102.63/17.18 (((setunionE2) =>
% 102.63/17.18 (((setunionsingleton1) =>
% 102.63/17.18 (((setunionsingleton2) =>
% 102.63/17.18 (((setunionsingleton) =>
% 102.63/17.18 (((singletonprop) =>
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% 102.63/17.18 (((singletonsuniq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (theprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstin) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR11) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR12) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR1) =>
% 102.63/17.18 ((
% 102.63/17.18 (upairequniteq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (kpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndin) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemEL) =>
% 102.63/17.18 ((
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% 102.63/17.18 (cartprodsndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrI) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrSub) =>
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% 102.63/17.18 ((
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% 102.63/17.18 (dpsetconstrEL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrER) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcImageSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (apProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (app) =>
% 102.63/17.18 ((
% 102.63/17.18 (infuncsetfunc) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcinfuncset) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall1) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1E2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp3) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcextLem) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp4) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq1) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq2) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2lamEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifp) =>
% 102.63/17.18 ((
% 102.63/17.18 (theeq) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrue) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueorfalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setminusT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setextT) =>
% 102.63/17.18 ((
% 102.63/17.18 (subsetTI) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTELcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTERcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT1) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT2) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT3) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub2) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTnotintersectT) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementImpComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementSubsetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementInPowersetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (contraSubsetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTcontraSubset) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTILcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTIRcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion2) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (intersectInPowersetIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpNotIn1) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpInComplement1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTE) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTEcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementUnionInPowersetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule0) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule4) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_4) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_5) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all2) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1SetBreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (choice2fnsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all1) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compEex) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIL) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIR) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionEcases) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionCommutes) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2Ex) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2W) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2A) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2B) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Ex) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Ex1) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Equiv) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1E) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1I) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncInInjFuncSet) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncInj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (leftInvIsSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjCantorThm) =>
% 102.63/17.18 ((
% 102.63/17.18 (foundation2) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself2) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSp) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSclos) =>
% 102.63/17.18 ((
% 102.63/17.18 (peano0notS) =>
% 102.63/17.18 ((
% 102.63/17.18 (peanoSinj) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintTransitive) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setunionTransitive) =>
% 102.63/17.18 ((
% 102.63/17.18 (ordinalMinLem1) =>
% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y0 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (ordinal @
% 102.63/17.18 Y0) =>
% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y1 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y2 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (in @
% 102.63/17.18 Y2 @
% 102.63/17.18 Y0) =>
% 102.63/17.18 ((
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @
% 102.63/17.18 Y2) =>
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1103])).
% 102.63/17.18 thf(zip_derived_cl1119, plain,
% 102.63/17.18 (~ (((symdiffI2) =>
% 102.63/17.18 (((symdiffIneg1) =>
% 102.63/17.18 (((symdiffIneg2) =>
% 102.63/17.18 (((secondinupair) =>
% 102.63/17.18 (((setukpairIL) =>
% 102.63/17.18 (((setukpairIR) =>
% 102.63/17.18 (((kpairiskpair) =>
% 102.63/17.18 (((kpairp) =>
% 102.63/17.18 (((singletonsubset) =>
% 102.63/17.18 (((singletoninpowerset) =>
% 102.63/17.18 (((singletoninpowunion) =>
% 102.63/17.18 (((upairset2E) =>
% 102.63/17.18 (((upairsubunion) =>
% 102.63/17.18 (((upairinpowunion) =>
% 102.63/17.18 (((ubforcartprodlem1) =>
% 102.63/17.18 (((ubforcartprodlem2) =>
% 102.63/17.18 (((ubforcartprodlem3) =>
% 102.63/17.18 (((cartprodpairin) =>
% 102.63/17.18 (((cartprodmempair1) =>
% 102.63/17.18 (((cartprodmempair) =>
% 102.63/17.18 (((setunionE2) =>
% 102.63/17.18 (((setunionsingleton1) =>
% 102.63/17.18 (((setunionsingleton2) =>
% 102.63/17.18 (((setunionsingleton) =>
% 102.63/17.18 (((singletonprop) =>
% 102.63/17.18 (((ex1E1) =>
% 102.63/17.18 (((ex1I) =>
% 102.63/17.18 (((ex1I2) =>
% 102.63/17.18 (((singletonsuniq) =>
% 102.63/17.18 (((setukpairinjL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (theprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstin) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR11) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR12) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR1) =>
% 102.63/17.18 ((
% 102.63/17.18 (upairequniteq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (kpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndin) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemEL) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemER) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodmempaircEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrI) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrSub) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrERa) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrER) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcImageSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (apProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (app) =>
% 102.63/17.18 ((
% 102.63/17.18 (infuncsetfunc) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcinfuncset) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall1) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1E2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp3) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcextLem) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp4) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq1) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq2) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2lamEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifp) =>
% 102.63/17.18 ((
% 102.63/17.18 (theeq) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrue) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueorfalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setminusT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setextT) =>
% 102.63/17.18 ((
% 102.63/17.18 (subsetTI) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTELcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTERcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT1) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT2) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT3) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub2) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTnotintersectT) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementImpComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementSubsetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementInPowersetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (contraSubsetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTcontraSubset) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTILcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTIRcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion2) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (intersectInPowersetIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpNotIn1) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpInComplement1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTE) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTEcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementUnionInPowersetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule0) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule4) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_4) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_5) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all2) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1SetBreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (choice2fnsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all1) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compEex) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIL) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIR) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionEcases) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionCommutes) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2Ex) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2W) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2A) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2B) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Ex) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Ex1) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Equiv) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1E) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1I) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncInInjFuncSet) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncInj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (leftInvIsSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjCantorThm) =>
% 102.63/17.18 ((
% 102.63/17.18 (foundation2) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself2) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSp) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSclos) =>
% 102.63/17.18 ((
% 102.63/17.18 (peano0notS) =>
% 102.63/17.18 ((
% 102.63/17.18 (peanoSinj) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintTransitive) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setunionTransitive) =>
% 102.63/17.18 ((
% 102.63/17.18 (ordinalMinLem1) =>
% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y0 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (ordinal @
% 102.63/17.18 Y0) =>
% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y1 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y2 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (in @
% 102.63/17.18 Y2 @
% 102.63/17.18 Y0) =>
% 102.63/17.18 ((
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @
% 102.63/17.18 Y2) =>
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1111])).
% 102.63/17.18 thf(zip_derived_cl1125, plain,
% 102.63/17.18 (~ (((symdiffIneg1) =>
% 102.63/17.18 (((symdiffIneg2) =>
% 102.63/17.18 (((secondinupair) =>
% 102.63/17.18 (((setukpairIL) =>
% 102.63/17.18 (((setukpairIR) =>
% 102.63/17.18 (((kpairiskpair) =>
% 102.63/17.18 (((kpairp) =>
% 102.63/17.18 (((singletonsubset) =>
% 102.63/17.18 (((singletoninpowerset) =>
% 102.63/17.18 (((singletoninpowunion) =>
% 102.63/17.18 (((upairset2E) =>
% 102.63/17.18 (((upairsubunion) =>
% 102.63/17.18 (((upairinpowunion) =>
% 102.63/17.18 (((ubforcartprodlem1) =>
% 102.63/17.18 (((ubforcartprodlem2) =>
% 102.63/17.18 (((ubforcartprodlem3) =>
% 102.63/17.18 (((cartprodpairin) =>
% 102.63/17.18 (((cartprodmempair1) =>
% 102.63/17.18 (((cartprodmempair) =>
% 102.63/17.18 (((setunionE2) =>
% 102.63/17.18 (((setunionsingleton1) =>
% 102.63/17.18 (((setunionsingleton2) =>
% 102.63/17.18 (((setunionsingleton) =>
% 102.63/17.18 (((singletonprop) =>
% 102.63/17.18 (((ex1E1) =>
% 102.63/17.18 (((ex1I) =>
% 102.63/17.18 (((ex1I2) =>
% 102.63/17.18 (((singletonsuniq) =>
% 102.63/17.18 (((setukpairinjL1) =>
% 102.63/17.18 (((kfstsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (theprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstin) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR11) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR12) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR1) =>
% 102.63/17.18 ((
% 102.63/17.18 (upairequniteq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (kpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndin) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemEL) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemER) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodmempaircEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrI) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrSub) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrERa) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrER) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcImageSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (apProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (app) =>
% 102.63/17.18 ((
% 102.63/17.18 (infuncsetfunc) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcinfuncset) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall1) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1E2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp3) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcextLem) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp4) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq1) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq2) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2lamEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifp) =>
% 102.63/17.18 ((
% 102.63/17.18 (theeq) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrue) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueorfalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setminusT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setextT) =>
% 102.63/17.18 ((
% 102.63/17.18 (subsetTI) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTELcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTERcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT1) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT2) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT3) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub2) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTnotintersectT) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementImpComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementSubsetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementInPowersetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (contraSubsetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTcontraSubset) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTILcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTIRcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion2) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (intersectInPowersetIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpNotIn1) =>
% 102.63/17.18 ((
% 102.63/17.18 (inComplementUnionImpInComplement1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTE) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTEcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementUnionInPowersetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan1) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2a) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b2) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2b) =>
% 102.63/17.18 ((
% 102.63/17.18 (demorgan2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule0) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz13rule4) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_1) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_2) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_3) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_4) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz1_5) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all2) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1SetBreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (choice2fnsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1all1) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln1) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1invE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1compEex) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIL) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionIR) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionI) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionE) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionEcases) =>
% 102.63/17.18 ((
% 102.63/17.18 (breln1unionCommutes) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2Ex) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2W) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2A) =>
% 102.63/17.18 ((
% 102.63/17.18 (woz2B) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Ex) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Ex1) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1Equiv) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1E) =>
% 102.63/17.18 ((
% 102.63/17.18 (image1I) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncInInjFuncSet) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (injFuncSetFuncInj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncIn) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjFuncSetFuncSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (leftInvIsSurj) =>
% 102.63/17.18 ((
% 102.63/17.18 (surjCantorThm) =>
% 102.63/17.18 ((
% 102.63/17.18 (foundation2) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself) =>
% 102.63/17.18 ((
% 102.63/17.18 (notinself2) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSp) =>
% 102.63/17.18 ((
% 102.63/17.18 (omegaSclos) =>
% 102.63/17.18 ((
% 102.63/17.18 (peano0notS) =>
% 102.63/17.18 ((
% 102.63/17.18 (peanoSinj) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintTransitive) =>
% 102.63/17.18 ((
% 102.63/17.18 (transitivesetOp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setunionTransitive) =>
% 102.63/17.18 ((
% 102.63/17.18 (ordinalMinLem1) =>
% 102.63/17.18 ((
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% 102.63/17.18 ^[Y0 : $i]:
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% 102.63/17.18 (ordinal @
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% 102.63/17.18 ((
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% 102.63/17.18 ((
% 102.63/17.18 (!!) @ (
% 102.63/17.18 ^[Y2 : $i]:
% 102.63/17.18 ((
% 102.63/17.18 (in @
% 102.63/17.18 Y2 @
% 102.63/17.18 Y0) =>
% 102.63/17.18 ((
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @
% 102.63/17.18 Y2) =>
% 102.63/17.18 (in @
% 102.63/17.18 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1119])).
% 102.63/17.18 thf(zip_derived_cl1131, plain,
% 102.63/17.18 (~ (((symdiffIneg2) =>
% 102.63/17.18 (((secondinupair) =>
% 102.63/17.18 (((setukpairIL) =>
% 102.63/17.18 (((setukpairIR) =>
% 102.63/17.18 (((kpairiskpair) =>
% 102.63/17.18 (((kpairp) =>
% 102.63/17.18 (((singletonsubset) =>
% 102.63/17.18 (((singletoninpowerset) =>
% 102.63/17.18 (((singletoninpowunion) =>
% 102.63/17.18 (((upairset2E) =>
% 102.63/17.18 (((upairsubunion) =>
% 102.63/17.18 (((upairinpowunion) =>
% 102.63/17.18 (((ubforcartprodlem1) =>
% 102.63/17.18 (((ubforcartprodlem2) =>
% 102.63/17.18 (((ubforcartprodlem3) =>
% 102.63/17.18 (((cartprodpairin) =>
% 102.63/17.18 (((cartprodmempair1) =>
% 102.63/17.18 (((cartprodmempair) =>
% 102.63/17.18 (((setunionE2) =>
% 102.63/17.18 (((setunionsingleton1) =>
% 102.63/17.18 (((setunionsingleton2) =>
% 102.63/17.18 (((setunionsingleton) =>
% 102.63/17.18 (((singletonprop) =>
% 102.63/17.18 (((ex1E1) =>
% 102.63/17.18 (((ex1I) =>
% 102.63/17.18 (((ex1I2) =>
% 102.63/17.18 (((singletonsuniq) =>
% 102.63/17.18 (((setukpairinjL1) =>
% 102.63/17.18 (((kfstsingleton) =>
% 102.63/17.18 (((theprop) =>
% 102.63/17.18 ((
% 102.63/17.18 (kfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstin) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjL) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR11) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR12) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR1) =>
% 102.63/17.18 ((
% 102.63/17.18 (upairequniteq) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR2) =>
% 102.63/17.18 ((
% 102.63/17.18 (setukpairinjR) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndsingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ksndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (kpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndin) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemEL) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairmemER) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodmempaircEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodfstpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodsndpairEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (cartprodpairsurjEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrI) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrSub) =>
% 102.63/17.18 ((
% 102.63/17.18 (setOfPairsIsBReln) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrERa) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL1) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrEL2) =>
% 102.63/17.18 ((
% 102.63/17.18 (dpsetconstrER) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcImageSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (apProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (app) =>
% 102.63/17.18 ((
% 102.63/17.18 (infuncsetfunc) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcinfuncset) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamProp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lamp) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2p) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall1) =>
% 102.63/17.18 ((
% 102.63/17.18 (brelnall2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ex1E2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp3) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcextLem) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcGraphProp4) =>
% 102.63/17.18 ((
% 102.63/17.18 (subbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (eqbreln) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext) =>
% 102.63/17.18 ((
% 102.63/17.18 (funcext2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq1) =>
% 102.63/17.18 ((
% 102.63/17.18 (ap2apEq2) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta1) =>
% 102.63/17.18 ((
% 102.63/17.18 (lam2lamEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (beta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (eta2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalseProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp1) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueProp2) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifSingleton) =>
% 102.63/17.18 ((
% 102.63/17.18 (ifp) =>
% 102.63/17.18 ((
% 102.63/17.18 (theeq) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrue) =>
% 102.63/17.18 ((
% 102.63/17.18 (iffalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (iftrueorfalse) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setminusT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementT_lem) =>
% 102.63/17.18 ((
% 102.63/17.18 (setextT) =>
% 102.63/17.18 ((
% 102.63/17.18 (subsetTI) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (powersetTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTELcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binintersectTERcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT1) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT2) =>
% 102.63/17.18 ((
% 102.63/17.18 (contrasubsetT3) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementI1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementE1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub1) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementSub2) =>
% 102.63/17.18 ((
% 102.63/17.18 (doubleComplementEq) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTnotintersectT) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementImpComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementSubsetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementInPowersetComplementIntersect) =>
% 102.63/17.18 ((
% 102.63/17.18 (contraSubsetComplement) =>
% 102.63/17.18 ((
% 102.63/17.18 (complementTcontraSubset) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTILcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (binunionTIRcontra) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInUnion2) =>
% 102.63/17.18 ((
% 102.63/17.18 (inIntersectImpInIntersectUnions) =>
% 102.63/17.18 ((
% 102.63/17.19 (intersectInPowersetIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpNotIn1) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpInComplement1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTE) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTEcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementUnionInPowersetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule0) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_5) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all2) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1SetBreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (choice2fnsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all1) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eqbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compEex) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIL) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIR) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionEcases) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionCommutes) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2Ex) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2W) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2A) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2B) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Ex) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Ex1) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Equiv) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1E) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1I) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncInInjFuncSet) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncInj) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncSurj) =>
% 102.63/17.19 ((
% 102.63/17.19 (leftInvIsSurj) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjCantorThm) =>
% 102.63/17.19 ((
% 102.63/17.19 (foundation2) =>
% 102.63/17.19 ((
% 102.63/17.19 (notinself) =>
% 102.63/17.19 ((
% 102.63/17.19 (notinself2) =>
% 102.63/17.19 ((
% 102.63/17.19 (omegaSp) =>
% 102.63/17.19 ((
% 102.63/17.19 (omegaSclos) =>
% 102.63/17.19 ((
% 102.63/17.19 (peano0notS) =>
% 102.63/17.19 ((
% 102.63/17.19 (peanoSinj) =>
% 102.63/17.19 ((
% 102.63/17.19 (transitivesetOp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintTransitive) =>
% 102.63/17.19 ((
% 102.63/17.19 (transitivesetOp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setunionTransitive) =>
% 102.63/17.19 ((
% 102.63/17.19 (ordinalMinLem1) =>
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y0 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (ordinal @
% 102.63/17.19 Y0) =>
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y1 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y2 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (in @
% 102.63/17.19 Y2 @
% 102.63/17.19 Y0) =>
% 102.63/17.19 ((
% 102.63/17.19 (in @
% 102.63/17.19 Y1 @
% 102.63/17.19 Y2) =>
% 102.63/17.19 (in @
% 102.63/17.19 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1125])).
% 102.63/17.19 thf(zip_derived_cl1138, plain,
% 102.63/17.19 (~ (((secondinupair) =>
% 102.63/17.19 (((setukpairIL) =>
% 102.63/17.19 (((setukpairIR) =>
% 102.63/17.19 (((kpairiskpair) =>
% 102.63/17.19 (((kpairp) =>
% 102.63/17.19 (((singletonsubset) =>
% 102.63/17.19 (((singletoninpowerset) =>
% 102.63/17.19 (((singletoninpowunion) =>
% 102.63/17.19 (((upairset2E) =>
% 102.63/17.19 (((upairsubunion) =>
% 102.63/17.19 (((upairinpowunion) =>
% 102.63/17.19 (((ubforcartprodlem1) =>
% 102.63/17.19 (((ubforcartprodlem2) =>
% 102.63/17.19 (((ubforcartprodlem3) =>
% 102.63/17.19 (((cartprodpairin) =>
% 102.63/17.19 (((cartprodmempair1) =>
% 102.63/17.19 (((cartprodmempair) =>
% 102.63/17.19 (((setunionE2) =>
% 102.63/17.19 (((setunionsingleton1) =>
% 102.63/17.19 (((setunionsingleton2) =>
% 102.63/17.19 (((setunionsingleton) =>
% 102.63/17.19 (((singletonprop) =>
% 102.63/17.19 (((ex1E1) =>
% 102.63/17.19 (((ex1I) =>
% 102.63/17.19 (((ex1I2) =>
% 102.63/17.19 (((singletonsuniq) =>
% 102.63/17.19 (((setukpairinjL1) =>
% 102.63/17.19 (((kfstsingleton) =>
% 102.63/17.19 (((theprop) =>
% 102.63/17.19 (((kfstpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodfstin) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjL2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjL) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR11) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR12) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR1) =>
% 102.63/17.19 ((
% 102.63/17.19 (upairequniteq) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (kpairsurjEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndin) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemEL) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemER) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodmempaircEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodfstpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairsurjEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrI) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrSub) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrERa) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrEL1) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrEL2) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrER) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcImageSingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (apProp) =>
% 102.63/17.19 ((
% 102.63/17.19 (app) =>
% 102.63/17.19 ((
% 102.63/17.19 (infuncsetfunc) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2p) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcinfuncset) =>
% 102.63/17.19 ((
% 102.63/17.19 (lamProp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lamp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2p) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall1) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ex1E2) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp3) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcextLem) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp4) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln) =>
% 102.63/17.19 ((
% 102.63/17.19 (eqbreln) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcext) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcext2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq1) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq2) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2lamEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifSingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifp) =>
% 102.63/17.19 ((
% 102.63/17.19 (theeq) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrue) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueorfalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setminusT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setextT) =>
% 102.63/17.19 ((
% 102.63/17.19 (subsetTI) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTELcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTERcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT1) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT2) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT3) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub2) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTnotintersectT) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementImpComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementSubsetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementInPowersetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (contraSubsetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTcontraSubset) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTILcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTIRcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion2) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (intersectInPowersetIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpNotIn1) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpInComplement1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTE) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTEcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementUnionInPowersetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule0) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_5) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all2) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1SetBreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (choice2fnsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all1) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eqbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compEex) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIL) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIR) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionEcases) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionCommutes) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2Ex) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2W) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2A) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2B) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Ex) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Ex1) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Equiv) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1E) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1I) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncInInjFuncSet) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncInj) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncSurj) =>
% 102.63/17.19 ((
% 102.63/17.19 (leftInvIsSurj) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjCantorThm) =>
% 102.63/17.19 ((
% 102.63/17.19 (foundation2) =>
% 102.63/17.19 ((
% 102.63/17.19 (notinself) =>
% 102.63/17.19 ((
% 102.63/17.19 (notinself2) =>
% 102.63/17.19 ((
% 102.63/17.19 (omegaSp) =>
% 102.63/17.19 ((
% 102.63/17.19 (omegaSclos) =>
% 102.63/17.19 ((
% 102.63/17.19 (peano0notS) =>
% 102.63/17.19 ((
% 102.63/17.19 (peanoSinj) =>
% 102.63/17.19 ((
% 102.63/17.19 (transitivesetOp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintTransitive) =>
% 102.63/17.19 ((
% 102.63/17.19 (transitivesetOp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setunionTransitive) =>
% 102.63/17.19 ((
% 102.63/17.19 (ordinalMinLem1) =>
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y0 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (ordinal @
% 102.63/17.19 Y0) =>
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y1 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y2 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (in @
% 102.63/17.19 Y2 @
% 102.63/17.19 Y0) =>
% 102.63/17.19 ((
% 102.63/17.19 (in @
% 102.63/17.19 Y1 @
% 102.63/17.19 Y2) =>
% 102.63/17.19 (in @
% 102.63/17.19 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1131])).
% 102.63/17.19 thf(zip_derived_cl1145, plain,
% 102.63/17.19 (~ (((setukpairIL) =>
% 102.63/17.19 (((setukpairIR) =>
% 102.63/17.19 (((kpairiskpair) =>
% 102.63/17.19 (((kpairp) =>
% 102.63/17.19 (((singletonsubset) =>
% 102.63/17.19 (((singletoninpowerset) =>
% 102.63/17.19 (((singletoninpowunion) =>
% 102.63/17.19 (((upairset2E) =>
% 102.63/17.19 (((upairsubunion) =>
% 102.63/17.19 (((upairinpowunion) =>
% 102.63/17.19 (((ubforcartprodlem1) =>
% 102.63/17.19 (((ubforcartprodlem2) =>
% 102.63/17.19 (((ubforcartprodlem3) =>
% 102.63/17.19 (((cartprodpairin) =>
% 102.63/17.19 (((cartprodmempair1) =>
% 102.63/17.19 (((cartprodmempair) =>
% 102.63/17.19 (((setunionE2) =>
% 102.63/17.19 (((setunionsingleton1) =>
% 102.63/17.19 (((setunionsingleton2) =>
% 102.63/17.19 (((setunionsingleton) =>
% 102.63/17.19 (((singletonprop) =>
% 102.63/17.19 (((ex1E1) =>
% 102.63/17.19 (((ex1I) =>
% 102.63/17.19 (((ex1I2) =>
% 102.63/17.19 (((singletonsuniq) =>
% 102.63/17.19 (((setukpairinjL1) =>
% 102.63/17.19 (((kfstsingleton) =>
% 102.63/17.19 (((theprop) =>
% 102.63/17.19 (((kfstpairEq) =>
% 102.63/17.19 (((cartprodfstin) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjL2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjL) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR11) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR12) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR1) =>
% 102.63/17.19 ((
% 102.63/17.19 (upairequniteq) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (kpairsurjEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndin) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemEL) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemER) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodmempaircEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodfstpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairsurjEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrI) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrSub) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrERa) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrEL1) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrEL2) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrER) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcImageSingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (apProp) =>
% 102.63/17.19 ((
% 102.63/17.19 (app) =>
% 102.63/17.19 ((
% 102.63/17.19 (infuncsetfunc) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2p) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcinfuncset) =>
% 102.63/17.19 ((
% 102.63/17.19 (lamProp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lamp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2p) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall1) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ex1E2) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp3) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcextLem) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp4) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln) =>
% 102.63/17.19 ((
% 102.63/17.19 (eqbreln) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcext) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcext2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq1) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq2) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2lamEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifSingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifp) =>
% 102.63/17.19 ((
% 102.63/17.19 (theeq) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrue) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueorfalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setminusT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setextT) =>
% 102.63/17.19 ((
% 102.63/17.19 (subsetTI) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTELcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTERcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT1) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT2) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT3) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub2) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTnotintersectT) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementImpComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementSubsetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementInPowersetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (contraSubsetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTcontraSubset) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTILcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTIRcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion2) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (intersectInPowersetIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpNotIn1) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpInComplement1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTE) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTEcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementUnionInPowersetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule0) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_5) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all2) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1SetBreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (choice2fnsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all1) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln1) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 (inComplementUnionImpInComplement1) =>
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% 102.63/17.19 ((
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% 102.63/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1145])).
% 102.63/17.19 thf(zip_derived_cl1162, plain,
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% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR11) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR12) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR1) =>
% 102.63/17.19 ((
% 102.63/17.19 (upairequniteq) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (kpairsurjEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndin) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemEL) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemER) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodmempaircEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodfstpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairsurjEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrI) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrSub) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrERa) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrEL1) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrEL2) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrER) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcImageSingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (apProp) =>
% 102.63/17.19 ((
% 102.63/17.19 (app) =>
% 102.63/17.19 ((
% 102.63/17.19 (infuncsetfunc) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2p) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcinfuncset) =>
% 102.63/17.19 ((
% 102.63/17.19 (lamProp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lamp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2p) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall1) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ex1E2) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp3) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcextLem) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp4) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln) =>
% 102.63/17.19 ((
% 102.63/17.19 (eqbreln) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcext) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcext2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq1) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq2) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2lamEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifSingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifp) =>
% 102.63/17.19 ((
% 102.63/17.19 (theeq) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrue) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueorfalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setminusT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setextT) =>
% 102.63/17.19 ((
% 102.63/17.19 (subsetTI) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTELcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTERcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT1) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT2) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT3) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub2) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTnotintersectT) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementImpComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementSubsetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementInPowersetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (contraSubsetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTcontraSubset) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTILcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTIRcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion2) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (intersectInPowersetIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpNotIn1) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpInComplement1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTE) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTEcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementUnionInPowersetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule0) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_5) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all2) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1SetBreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (choice2fnsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all1) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eqbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compEex) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIL) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIR) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionEcases) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionCommutes) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2Ex) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2W) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2A) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2B) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Ex) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Ex1) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Equiv) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1E) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1I) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncInInjFuncSet) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncInj) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncSurj) =>
% 102.63/17.19 ((
% 102.63/17.19 (leftInvIsSurj) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjCantorThm) =>
% 102.63/17.19 ((
% 102.63/17.19 (foundation2) =>
% 102.63/17.19 ((
% 102.63/17.19 (notinself) =>
% 102.63/17.19 ((
% 102.63/17.19 (notinself2) =>
% 102.63/17.19 ((
% 102.63/17.19 (omegaSp) =>
% 102.63/17.19 ((
% 102.63/17.19 (omegaSclos) =>
% 102.63/17.19 ((
% 102.63/17.19 (peano0notS) =>
% 102.63/17.19 ((
% 102.63/17.19 (peanoSinj) =>
% 102.63/17.19 ((
% 102.63/17.19 (transitivesetOp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintTransitive) =>
% 102.63/17.19 ((
% 102.63/17.19 (transitivesetOp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setunionTransitive) =>
% 102.63/17.19 ((
% 102.63/17.19 (ordinalMinLem1) =>
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y0 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (ordinal @
% 102.63/17.19 Y0) =>
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y1 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y2 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (in @
% 102.63/17.19 Y2 @
% 102.63/17.19 Y0) =>
% 102.63/17.19 ((
% 102.63/17.19 (in @
% 102.63/17.19 Y1 @
% 102.63/17.19 Y2) =>
% 102.63/17.19 (in @
% 102.63/17.19 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1153])).
% 102.63/17.19 thf(zip_derived_cl1172, plain,
% 102.63/17.19 (~ (((kpairp) =>
% 102.63/17.19 (((singletonsubset) =>
% 102.63/17.19 (((singletoninpowerset) =>
% 102.63/17.19 (((singletoninpowunion) =>
% 102.63/17.19 (((upairset2E) =>
% 102.63/17.19 (((upairsubunion) =>
% 102.63/17.19 (((upairinpowunion) =>
% 102.63/17.19 (((ubforcartprodlem1) =>
% 102.63/17.19 (((ubforcartprodlem2) =>
% 102.63/17.19 (((ubforcartprodlem3) =>
% 102.63/17.19 (((cartprodpairin) =>
% 102.63/17.19 (((cartprodmempair1) =>
% 102.63/17.19 (((cartprodmempair) =>
% 102.63/17.19 (((setunionE2) =>
% 102.63/17.19 (((setunionsingleton1) =>
% 102.63/17.19 (((setunionsingleton2) =>
% 102.63/17.19 (((setunionsingleton) =>
% 102.63/17.19 (((singletonprop) =>
% 102.63/17.19 (((ex1E1) =>
% 102.63/17.19 (((ex1I) =>
% 102.63/17.19 (((ex1I2) =>
% 102.63/17.19 (((singletonsuniq) =>
% 102.63/17.19 (((setukpairinjL1) =>
% 102.63/17.19 (((kfstsingleton) =>
% 102.63/17.19 (((theprop) =>
% 102.63/17.19 (((kfstpairEq) =>
% 102.63/17.19 (((cartprodfstin) =>
% 102.63/17.19 (((setukpairinjL2) =>
% 102.63/17.19 (((setukpairinjL) =>
% 102.63/17.19 (((setukpairinjR11) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR12) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR1) =>
% 102.63/17.19 ((
% 102.63/17.19 (upairequniteq) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (kpairsurjEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndin) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemEL) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemER) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodmempaircEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodfstpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairsurjEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrI) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrSub) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrERa) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrEL1) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrEL2) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrER) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcImageSingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (apProp) =>
% 102.63/17.19 ((
% 102.63/17.19 (app) =>
% 102.63/17.19 ((
% 102.63/17.19 (infuncsetfunc) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2p) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcinfuncset) =>
% 102.63/17.19 ((
% 102.63/17.19 (lamProp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lamp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2p) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall1) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ex1E2) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp3) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcextLem) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp4) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln) =>
% 102.63/17.19 ((
% 102.63/17.19 (eqbreln) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcext) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcext2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq1) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq2) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2lamEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifSingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifp) =>
% 102.63/17.19 ((
% 102.63/17.19 (theeq) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrue) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueorfalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setminusT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setextT) =>
% 102.63/17.19 ((
% 102.63/17.19 (subsetTI) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTELcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTERcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT1) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT2) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT3) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub2) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTnotintersectT) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementImpComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementSubsetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementInPowersetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (contraSubsetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTcontraSubset) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTILcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTIRcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion2) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (intersectInPowersetIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpNotIn1) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpInComplement1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTE) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTEcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementUnionInPowersetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule0) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_5) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all2) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1SetBreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (choice2fnsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all1) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eqbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compEex) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIL) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIR) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionEcases) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionCommutes) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2Ex) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2W) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2A) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2B) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Ex) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Ex1) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Equiv) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1E) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1I) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncInInjFuncSet) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncInj) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncSurj) =>
% 102.63/17.19 ((
% 102.63/17.19 (leftInvIsSurj) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjCantorThm) =>
% 102.63/17.19 ((
% 102.63/17.19 (foundation2) =>
% 102.63/17.19 ((
% 102.63/17.19 (notinself) =>
% 102.63/17.19 ((
% 102.63/17.19 (notinself2) =>
% 102.63/17.19 ((
% 102.63/17.19 (omegaSp) =>
% 102.63/17.19 ((
% 102.63/17.19 (omegaSclos) =>
% 102.63/17.19 ((
% 102.63/17.19 (peano0notS) =>
% 102.63/17.19 ((
% 102.63/17.19 (peanoSinj) =>
% 102.63/17.19 ((
% 102.63/17.19 (transitivesetOp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintTransitive) =>
% 102.63/17.19 ((
% 102.63/17.19 (transitivesetOp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setunionTransitive) =>
% 102.63/17.19 ((
% 102.63/17.19 (ordinalMinLem1) =>
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y0 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (ordinal @
% 102.63/17.19 Y0) =>
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y1 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y2 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (in @
% 102.63/17.19 Y2 @
% 102.63/17.19 Y0) =>
% 102.63/17.19 ((
% 102.63/17.19 (in @
% 102.63/17.19 Y1 @
% 102.63/17.19 Y2) =>
% 102.63/17.19 (in @
% 102.63/17.19 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1162])).
% 102.63/17.19 thf(zip_derived_cl1185, plain,
% 102.63/17.19 (~ (((singletonsubset) =>
% 102.63/17.19 (((singletoninpowerset) =>
% 102.63/17.19 (((singletoninpowunion) =>
% 102.63/17.19 (((upairset2E) =>
% 102.63/17.19 (((upairsubunion) =>
% 102.63/17.19 (((upairinpowunion) =>
% 102.63/17.19 (((ubforcartprodlem1) =>
% 102.63/17.19 (((ubforcartprodlem2) =>
% 102.63/17.19 (((ubforcartprodlem3) =>
% 102.63/17.19 (((cartprodpairin) =>
% 102.63/17.19 (((cartprodmempair1) =>
% 102.63/17.19 (((cartprodmempair) =>
% 102.63/17.19 (((setunionE2) =>
% 102.63/17.19 (((setunionsingleton1) =>
% 102.63/17.19 (((setunionsingleton2) =>
% 102.63/17.19 (((setunionsingleton) =>
% 102.63/17.19 (((singletonprop) =>
% 102.63/17.19 (((ex1E1) =>
% 102.63/17.19 (((ex1I) =>
% 102.63/17.19 (((ex1I2) =>
% 102.63/17.19 (((singletonsuniq) =>
% 102.63/17.19 (((setukpairinjL1) =>
% 102.63/17.19 (((kfstsingleton) =>
% 102.63/17.19 (((theprop) =>
% 102.63/17.19 (((kfstpairEq) =>
% 102.63/17.19 (((cartprodfstin) =>
% 102.63/17.19 (((setukpairinjL2) =>
% 102.63/17.19 (((setukpairinjL) =>
% 102.63/17.19 (((setukpairinjR11) =>
% 102.63/17.19 (((setukpairinjR12) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR1) =>
% 102.63/17.19 ((
% 102.63/17.19 (upairequniteq) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (kpairsurjEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndin) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemEL) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemER) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodmempaircEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodfstpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairsurjEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrI) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrSub) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrERa) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrEL1) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrEL2) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrER) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcImageSingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (apProp) =>
% 102.63/17.19 ((
% 102.63/17.19 (app) =>
% 102.63/17.19 ((
% 102.63/17.19 (infuncsetfunc) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2p) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcinfuncset) =>
% 102.63/17.19 ((
% 102.63/17.19 (lamProp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lamp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2p) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall1) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ex1E2) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp3) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcextLem) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp4) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln) =>
% 102.63/17.19 ((
% 102.63/17.19 (eqbreln) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcext) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcext2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq1) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq2) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2lamEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifSingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifp) =>
% 102.63/17.19 ((
% 102.63/17.19 (theeq) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrue) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueorfalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setminusT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setextT) =>
% 102.63/17.19 ((
% 102.63/17.19 (subsetTI) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTELcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTERcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT1) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT2) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT3) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub2) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTnotintersectT) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementImpComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementSubsetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementInPowersetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (contraSubsetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTcontraSubset) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTILcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTIRcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion2) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (intersectInPowersetIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpNotIn1) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpInComplement1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTE) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTEcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementUnionInPowersetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule0) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_5) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all2) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1SetBreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (choice2fnsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all1) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eqbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invE) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (breln1compI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compEex) =>
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% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIL) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIR) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionEcases) =>
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% 102.63/17.19 (breln1unionCommutes) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2Ex) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2W) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 (image1E) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1I) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncInInjFuncSet) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncInj) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncSurj) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (notinself2) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (peano0notS) =>
% 102.63/17.19 ((
% 102.63/17.19 (peanoSinj) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (binintTransitive) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 Y1 @
% 102.63/17.19 Y2) =>
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% 102.63/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1172])).
% 102.63/17.19 thf(zip_derived_cl1195, plain,
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% 102.63/17.19 (((singletoninpowunion) =>
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% 102.63/17.19 (((ubforcartprodlem2) =>
% 102.63/17.19 (((ubforcartprodlem3) =>
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% 102.63/17.19 (((cartprodmempair1) =>
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% 102.63/17.19 (((theprop) =>
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% 102.63/17.19 (((setukpairinjR12) =>
% 102.63/17.19 (((setukpairinjR1) =>
% 102.63/17.19 ((
% 102.63/17.19 (upairequniteq) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndpairEq) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndin) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemEL) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemER) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodmempaircEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodfstpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairsurjEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrI) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrSub) =>
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% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrER) =>
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% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (ap2p) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (lamProp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lamp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2p) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall1) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ex1E2) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp3) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcextLem) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp4) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (funcext) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcext2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq1) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq2) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2lamEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta2) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp2) =>
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% 102.63/17.19 (ifSingleton) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (theeq) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrue) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (binunionT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetT_lem) =>
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% 102.63/17.19 (setminusT_lem) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 (complementTE1) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (binintersectTERcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT1) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT2) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT3) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub2) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTnotintersectT) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementImpComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementSubsetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementInPowersetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (contraSubsetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTcontraSubset) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTILcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTIRcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion2) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (intersectInPowersetIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpNotIn1) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpInComplement1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTE) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTEcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementUnionInPowersetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule0) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_5) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all2) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1SetBreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (choice2fnsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all1) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eqbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compEex) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIL) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIR) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionEcases) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionCommutes) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2Ex) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2W) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (woz2B) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Ex) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (image1E) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1I) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncInInjFuncSet) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncInj) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncSurj) =>
% 102.63/17.19 ((
% 102.63/17.19 (leftInvIsSurj) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjCantorThm) =>
% 102.63/17.19 ((
% 102.63/17.19 (foundation2) =>
% 102.63/17.19 ((
% 102.63/17.19 (notinself) =>
% 102.63/17.19 ((
% 102.63/17.19 (notinself2) =>
% 102.63/17.19 ((
% 102.63/17.19 (omegaSp) =>
% 102.63/17.19 ((
% 102.63/17.19 (omegaSclos) =>
% 102.63/17.19 ((
% 102.63/17.19 (peano0notS) =>
% 102.63/17.19 ((
% 102.63/17.19 (peanoSinj) =>
% 102.63/17.19 ((
% 102.63/17.19 (transitivesetOp1) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (transitivesetOp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setunionTransitive) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
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% 102.63/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1185])).
% 102.63/17.19 thf(zip_derived_cl1202, plain,
% 102.63/17.19 (~ (((singletoninpowunion) =>
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% 102.63/17.19 (((upairsubunion) =>
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% 102.63/17.19 (((cartprodmempair1) =>
% 102.63/17.19 (((cartprodmempair) =>
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% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (ksndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (kpairsurjEq) =>
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% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemER) =>
% 102.63/17.19 ((
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% 102.63/17.19 (cartprodsndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairsurjEq) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrSub) =>
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% 102.63/17.19 (funcextLem) =>
% 102.63/17.19 ((
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% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq2) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2lamEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifSingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifp) =>
% 102.63/17.19 ((
% 102.63/17.19 (theeq) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrue) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueorfalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setminusT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setextT) =>
% 102.63/17.19 ((
% 102.63/17.19 (subsetTI) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTELcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTERcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT1) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT2) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT3) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub2) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTnotintersectT) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementImpComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementSubsetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementInPowersetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (contraSubsetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTcontraSubset) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTILcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTIRcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInUnion2) =>
% 102.63/17.19 ((
% 102.63/17.19 (inIntersectImpInIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (intersectInPowersetIntersectUnions) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpNotIn1) =>
% 102.63/17.19 ((
% 102.63/17.19 (inComplementUnionImpInComplement1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTE) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionTEcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementUnionInPowersetComplement) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan1) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2a) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b2) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2b) =>
% 102.63/17.19 ((
% 102.63/17.19 (demorgan2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule0) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz13rule4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_1) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_2) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_3) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_4) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz1_5) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all2) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1SetBreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (choice2fnsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1all1) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eqbreln1) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1invE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1compEex) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionprop) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIL) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionIR) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionI) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionE) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionEcases) =>
% 102.63/17.19 ((
% 102.63/17.19 (breln1unionCommutes) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2Ex) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2W) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2A) =>
% 102.63/17.19 ((
% 102.63/17.19 (woz2B) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Ex) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Ex1) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1Equiv) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1E) =>
% 102.63/17.19 ((
% 102.63/17.19 (image1I) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncInInjFuncSet) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (injFuncSetFuncInj) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncIn) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjFuncSetFuncSurj) =>
% 102.63/17.19 ((
% 102.63/17.19 (leftInvIsSurj) =>
% 102.63/17.19 ((
% 102.63/17.19 (surjCantorThm) =>
% 102.63/17.19 ((
% 102.63/17.19 (foundation2) =>
% 102.63/17.19 ((
% 102.63/17.19 (notinself) =>
% 102.63/17.19 ((
% 102.63/17.19 (notinself2) =>
% 102.63/17.19 ((
% 102.63/17.19 (omegaSp) =>
% 102.63/17.19 ((
% 102.63/17.19 (omegaSclos) =>
% 102.63/17.19 ((
% 102.63/17.19 (peano0notS) =>
% 102.63/17.19 ((
% 102.63/17.19 (peanoSinj) =>
% 102.63/17.19 ((
% 102.63/17.19 (transitivesetOp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintTransitive) =>
% 102.63/17.19 ((
% 102.63/17.19 (transitivesetOp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setunionTransitive) =>
% 102.63/17.19 ((
% 102.63/17.19 (ordinalMinLem1) =>
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y0 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (ordinal @
% 102.63/17.19 Y0) =>
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y1 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (!!) @ (
% 102.63/17.19 ^[Y2 : $i]:
% 102.63/17.19 ((
% 102.63/17.19 (in @
% 102.63/17.19 Y2 @
% 102.63/17.19 Y0) =>
% 102.63/17.19 ((
% 102.63/17.19 (in @
% 102.63/17.19 Y1 @
% 102.63/17.19 Y2) =>
% 102.63/17.19 (in @
% 102.63/17.19 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1195])).
% 102.63/17.19 thf(zip_derived_cl1207, plain,
% 102.63/17.19 (~ (((upairset2E) =>
% 102.63/17.19 (((upairsubunion) =>
% 102.63/17.19 (((upairinpowunion) =>
% 102.63/17.19 (((ubforcartprodlem1) =>
% 102.63/17.19 (((ubforcartprodlem2) =>
% 102.63/17.19 (((ubforcartprodlem3) =>
% 102.63/17.19 (((cartprodpairin) =>
% 102.63/17.19 (((cartprodmempair1) =>
% 102.63/17.19 (((cartprodmempair) =>
% 102.63/17.19 (((setunionE2) =>
% 102.63/17.19 (((setunionsingleton1) =>
% 102.63/17.19 (((setunionsingleton2) =>
% 102.63/17.19 (((setunionsingleton) =>
% 102.63/17.19 (((singletonprop) =>
% 102.63/17.19 (((ex1E1) =>
% 102.63/17.19 (((ex1I) =>
% 102.63/17.19 (((ex1I2) =>
% 102.63/17.19 (((singletonsuniq) =>
% 102.63/17.19 (((setukpairinjL1) =>
% 102.63/17.19 (((kfstsingleton) =>
% 102.63/17.19 (((theprop) =>
% 102.63/17.19 (((kfstpairEq) =>
% 102.63/17.19 (((cartprodfstin) =>
% 102.63/17.19 (((setukpairinjL2) =>
% 102.63/17.19 (((setukpairinjL) =>
% 102.63/17.19 (((setukpairinjR11) =>
% 102.63/17.19 (((setukpairinjR12) =>
% 102.63/17.19 (((setukpairinjR1) =>
% 102.63/17.19 (((upairequniteq) =>
% 102.63/17.19 (((setukpairinjR2) =>
% 102.63/17.19 ((
% 102.63/17.19 (setukpairinjR) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndsingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ksndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (kpairsurjEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndin) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemEL) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairmemER) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodmempaircEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodfstpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodsndpairEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (cartprodpairsurjEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrI) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrSub) =>
% 102.63/17.19 ((
% 102.63/17.19 (setOfPairsIsBReln) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrERa) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrEL1) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrEL2) =>
% 102.63/17.19 ((
% 102.63/17.19 (dpsetconstrER) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcImageSingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (apProp) =>
% 102.63/17.19 ((
% 102.63/17.19 (app) =>
% 102.63/17.19 ((
% 102.63/17.19 (infuncsetfunc) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2p) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcinfuncset) =>
% 102.63/17.19 ((
% 102.63/17.19 (lamProp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lamp) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2p) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall1) =>
% 102.63/17.19 ((
% 102.63/17.19 (brelnall2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ex1E2) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp3) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcextLem) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcGraphProp4) =>
% 102.63/17.19 ((
% 102.63/17.19 (subbreln) =>
% 102.63/17.19 ((
% 102.63/17.19 (eqbreln) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcext) =>
% 102.63/17.19 ((
% 102.63/17.19 (funcext2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq1) =>
% 102.63/17.19 ((
% 102.63/17.19 (ap2apEq2) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta1) =>
% 102.63/17.19 ((
% 102.63/17.19 (lam2lamEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (beta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (eta2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalseProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp1) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueProp2) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifSingleton) =>
% 102.63/17.19 ((
% 102.63/17.19 (ifp) =>
% 102.63/17.19 ((
% 102.63/17.19 (theeq) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrue) =>
% 102.63/17.19 ((
% 102.63/17.19 (iffalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (iftrueorfalse) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (binunionT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setminusT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementT_lem) =>
% 102.63/17.19 ((
% 102.63/17.19 (setextT) =>
% 102.63/17.19 ((
% 102.63/17.19 (subsetTI) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (powersetTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTELcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (binintersectTERcontra) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT1) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT2) =>
% 102.63/17.19 ((
% 102.63/17.19 (contrasubsetT3) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementI1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementE1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub1) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementSub2) =>
% 102.63/17.19 ((
% 102.63/17.19 (doubleComplementEq) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementTnotintersectT) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementImpComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementSubsetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (complementInPowersetComplementIntersect) =>
% 102.63/17.19 ((
% 102.63/17.19 (contraSubsetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTcontraSubset) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTILcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTIRcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion2) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (intersectInPowersetIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpNotIn1) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpInComplement1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTE) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTEcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementUnionInPowersetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule0) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_5) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all2) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1SetBreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (choice2fnsingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all1) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compEex) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIL) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIR) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionEcases) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionCommutes) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2W) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2A) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2B) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex1) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Equiv) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1E) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1I) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncInInjFuncSet) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncInj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (leftInvIsSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjCantorThm) =>
% 102.63/17.20 ((
% 102.63/17.20 (foundation2) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself2) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSp) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSclos) =>
% 102.63/17.20 ((
% 102.63/17.20 (peano0notS) =>
% 102.63/17.20 ((
% 102.63/17.20 (peanoSinj) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (setunionTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (ordinalMinLem1) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y0 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (ordinal @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y1 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y2 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y2 @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @
% 102.63/17.20 Y2) =>
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1202])).
% 102.63/17.20 thf(zip_derived_cl1212, plain,
% 102.63/17.20 (~ (((upairsubunion) =>
% 102.63/17.20 (((upairinpowunion) =>
% 102.63/17.20 (((ubforcartprodlem1) =>
% 102.63/17.20 (((ubforcartprodlem2) =>
% 102.63/17.20 (((ubforcartprodlem3) =>
% 102.63/17.20 (((cartprodpairin) =>
% 102.63/17.20 (((cartprodmempair1) =>
% 102.63/17.20 (((cartprodmempair) =>
% 102.63/17.20 (((setunionE2) =>
% 102.63/17.20 (((setunionsingleton1) =>
% 102.63/17.20 (((setunionsingleton2) =>
% 102.63/17.20 (((setunionsingleton) =>
% 102.63/17.20 (((singletonprop) =>
% 102.63/17.20 (((ex1E1) =>
% 102.63/17.20 (((ex1I) =>
% 102.63/17.20 (((ex1I2) =>
% 102.63/17.20 (((singletonsuniq) =>
% 102.63/17.20 (((setukpairinjL1) =>
% 102.63/17.20 (((kfstsingleton) =>
% 102.63/17.20 (((theprop) =>
% 102.63/17.20 (((kfstpairEq) =>
% 102.63/17.20 (((cartprodfstin) =>
% 102.63/17.20 (((setukpairinjL2) =>
% 102.63/17.20 (((setukpairinjL) =>
% 102.63/17.20 (((setukpairinjR11) =>
% 102.63/17.20 (((setukpairinjR12) =>
% 102.63/17.20 (((setukpairinjR1) =>
% 102.63/17.20 (((upairequniteq) =>
% 102.63/17.20 (((setukpairinjR2) =>
% 102.63/17.20 (((setukpairinjR) =>
% 102.63/17.20 ((
% 102.63/17.20 (ksndsingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (ksndpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (kpairsurjEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodsndin) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairmemEL) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairmemER) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodmempaircEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodfstpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodsndpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairsurjEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrI) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrSub) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrERa) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL1) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL2) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrER) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcImageSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (apProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (app) =>
% 102.63/17.20 ((
% 102.63/17.20 (infuncsetfunc) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcinfuncset) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall1) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ex1E2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp3) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcextLem) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp4) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq1) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq2) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2lamEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifp) =>
% 102.63/17.20 ((
% 102.63/17.20 (theeq) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrue) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueorfalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setminusT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setextT) =>
% 102.63/17.20 ((
% 102.63/17.20 (subsetTI) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTELcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTERcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT1) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT2) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT3) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub2) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTnotintersectT) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementImpComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementSubsetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementInPowersetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (contraSubsetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTcontraSubset) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTILcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTIRcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion2) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (intersectInPowersetIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpNotIn1) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpInComplement1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTE) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTEcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementUnionInPowersetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule0) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_5) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all2) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1SetBreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (choice2fnsingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all1) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compEex) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIL) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIR) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionEcases) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionCommutes) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2W) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2A) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2B) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex1) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Equiv) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1E) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1I) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncInInjFuncSet) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncInj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (leftInvIsSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjCantorThm) =>
% 102.63/17.20 ((
% 102.63/17.20 (foundation2) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself2) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSp) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSclos) =>
% 102.63/17.20 ((
% 102.63/17.20 (peano0notS) =>
% 102.63/17.20 ((
% 102.63/17.20 (peanoSinj) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (setunionTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (ordinalMinLem1) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y0 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (ordinal @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y1 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y2 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y2 @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @
% 102.63/17.20 Y2) =>
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1207])).
% 102.63/17.20 thf(zip_derived_cl1218, plain,
% 102.63/17.20 (~ (((upairinpowunion) =>
% 102.63/17.20 (((ubforcartprodlem1) =>
% 102.63/17.20 (((ubforcartprodlem2) =>
% 102.63/17.20 (((ubforcartprodlem3) =>
% 102.63/17.20 (((cartprodpairin) =>
% 102.63/17.20 (((cartprodmempair1) =>
% 102.63/17.20 (((cartprodmempair) =>
% 102.63/17.20 (((setunionE2) =>
% 102.63/17.20 (((setunionsingleton1) =>
% 102.63/17.20 (((setunionsingleton2) =>
% 102.63/17.20 (((setunionsingleton) =>
% 102.63/17.20 (((singletonprop) =>
% 102.63/17.20 (((ex1E1) =>
% 102.63/17.20 (((ex1I) =>
% 102.63/17.20 (((ex1I2) =>
% 102.63/17.20 (((singletonsuniq) =>
% 102.63/17.20 (((setukpairinjL1) =>
% 102.63/17.20 (((kfstsingleton) =>
% 102.63/17.20 (((theprop) =>
% 102.63/17.20 (((kfstpairEq) =>
% 102.63/17.20 (((cartprodfstin) =>
% 102.63/17.20 (((setukpairinjL2) =>
% 102.63/17.20 (((setukpairinjL) =>
% 102.63/17.20 (((setukpairinjR11) =>
% 102.63/17.20 (((setukpairinjR12) =>
% 102.63/17.20 (((setukpairinjR1) =>
% 102.63/17.20 (((upairequniteq) =>
% 102.63/17.20 (((setukpairinjR2) =>
% 102.63/17.20 (((setukpairinjR) =>
% 102.63/17.20 (((ksndsingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (ksndpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (kpairsurjEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodsndin) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairmemEL) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairmemER) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodmempaircEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodfstpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodsndpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairsurjEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrI) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrSub) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrERa) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL1) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL2) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrER) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcImageSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (apProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (app) =>
% 102.63/17.20 ((
% 102.63/17.20 (infuncsetfunc) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcinfuncset) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall1) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ex1E2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp3) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcextLem) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp4) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq1) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq2) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2lamEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifp) =>
% 102.63/17.20 ((
% 102.63/17.20 (theeq) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrue) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueorfalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setminusT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setextT) =>
% 102.63/17.20 ((
% 102.63/17.20 (subsetTI) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTELcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTERcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT1) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT2) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT3) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub2) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTnotintersectT) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementImpComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementSubsetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementInPowersetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (contraSubsetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTcontraSubset) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTILcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTIRcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion2) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (intersectInPowersetIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpNotIn1) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpInComplement1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTE) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTEcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementUnionInPowersetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule0) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_5) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all2) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1SetBreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (choice2fnsingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all1) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compEex) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIL) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIR) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionEcases) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionCommutes) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2W) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2A) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2B) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex1) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Equiv) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1E) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1I) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncInInjFuncSet) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncInj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (leftInvIsSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjCantorThm) =>
% 102.63/17.20 ((
% 102.63/17.20 (foundation2) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself2) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSp) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSclos) =>
% 102.63/17.20 ((
% 102.63/17.20 (peano0notS) =>
% 102.63/17.20 ((
% 102.63/17.20 (peanoSinj) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (setunionTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (ordinalMinLem1) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y0 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (ordinal @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y1 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y2 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y2 @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @
% 102.63/17.20 Y2) =>
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1212])).
% 102.63/17.20 thf(zip_derived_cl1224, plain,
% 102.63/17.20 (~ (((ubforcartprodlem1) =>
% 102.63/17.20 (((ubforcartprodlem2) =>
% 102.63/17.20 (((ubforcartprodlem3) =>
% 102.63/17.20 (((cartprodpairin) =>
% 102.63/17.20 (((cartprodmempair1) =>
% 102.63/17.20 (((cartprodmempair) =>
% 102.63/17.20 (((setunionE2) =>
% 102.63/17.20 (((setunionsingleton1) =>
% 102.63/17.20 (((setunionsingleton2) =>
% 102.63/17.20 (((setunionsingleton) =>
% 102.63/17.20 (((singletonprop) =>
% 102.63/17.20 (((ex1E1) =>
% 102.63/17.20 (((ex1I) =>
% 102.63/17.20 (((ex1I2) =>
% 102.63/17.20 (((singletonsuniq) =>
% 102.63/17.20 (((setukpairinjL1) =>
% 102.63/17.20 (((kfstsingleton) =>
% 102.63/17.20 (((theprop) =>
% 102.63/17.20 (((kfstpairEq) =>
% 102.63/17.20 (((cartprodfstin) =>
% 102.63/17.20 (((setukpairinjL2) =>
% 102.63/17.20 (((setukpairinjL) =>
% 102.63/17.20 (((setukpairinjR11) =>
% 102.63/17.20 (((setukpairinjR12) =>
% 102.63/17.20 (((setukpairinjR1) =>
% 102.63/17.20 (((upairequniteq) =>
% 102.63/17.20 (((setukpairinjR2) =>
% 102.63/17.20 (((setukpairinjR) =>
% 102.63/17.20 (((ksndsingleton) =>
% 102.63/17.20 (((ksndpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (kpairsurjEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodsndin) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairmemEL) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairmemER) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodmempaircEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodfstpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodsndpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairsurjEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrI) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrSub) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrERa) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL1) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL2) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrER) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcImageSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (apProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (app) =>
% 102.63/17.20 ((
% 102.63/17.20 (infuncsetfunc) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcinfuncset) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall1) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ex1E2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp3) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcextLem) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp4) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq1) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq2) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2lamEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifp) =>
% 102.63/17.20 ((
% 102.63/17.20 (theeq) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrue) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueorfalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setminusT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setextT) =>
% 102.63/17.20 ((
% 102.63/17.20 (subsetTI) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTELcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTERcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT1) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT2) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT3) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub2) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTnotintersectT) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementImpComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementSubsetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementInPowersetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (contraSubsetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTcontraSubset) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTILcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTIRcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion2) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (intersectInPowersetIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpNotIn1) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpInComplement1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTE) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTEcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementUnionInPowersetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule0) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_5) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all2) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1SetBreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (choice2fnsingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all1) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compEex) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIL) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIR) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionEcases) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionCommutes) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2W) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2A) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2B) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex1) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Equiv) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1E) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1I) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncInInjFuncSet) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncInj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (leftInvIsSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjCantorThm) =>
% 102.63/17.20 ((
% 102.63/17.20 (foundation2) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself2) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSp) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSclos) =>
% 102.63/17.20 ((
% 102.63/17.20 (peano0notS) =>
% 102.63/17.20 ((
% 102.63/17.20 (peanoSinj) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (setunionTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (ordinalMinLem1) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y0 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (ordinal @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y1 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y2 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y2 @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @
% 102.63/17.20 Y2) =>
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1218])).
% 102.63/17.20 thf(zip_derived_cl1230, plain,
% 102.63/17.20 (~ (((ubforcartprodlem2) =>
% 102.63/17.20 (((ubforcartprodlem3) =>
% 102.63/17.20 (((cartprodpairin) =>
% 102.63/17.20 (((cartprodmempair1) =>
% 102.63/17.20 (((cartprodmempair) =>
% 102.63/17.20 (((setunionE2) =>
% 102.63/17.20 (((setunionsingleton1) =>
% 102.63/17.20 (((setunionsingleton2) =>
% 102.63/17.20 (((setunionsingleton) =>
% 102.63/17.20 (((singletonprop) =>
% 102.63/17.20 (((ex1E1) =>
% 102.63/17.20 (((ex1I) =>
% 102.63/17.20 (((ex1I2) =>
% 102.63/17.20 (((singletonsuniq) =>
% 102.63/17.20 (((setukpairinjL1) =>
% 102.63/17.20 (((kfstsingleton) =>
% 102.63/17.20 (((theprop) =>
% 102.63/17.20 (((kfstpairEq) =>
% 102.63/17.20 (((cartprodfstin) =>
% 102.63/17.20 (((setukpairinjL2) =>
% 102.63/17.20 (((setukpairinjL) =>
% 102.63/17.20 (((setukpairinjR11) =>
% 102.63/17.20 (((setukpairinjR12) =>
% 102.63/17.20 (((setukpairinjR1) =>
% 102.63/17.20 (((upairequniteq) =>
% 102.63/17.20 (((setukpairinjR2) =>
% 102.63/17.20 (((setukpairinjR) =>
% 102.63/17.20 (((ksndsingleton) =>
% 102.63/17.20 (((ksndpairEq) =>
% 102.63/17.20 (((kpairsurjEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodsndin) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairmemEL) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairmemER) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodmempaircEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodfstpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodsndpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairsurjEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrI) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrSub) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrERa) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL1) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL2) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrER) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcImageSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (apProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (app) =>
% 102.63/17.20 ((
% 102.63/17.20 (infuncsetfunc) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcinfuncset) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall1) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ex1E2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp3) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcextLem) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp4) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq1) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq2) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2lamEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifp) =>
% 102.63/17.20 ((
% 102.63/17.20 (theeq) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrue) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueorfalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setminusT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setextT) =>
% 102.63/17.20 ((
% 102.63/17.20 (subsetTI) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTELcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTERcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT1) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT2) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT3) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub2) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTnotintersectT) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementImpComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementSubsetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementInPowersetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (contraSubsetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTcontraSubset) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTILcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTIRcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion2) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (intersectInPowersetIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpNotIn1) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpInComplement1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTE) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTEcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementUnionInPowersetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule0) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_5) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all2) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1SetBreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (choice2fnsingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all1) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compEex) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIL) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIR) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionEcases) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionCommutes) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2W) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2A) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2B) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex1) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Equiv) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1E) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1I) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncInInjFuncSet) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncInj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (leftInvIsSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjCantorThm) =>
% 102.63/17.20 ((
% 102.63/17.20 (foundation2) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself2) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSp) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSclos) =>
% 102.63/17.20 ((
% 102.63/17.20 (peano0notS) =>
% 102.63/17.20 ((
% 102.63/17.20 (peanoSinj) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (setunionTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (ordinalMinLem1) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y0 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (ordinal @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y1 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y2 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y2 @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @
% 102.63/17.20 Y2) =>
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1224])).
% 102.63/17.20 thf(zip_derived_cl1237, plain,
% 102.63/17.20 (~ (((ubforcartprodlem3) =>
% 102.63/17.20 (((cartprodpairin) =>
% 102.63/17.20 (((cartprodmempair1) =>
% 102.63/17.20 (((cartprodmempair) =>
% 102.63/17.20 (((setunionE2) =>
% 102.63/17.20 (((setunionsingleton1) =>
% 102.63/17.20 (((setunionsingleton2) =>
% 102.63/17.20 (((setunionsingleton) =>
% 102.63/17.20 (((singletonprop) =>
% 102.63/17.20 (((ex1E1) =>
% 102.63/17.20 (((ex1I) =>
% 102.63/17.20 (((ex1I2) =>
% 102.63/17.20 (((singletonsuniq) =>
% 102.63/17.20 (((setukpairinjL1) =>
% 102.63/17.20 (((kfstsingleton) =>
% 102.63/17.20 (((theprop) =>
% 102.63/17.20 (((kfstpairEq) =>
% 102.63/17.20 (((cartprodfstin) =>
% 102.63/17.20 (((setukpairinjL2) =>
% 102.63/17.20 (((setukpairinjL) =>
% 102.63/17.20 (((setukpairinjR11) =>
% 102.63/17.20 (((setukpairinjR12) =>
% 102.63/17.20 (((setukpairinjR1) =>
% 102.63/17.20 (((upairequniteq) =>
% 102.63/17.20 (((setukpairinjR2) =>
% 102.63/17.20 (((setukpairinjR) =>
% 102.63/17.20 (((ksndsingleton) =>
% 102.63/17.20 (((ksndpairEq) =>
% 102.63/17.20 (((kpairsurjEq) =>
% 102.63/17.20 (((cartprodsndin) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairmemEL) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairmemER) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodmempaircEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodfstpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodsndpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairsurjEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrI) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrSub) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrERa) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL1) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL2) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrER) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcImageSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (apProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (app) =>
% 102.63/17.20 ((
% 102.63/17.20 (infuncsetfunc) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcinfuncset) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall1) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ex1E2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp3) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcextLem) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp4) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq1) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq2) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2lamEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifp) =>
% 102.63/17.20 ((
% 102.63/17.20 (theeq) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrue) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueorfalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setminusT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setextT) =>
% 102.63/17.20 ((
% 102.63/17.20 (subsetTI) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTELcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTERcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT1) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT2) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT3) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub2) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTnotintersectT) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementImpComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementSubsetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementInPowersetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (contraSubsetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTcontraSubset) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTILcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTIRcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion2) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (intersectInPowersetIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpNotIn1) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpInComplement1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTE) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTEcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementUnionInPowersetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule0) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_5) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all2) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1SetBreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (choice2fnsingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all1) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compEex) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIL) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIR) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionEcases) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionCommutes) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2W) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2A) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2B) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex1) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Equiv) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1E) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1I) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncInInjFuncSet) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncInj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (leftInvIsSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjCantorThm) =>
% 102.63/17.20 ((
% 102.63/17.20 (foundation2) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself2) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSp) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSclos) =>
% 102.63/17.20 ((
% 102.63/17.20 (peano0notS) =>
% 102.63/17.20 ((
% 102.63/17.20 (peanoSinj) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (setunionTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (ordinalMinLem1) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y0 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (ordinal @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y1 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y2 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y2 @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @
% 102.63/17.20 Y2) =>
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1230])).
% 102.63/17.20 thf(zip_derived_cl1244, plain,
% 102.63/17.20 (~ (((cartprodpairin) =>
% 102.63/17.20 (((cartprodmempair1) =>
% 102.63/17.20 (((cartprodmempair) =>
% 102.63/17.20 (((setunionE2) =>
% 102.63/17.20 (((setunionsingleton1) =>
% 102.63/17.20 (((setunionsingleton2) =>
% 102.63/17.20 (((setunionsingleton) =>
% 102.63/17.20 (((singletonprop) =>
% 102.63/17.20 (((ex1E1) =>
% 102.63/17.20 (((ex1I) =>
% 102.63/17.20 (((ex1I2) =>
% 102.63/17.20 (((singletonsuniq) =>
% 102.63/17.20 (((setukpairinjL1) =>
% 102.63/17.20 (((kfstsingleton) =>
% 102.63/17.20 (((theprop) =>
% 102.63/17.20 (((kfstpairEq) =>
% 102.63/17.20 (((cartprodfstin) =>
% 102.63/17.20 (((setukpairinjL2) =>
% 102.63/17.20 (((setukpairinjL) =>
% 102.63/17.20 (((setukpairinjR11) =>
% 102.63/17.20 (((setukpairinjR12) =>
% 102.63/17.20 (((setukpairinjR1) =>
% 102.63/17.20 (((upairequniteq) =>
% 102.63/17.20 (((setukpairinjR2) =>
% 102.63/17.20 (((setukpairinjR) =>
% 102.63/17.20 (((ksndsingleton) =>
% 102.63/17.20 (((ksndpairEq) =>
% 102.63/17.20 (((kpairsurjEq) =>
% 102.63/17.20 (((cartprodsndin) =>
% 102.63/17.20 (((cartprodpairmemEL) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairmemER) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodmempaircEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodfstpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodsndpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairsurjEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrI) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrSub) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrERa) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL1) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL2) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrER) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcImageSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (apProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (app) =>
% 102.63/17.20 ((
% 102.63/17.20 (infuncsetfunc) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcinfuncset) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall1) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ex1E2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp3) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcextLem) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp4) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq1) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq2) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2lamEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifp) =>
% 102.63/17.20 ((
% 102.63/17.20 (theeq) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrue) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueorfalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setminusT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setextT) =>
% 102.63/17.20 ((
% 102.63/17.20 (subsetTI) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTELcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTERcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT1) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT2) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT3) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub2) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTnotintersectT) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementImpComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementSubsetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementInPowersetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (contraSubsetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTcontraSubset) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTILcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTIRcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion2) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (intersectInPowersetIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpNotIn1) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpInComplement1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTE) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTEcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementUnionInPowersetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule0) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_5) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all2) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1SetBreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (choice2fnsingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all1) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compEex) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIL) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIR) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionEcases) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionCommutes) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2W) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2A) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2B) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex1) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Equiv) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1E) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1I) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncInInjFuncSet) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncInj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (leftInvIsSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjCantorThm) =>
% 102.63/17.20 ((
% 102.63/17.20 (foundation2) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself2) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSp) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSclos) =>
% 102.63/17.20 ((
% 102.63/17.20 (peano0notS) =>
% 102.63/17.20 ((
% 102.63/17.20 (peanoSinj) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (setunionTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (ordinalMinLem1) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y0 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (ordinal @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y1 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y2 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y2 @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @
% 102.63/17.20 Y2) =>
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1237])).
% 102.63/17.20 thf(zip_derived_cl1252, plain,
% 102.63/17.20 (~ (((cartprodmempair1) =>
% 102.63/17.20 (((cartprodmempair) =>
% 102.63/17.20 (((setunionE2) =>
% 102.63/17.20 (((setunionsingleton1) =>
% 102.63/17.20 (((setunionsingleton2) =>
% 102.63/17.20 (((setunionsingleton) =>
% 102.63/17.20 (((singletonprop) =>
% 102.63/17.20 (((ex1E1) =>
% 102.63/17.20 (((ex1I) =>
% 102.63/17.20 (((ex1I2) =>
% 102.63/17.20 (((singletonsuniq) =>
% 102.63/17.20 (((setukpairinjL1) =>
% 102.63/17.20 (((kfstsingleton) =>
% 102.63/17.20 (((theprop) =>
% 102.63/17.20 (((kfstpairEq) =>
% 102.63/17.20 (((cartprodfstin) =>
% 102.63/17.20 (((setukpairinjL2) =>
% 102.63/17.20 (((setukpairinjL) =>
% 102.63/17.20 (((setukpairinjR11) =>
% 102.63/17.20 (((setukpairinjR12) =>
% 102.63/17.20 (((setukpairinjR1) =>
% 102.63/17.20 (((upairequniteq) =>
% 102.63/17.20 (((setukpairinjR2) =>
% 102.63/17.20 (((setukpairinjR) =>
% 102.63/17.20 (((ksndsingleton) =>
% 102.63/17.20 (((ksndpairEq) =>
% 102.63/17.20 (((kpairsurjEq) =>
% 102.63/17.20 (((cartprodsndin) =>
% 102.63/17.20 (((cartprodpairmemEL) =>
% 102.63/17.20 (((cartprodpairmemER) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodmempaircEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodfstpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodsndpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairsurjEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrI) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrSub) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrERa) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL1) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL2) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrER) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcImageSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (apProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (app) =>
% 102.63/17.20 ((
% 102.63/17.20 (infuncsetfunc) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcinfuncset) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall1) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ex1E2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp3) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcextLem) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp4) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq1) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq2) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2lamEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifp) =>
% 102.63/17.20 ((
% 102.63/17.20 (theeq) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrue) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueorfalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setminusT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setextT) =>
% 102.63/17.20 ((
% 102.63/17.20 (subsetTI) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTELcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTERcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT1) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT2) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT3) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub2) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTnotintersectT) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementImpComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementSubsetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementInPowersetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (contraSubsetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTcontraSubset) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTILcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTIRcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion2) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (intersectInPowersetIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpNotIn1) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpInComplement1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTE) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTEcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementUnionInPowersetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule0) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_5) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all2) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1SetBreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (choice2fnsingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all1) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compEex) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIL) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIR) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionEcases) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionCommutes) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2W) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2A) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2B) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex1) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Equiv) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1E) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1I) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncInInjFuncSet) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncInj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (leftInvIsSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjCantorThm) =>
% 102.63/17.20 ((
% 102.63/17.20 (foundation2) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself2) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSp) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSclos) =>
% 102.63/17.20 ((
% 102.63/17.20 (peano0notS) =>
% 102.63/17.20 ((
% 102.63/17.20 (peanoSinj) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (setunionTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (ordinalMinLem1) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y0 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (ordinal @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y1 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y2 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y2 @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @
% 102.63/17.20 Y2) =>
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1244])).
% 102.63/17.20 thf(zip_derived_cl1261, plain,
% 102.63/17.20 (~ (((cartprodmempair) =>
% 102.63/17.20 (((setunionE2) =>
% 102.63/17.20 (((setunionsingleton1) =>
% 102.63/17.20 (((setunionsingleton2) =>
% 102.63/17.20 (((setunionsingleton) =>
% 102.63/17.20 (((singletonprop) =>
% 102.63/17.20 (((ex1E1) =>
% 102.63/17.20 (((ex1I) =>
% 102.63/17.20 (((ex1I2) =>
% 102.63/17.20 (((singletonsuniq) =>
% 102.63/17.20 (((setukpairinjL1) =>
% 102.63/17.20 (((kfstsingleton) =>
% 102.63/17.20 (((theprop) =>
% 102.63/17.20 (((kfstpairEq) =>
% 102.63/17.20 (((cartprodfstin) =>
% 102.63/17.20 (((setukpairinjL2) =>
% 102.63/17.20 (((setukpairinjL) =>
% 102.63/17.20 (((setukpairinjR11) =>
% 102.63/17.20 (((setukpairinjR12) =>
% 102.63/17.20 (((setukpairinjR1) =>
% 102.63/17.20 (((upairequniteq) =>
% 102.63/17.20 (((setukpairinjR2) =>
% 102.63/17.20 (((setukpairinjR) =>
% 102.63/17.20 (((ksndsingleton) =>
% 102.63/17.20 (((ksndpairEq) =>
% 102.63/17.20 (((kpairsurjEq) =>
% 102.63/17.20 (((cartprodsndin) =>
% 102.63/17.20 (((cartprodpairmemEL) =>
% 102.63/17.20 (((cartprodpairmemER) =>
% 102.63/17.20 (((cartprodmempaircEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodfstpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodsndpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairsurjEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrI) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrSub) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrERa) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL1) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL2) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrER) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcImageSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (apProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (app) =>
% 102.63/17.20 ((
% 102.63/17.20 (infuncsetfunc) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcinfuncset) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall1) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ex1E2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp3) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcextLem) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp4) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq1) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq2) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2lamEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifp) =>
% 102.63/17.20 ((
% 102.63/17.20 (theeq) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrue) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueorfalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setminusT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setextT) =>
% 102.63/17.20 ((
% 102.63/17.20 (subsetTI) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTELcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTERcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT1) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT2) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT3) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub2) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTnotintersectT) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementImpComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementSubsetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementInPowersetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (contraSubsetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTcontraSubset) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTILcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTIRcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion2) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (intersectInPowersetIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpNotIn1) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpInComplement1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTE) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTEcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementUnionInPowersetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule0) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_5) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all2) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1SetBreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (choice2fnsingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all1) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compEex) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIL) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIR) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionEcases) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionCommutes) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2W) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2A) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2B) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex1) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Equiv) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1E) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1I) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncInInjFuncSet) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncInj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (leftInvIsSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjCantorThm) =>
% 102.63/17.20 ((
% 102.63/17.20 (foundation2) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself2) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSp) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSclos) =>
% 102.63/17.20 ((
% 102.63/17.20 (peano0notS) =>
% 102.63/17.20 ((
% 102.63/17.20 (peanoSinj) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (setunionTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (ordinalMinLem1) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y0 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (ordinal @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y1 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y2 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y2 @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @
% 102.63/17.20 Y2) =>
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1252])).
% 102.63/17.20 thf(zip_derived_cl1270, plain,
% 102.63/17.20 (~ (((setunionE2) =>
% 102.63/17.20 (((setunionsingleton1) =>
% 102.63/17.20 (((setunionsingleton2) =>
% 102.63/17.20 (((setunionsingleton) =>
% 102.63/17.20 (((singletonprop) =>
% 102.63/17.20 (((ex1E1) =>
% 102.63/17.20 (((ex1I) =>
% 102.63/17.20 (((ex1I2) =>
% 102.63/17.20 (((singletonsuniq) =>
% 102.63/17.20 (((setukpairinjL1) =>
% 102.63/17.20 (((kfstsingleton) =>
% 102.63/17.20 (((theprop) =>
% 102.63/17.20 (((kfstpairEq) =>
% 102.63/17.20 (((cartprodfstin) =>
% 102.63/17.20 (((setukpairinjL2) =>
% 102.63/17.20 (((setukpairinjL) =>
% 102.63/17.20 (((setukpairinjR11) =>
% 102.63/17.20 (((setukpairinjR12) =>
% 102.63/17.20 (((setukpairinjR1) =>
% 102.63/17.20 (((upairequniteq) =>
% 102.63/17.20 (((setukpairinjR2) =>
% 102.63/17.20 (((setukpairinjR) =>
% 102.63/17.20 (((ksndsingleton) =>
% 102.63/17.20 (((ksndpairEq) =>
% 102.63/17.20 (((kpairsurjEq) =>
% 102.63/17.20 (((cartprodsndin) =>
% 102.63/17.20 (((cartprodpairmemEL) =>
% 102.63/17.20 (((cartprodpairmemER) =>
% 102.63/17.20 (((cartprodmempaircEq) =>
% 102.63/17.20 (((cartprodfstpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodsndpairEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (cartprodpairsurjEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrI) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrSub) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrERa) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL1) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrEL2) =>
% 102.63/17.20 ((
% 102.63/17.20 (dpsetconstrER) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcImageSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (apProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (app) =>
% 102.63/17.20 ((
% 102.63/17.20 (infuncsetfunc) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcinfuncset) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamProp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lamp) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2p) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall1) =>
% 102.63/17.20 ((
% 102.63/17.20 (brelnall2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ex1E2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp3) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcextLem) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcGraphProp4) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext) =>
% 102.63/17.20 ((
% 102.63/17.20 (funcext2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq1) =>
% 102.63/17.20 ((
% 102.63/17.20 (ap2apEq2) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta1) =>
% 102.63/17.20 ((
% 102.63/17.20 (lam2lamEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (beta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (eta2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalseProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueProp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifSingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (ifp) =>
% 102.63/17.20 ((
% 102.63/17.20 (theeq) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrue) =>
% 102.63/17.20 ((
% 102.63/17.20 (iffalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (iftrueorfalse) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setminusT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementT_lem) =>
% 102.63/17.20 ((
% 102.63/17.20 (setextT) =>
% 102.63/17.20 ((
% 102.63/17.20 (subsetTI) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (powersetTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTELcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintersectTERcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT1) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT2) =>
% 102.63/17.20 ((
% 102.63/17.20 (contrasubsetT3) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementI1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementE1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub1) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementSub2) =>
% 102.63/17.20 ((
% 102.63/17.20 (doubleComplementEq) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTnotintersectT) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementImpComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementSubsetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementInPowersetComplementIntersect) =>
% 102.63/17.20 ((
% 102.63/17.20 (contraSubsetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementTcontraSubset) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTILcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTIRcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInUnion2) =>
% 102.63/17.20 ((
% 102.63/17.20 (inIntersectImpInIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (intersectInPowersetIntersectUnions) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpNotIn1) =>
% 102.63/17.20 ((
% 102.63/17.20 (inComplementUnionImpInComplement1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTE) =>
% 102.63/17.20 ((
% 102.63/17.20 (binunionTEcontra) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a1) =>
% 102.63/17.20 ((
% 102.63/17.20 (complementUnionInPowersetComplement) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan1) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2a) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b2) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2b) =>
% 102.63/17.20 ((
% 102.63/17.20 (demorgan2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule0) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz13rule4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_1) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_2) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_3) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_4) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz1_5) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all2) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1SetBreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (choice2fnsingleton) =>
% 102.63/17.20 ((
% 102.63/17.20 (setOfPairsIsBReln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1all1) =>
% 102.63/17.20 ((
% 102.63/17.20 (subbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (eqbreln1) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1invE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1compEex) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionprop) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIL) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionIR) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionI) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionE) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionEcases) =>
% 102.63/17.20 ((
% 102.63/17.20 (breln1unionCommutes) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2W) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2A) =>
% 102.63/17.20 ((
% 102.63/17.20 (woz2B) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Ex1) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1Equiv) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1E) =>
% 102.63/17.20 ((
% 102.63/17.20 (image1I) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncInInjFuncSet) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (injFuncSetFuncInj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncIn) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjFuncSetFuncSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (leftInvIsSurj) =>
% 102.63/17.20 ((
% 102.63/17.20 (surjCantorThm) =>
% 102.63/17.20 ((
% 102.63/17.20 (foundation2) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself) =>
% 102.63/17.20 ((
% 102.63/17.20 (notinself2) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSp) =>
% 102.63/17.20 ((
% 102.63/17.20 (omegaSclos) =>
% 102.63/17.20 ((
% 102.63/17.20 (peano0notS) =>
% 102.63/17.20 ((
% 102.63/17.20 (peanoSinj) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp1) =>
% 102.63/17.20 ((
% 102.63/17.20 (binintTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (transitivesetOp2) =>
% 102.63/17.20 ((
% 102.63/17.20 (setunionTransitive) =>
% 102.63/17.20 ((
% 102.63/17.20 (ordinalMinLem1) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y0 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (ordinal @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y1 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (!!) @ (
% 102.63/17.20 ^[Y2 : $i]:
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y2 @
% 102.63/17.20 Y0) =>
% 102.63/17.20 ((
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @
% 102.63/17.20 Y2) =>
% 102.63/17.20 (in @
% 102.63/17.20 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1261])).
% 102.63/17.20 thf(zip_derived_cl1279, plain,
% 102.63/17.20 (~ (((setunionsingleton1) =>
% 102.63/17.20 (((setunionsingleton2) =>
% 102.63/17.20 (((setunionsingleton) =>
% 102.63/17.20 (((singletonprop) =>
% 102.63/17.20 (((ex1E1) =>
% 102.63/17.20 (((ex1I) =>
% 102.63/17.20 (((ex1I2) =>
% 102.63/17.20 (((singletonsuniq) =>
% 102.63/17.20 (((setukpairinjL1) =>
% 102.63/17.20 (((kfstsingleton) =>
% 102.63/17.20 (((theprop) =>
% 102.63/17.20 (((kfstpairEq) =>
% 102.63/17.20 (((cartprodfstin) =>
% 102.63/17.20 (((setukpairinjL2) =>
% 102.63/17.20 (((setukpairinjL) =>
% 102.63/17.20 (((setukpairinjR11) =>
% 102.63/17.20 (((setukpairinjR12) =>
% 102.63/17.20 (((setukpairinjR1) =>
% 102.63/17.20 (((upairequniteq) =>
% 102.63/17.20 (((setukpairinjR2) =>
% 102.63/17.20 (((setukpairinjR) =>
% 102.63/17.20 (((ksndsingleton) =>
% 102.63/17.20 (((ksndpairEq) =>
% 102.63/17.20 (((kpairsurjEq) =>
% 102.63/17.20 (((cartprodsndin) =>
% 102.63/17.21 (((cartprodpairmemEL) =>
% 102.63/17.21 (((cartprodpairmemER) =>
% 102.63/17.21 (((cartprodmempaircEq) =>
% 102.63/17.21 (((cartprodfstpairEq) =>
% 102.63/17.21 (((cartprodsndpairEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (cartprodpairsurjEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrI) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrSub) =>
% 102.63/17.21 ((
% 102.63/17.21 (setOfPairsIsBReln) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrERa) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrEL1) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrEL2) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrER) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcImageSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (apProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (app) =>
% 102.63/17.21 ((
% 102.63/17.21 (infuncsetfunc) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcinfuncset) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall1) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ex1E2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp3) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcextLem) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp4) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq1) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq2) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2lamEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifp) =>
% 102.63/17.21 ((
% 102.63/17.21 (theeq) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrue) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueorfalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setminusT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setextT) =>
% 102.63/17.21 ((
% 102.63/17.21 (subsetTI) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTELcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTERcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT1) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT2) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT3) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub2) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTnotintersectT) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementImpComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementSubsetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementInPowersetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (contraSubsetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTcontraSubset) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTILcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTIRcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion2) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (intersectInPowersetIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpNotIn1) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpInComplement1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTE) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTEcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementUnionInPowersetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule0) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_5) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all2) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1SetBreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (choice2fnsingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (setOfPairsIsBReln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all1) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compEex) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIL) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIR) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionEcases) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionCommutes) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2W) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2A) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2B) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex1) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Equiv) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1E) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1I) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncInInjFuncSet) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncInj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (leftInvIsSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjCantorThm) =>
% 102.63/17.21 ((
% 102.63/17.21 (foundation2) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself2) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSp) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSclos) =>
% 102.63/17.21 ((
% 102.63/17.21 (peano0notS) =>
% 102.63/17.21 ((
% 102.63/17.21 (peanoSinj) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (setunionTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (ordinalMinLem1) =>
% 102.63/17.21 ((
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% 102.63/17.21 ^[Y0 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (ordinal @
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% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y1 : $i]:
% 102.63/17.21 ((
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% 102.63/17.21 ^[Y2 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y2 @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @
% 102.63/17.21 Y2) =>
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1270])).
% 102.63/17.21 thf(zip_derived_cl1288, plain,
% 102.63/17.21 (~ (((setunionsingleton2) =>
% 102.63/17.21 (((setunionsingleton) =>
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% 102.63/17.21 (((setukpairinjL) =>
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% 102.63/17.21 (((setukpairinjR12) =>
% 102.63/17.21 (((setukpairinjR1) =>
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% 102.63/17.21 (((setukpairinjR) =>
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% 102.63/17.21 (((ksndpairEq) =>
% 102.63/17.21 (((kpairsurjEq) =>
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% 102.63/17.21 (((cartprodpairmemEL) =>
% 102.63/17.21 (((cartprodpairmemER) =>
% 102.63/17.21 (((cartprodmempaircEq) =>
% 102.63/17.21 (((cartprodfstpairEq) =>
% 102.63/17.21 (((cartprodsndpairEq) =>
% 102.63/17.21 (((cartprodpairsurjEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrI) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrSub) =>
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% 102.63/17.21 (dpsetconstrEL1) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrEL2) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrER) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcImageSingleton) =>
% 102.63/17.21 ((
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% 102.63/17.21 ((
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% 102.63/17.21 ((
% 102.63/17.21 (infuncsetfunc) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcinfuncset) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2p) =>
% 102.63/17.21 ((
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% 102.63/17.21 ((
% 102.63/17.21 (brelnall2) =>
% 102.63/17.21 ((
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% 102.63/17.21 ((
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% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp2) =>
% 102.63/17.21 ((
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% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp4) =>
% 102.63/17.21 ((
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% 102.63/17.21 ((
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% 102.63/17.21 ((
% 102.63/17.21 (funcext) =>
% 102.63/17.21 ((
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% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq1) =>
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% 102.63/17.21 ((
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% 102.63/17.21 ((
% 102.63/17.21 (eta2) =>
% 102.63/17.21 ((
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% 102.63/17.21 ((
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% 102.63/17.21 ((
% 102.63/17.21 (iftrue) =>
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% 102.63/17.21 (iffalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueorfalse) =>
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% 102.63/17.21 ((
% 102.63/17.21 (binunionT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setminusT_lem) =>
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% 102.63/17.21 ((
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% 102.63/17.21 ((
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% 102.63/17.21 ((
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% 102.63/17.21 ((
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% 102.63/17.21 ((
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% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT2) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT3) =>
% 102.63/17.21 ((
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% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub2) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTnotintersectT) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementImpComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementSubsetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementInPowersetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (contraSubsetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTcontraSubset) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTILcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTIRcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion2) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (intersectInPowersetIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpNotIn1) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpInComplement1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTE) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTEcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementUnionInPowersetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule0) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_5) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all2) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1SetBreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (choice2fnsingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (setOfPairsIsBReln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all1) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compEex) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIL) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIR) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionEcases) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionCommutes) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2W) =>
% 102.63/17.21 ((
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% 102.63/17.21 ((
% 102.63/17.21 (woz2B) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex1) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Equiv) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1E) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1I) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncInInjFuncSet) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncInj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (leftInvIsSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjCantorThm) =>
% 102.63/17.21 ((
% 102.63/17.21 (foundation2) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself2) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSp) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSclos) =>
% 102.63/17.21 ((
% 102.63/17.21 (peano0notS) =>
% 102.63/17.21 ((
% 102.63/17.21 (peanoSinj) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (setunionTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (ordinalMinLem1) =>
% 102.63/17.21 ((
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% 102.63/17.21 ^[Y0 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (ordinal @
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% 102.63/17.21 ((
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% 102.63/17.21 ((
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% 102.63/17.21 ((
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% 102.63/17.21 (in @
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% 102.63/17.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1279])).
% 102.63/17.21 thf(zip_derived_cl1297, plain,
% 102.63/17.21 (~ (((setunionsingleton) =>
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% 102.63/17.21 (complementImpComplementIntersect) =>
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% 102.63/17.21 (complementSubsetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementInPowersetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (contraSubsetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTcontraSubset) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTILcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTIRcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion2) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (intersectInPowersetIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpNotIn1) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpInComplement1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTE) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTEcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementUnionInPowersetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule0) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_5) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all2) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1SetBreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (choice2fnsingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (setOfPairsIsBReln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all1) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compEex) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIL) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIR) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionEcases) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionCommutes) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2W) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2A) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2B) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex1) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Equiv) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1E) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1I) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncInInjFuncSet) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncInj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (leftInvIsSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjCantorThm) =>
% 102.63/17.21 ((
% 102.63/17.21 (foundation2) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself2) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSp) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSclos) =>
% 102.63/17.21 ((
% 102.63/17.21 (peano0notS) =>
% 102.63/17.21 ((
% 102.63/17.21 (peanoSinj) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (setunionTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (ordinalMinLem1) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y0 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (ordinal @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y1 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y2 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y2 @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @
% 102.63/17.21 Y2) =>
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])).
% 102.63/17.21 thf(zip_derived_cl1306, plain,
% 102.63/17.21 (~ (((singletonprop) =>
% 102.63/17.21 (((ex1E1) =>
% 102.63/17.21 (((ex1I) =>
% 102.63/17.21 (((ex1I2) =>
% 102.63/17.21 (((singletonsuniq) =>
% 102.63/17.21 (((setukpairinjL1) =>
% 102.63/17.21 (((kfstsingleton) =>
% 102.63/17.21 (((theprop) =>
% 102.63/17.21 (((kfstpairEq) =>
% 102.63/17.21 (((cartprodfstin) =>
% 102.63/17.21 (((setukpairinjL2) =>
% 102.63/17.21 (((setukpairinjL) =>
% 102.63/17.21 (((setukpairinjR11) =>
% 102.63/17.21 (((setukpairinjR12) =>
% 102.63/17.21 (((setukpairinjR1) =>
% 102.63/17.21 (((upairequniteq) =>
% 102.63/17.21 (((setukpairinjR2) =>
% 102.63/17.21 (((setukpairinjR) =>
% 102.63/17.21 (((ksndsingleton) =>
% 102.63/17.21 (((ksndpairEq) =>
% 102.63/17.21 (((kpairsurjEq) =>
% 102.63/17.21 (((cartprodsndin) =>
% 102.63/17.21 (((cartprodpairmemEL) =>
% 102.63/17.21 (((cartprodpairmemER) =>
% 102.63/17.21 (((cartprodmempaircEq) =>
% 102.63/17.21 (((cartprodfstpairEq) =>
% 102.63/17.21 (((cartprodsndpairEq) =>
% 102.63/17.21 (((cartprodpairsurjEq) =>
% 102.63/17.21 (((dpsetconstrI) =>
% 102.63/17.21 (((dpsetconstrSub) =>
% 102.63/17.21 ((
% 102.63/17.21 (setOfPairsIsBReln) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrERa) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrEL1) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrEL2) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrER) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcImageSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (apProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (app) =>
% 102.63/17.21 ((
% 102.63/17.21 (infuncsetfunc) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcinfuncset) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall1) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ex1E2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp3) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcextLem) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp4) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq1) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq2) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2lamEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifp) =>
% 102.63/17.21 ((
% 102.63/17.21 (theeq) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrue) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueorfalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setminusT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setextT) =>
% 102.63/17.21 ((
% 102.63/17.21 (subsetTI) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTELcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTERcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT1) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT2) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT3) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub2) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTnotintersectT) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementImpComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementSubsetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementInPowersetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (contraSubsetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTcontraSubset) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTILcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTIRcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion2) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (intersectInPowersetIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpNotIn1) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpInComplement1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTE) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTEcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementUnionInPowersetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule0) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_5) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all2) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1SetBreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (choice2fnsingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (setOfPairsIsBReln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all1) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compEex) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIL) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIR) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionEcases) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionCommutes) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2W) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2A) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2B) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex1) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Equiv) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1E) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1I) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncInInjFuncSet) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncInj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (leftInvIsSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjCantorThm) =>
% 102.63/17.21 ((
% 102.63/17.21 (foundation2) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself2) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSp) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSclos) =>
% 102.63/17.21 ((
% 102.63/17.21 (peano0notS) =>
% 102.63/17.21 ((
% 102.63/17.21 (peanoSinj) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (setunionTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (ordinalMinLem1) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y0 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (ordinal @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y1 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y2 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y2 @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @
% 102.63/17.21 Y2) =>
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1297])).
% 102.63/17.21 thf(zip_derived_cl1314, plain,
% 102.63/17.21 (~ (((ex1E1) =>
% 102.63/17.21 (((ex1I) =>
% 102.63/17.21 (((ex1I2) =>
% 102.63/17.21 (((singletonsuniq) =>
% 102.63/17.21 (((setukpairinjL1) =>
% 102.63/17.21 (((kfstsingleton) =>
% 102.63/17.21 (((theprop) =>
% 102.63/17.21 (((kfstpairEq) =>
% 102.63/17.21 (((cartprodfstin) =>
% 102.63/17.21 (((setukpairinjL2) =>
% 102.63/17.21 (((setukpairinjL) =>
% 102.63/17.21 (((setukpairinjR11) =>
% 102.63/17.21 (((setukpairinjR12) =>
% 102.63/17.21 (((setukpairinjR1) =>
% 102.63/17.21 (((upairequniteq) =>
% 102.63/17.21 (((setukpairinjR2) =>
% 102.63/17.21 (((setukpairinjR) =>
% 102.63/17.21 (((ksndsingleton) =>
% 102.63/17.21 (((ksndpairEq) =>
% 102.63/17.21 (((kpairsurjEq) =>
% 102.63/17.21 (((cartprodsndin) =>
% 102.63/17.21 (((cartprodpairmemEL) =>
% 102.63/17.21 (((cartprodpairmemER) =>
% 102.63/17.21 (((cartprodmempaircEq) =>
% 102.63/17.21 (((cartprodfstpairEq) =>
% 102.63/17.21 (((cartprodsndpairEq) =>
% 102.63/17.21 (((cartprodpairsurjEq) =>
% 102.63/17.21 (((dpsetconstrI) =>
% 102.63/17.21 (((dpsetconstrSub) =>
% 102.63/17.21 (((setOfPairsIsBReln) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrERa) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrEL1) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrEL2) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrER) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcImageSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (apProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (app) =>
% 102.63/17.21 ((
% 102.63/17.21 (infuncsetfunc) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcinfuncset) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall1) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ex1E2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp3) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcextLem) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp4) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq1) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq2) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2lamEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifp) =>
% 102.63/17.21 ((
% 102.63/17.21 (theeq) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrue) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueorfalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setminusT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setextT) =>
% 102.63/17.21 ((
% 102.63/17.21 (subsetTI) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTELcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTERcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT1) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT2) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT3) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub2) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTnotintersectT) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementImpComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementSubsetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementInPowersetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (contraSubsetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTcontraSubset) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTILcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTIRcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion2) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (intersectInPowersetIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpNotIn1) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpInComplement1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTE) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTEcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementUnionInPowersetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule0) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_5) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all2) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1SetBreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (choice2fnsingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (setOfPairsIsBReln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all1) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compEex) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIL) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIR) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionEcases) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionCommutes) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2W) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2A) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2B) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex1) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Equiv) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1E) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1I) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncInInjFuncSet) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncInj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (leftInvIsSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjCantorThm) =>
% 102.63/17.21 ((
% 102.63/17.21 (foundation2) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself2) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSp) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSclos) =>
% 102.63/17.21 ((
% 102.63/17.21 (peano0notS) =>
% 102.63/17.21 ((
% 102.63/17.21 (peanoSinj) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (setunionTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (ordinalMinLem1) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y0 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (ordinal @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y1 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y2 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y2 @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @
% 102.63/17.21 Y2) =>
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1306])).
% 102.63/17.21 thf(zip_derived_cl1321, plain,
% 102.63/17.21 (~ (((ex1I) =>
% 102.63/17.21 (((ex1I2) =>
% 102.63/17.21 (((singletonsuniq) =>
% 102.63/17.21 (((setukpairinjL1) =>
% 102.63/17.21 (((kfstsingleton) =>
% 102.63/17.21 (((theprop) =>
% 102.63/17.21 (((kfstpairEq) =>
% 102.63/17.21 (((cartprodfstin) =>
% 102.63/17.21 (((setukpairinjL2) =>
% 102.63/17.21 (((setukpairinjL) =>
% 102.63/17.21 (((setukpairinjR11) =>
% 102.63/17.21 (((setukpairinjR12) =>
% 102.63/17.21 (((setukpairinjR1) =>
% 102.63/17.21 (((upairequniteq) =>
% 102.63/17.21 (((setukpairinjR2) =>
% 102.63/17.21 (((setukpairinjR) =>
% 102.63/17.21 (((ksndsingleton) =>
% 102.63/17.21 (((ksndpairEq) =>
% 102.63/17.21 (((kpairsurjEq) =>
% 102.63/17.21 (((cartprodsndin) =>
% 102.63/17.21 (((cartprodpairmemEL) =>
% 102.63/17.21 (((cartprodpairmemER) =>
% 102.63/17.21 (((cartprodmempaircEq) =>
% 102.63/17.21 (((cartprodfstpairEq) =>
% 102.63/17.21 (((cartprodsndpairEq) =>
% 102.63/17.21 (((cartprodpairsurjEq) =>
% 102.63/17.21 (((dpsetconstrI) =>
% 102.63/17.21 (((dpsetconstrSub) =>
% 102.63/17.21 (((setOfPairsIsBReln) =>
% 102.63/17.21 (((dpsetconstrERa) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrEL1) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrEL2) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrER) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcImageSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (apProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (app) =>
% 102.63/17.21 ((
% 102.63/17.21 (infuncsetfunc) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcinfuncset) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall1) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ex1E2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp3) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcextLem) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp4) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq1) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq2) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2lamEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifp) =>
% 102.63/17.21 ((
% 102.63/17.21 (theeq) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrue) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueorfalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setminusT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setextT) =>
% 102.63/17.21 ((
% 102.63/17.21 (subsetTI) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTELcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTERcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT1) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT2) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT3) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub2) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTnotintersectT) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementImpComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementSubsetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementInPowersetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (contraSubsetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTcontraSubset) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTILcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTIRcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion2) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (intersectInPowersetIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpNotIn1) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpInComplement1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTE) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTEcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementUnionInPowersetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule0) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_5) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all2) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1SetBreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (choice2fnsingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (setOfPairsIsBReln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all1) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compEex) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIL) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIR) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionEcases) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionCommutes) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2W) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2A) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2B) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex1) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Equiv) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1E) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1I) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncInInjFuncSet) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncInj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (leftInvIsSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjCantorThm) =>
% 102.63/17.21 ((
% 102.63/17.21 (foundation2) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself2) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSp) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSclos) =>
% 102.63/17.21 ((
% 102.63/17.21 (peano0notS) =>
% 102.63/17.21 ((
% 102.63/17.21 (peanoSinj) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (setunionTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (ordinalMinLem1) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y0 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (ordinal @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y1 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y2 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y2 @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @
% 102.63/17.21 Y2) =>
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1314])).
% 102.63/17.21 thf(zip_derived_cl1328, plain,
% 102.63/17.21 (~ (((ex1I2) =>
% 102.63/17.21 (((singletonsuniq) =>
% 102.63/17.21 (((setukpairinjL1) =>
% 102.63/17.21 (((kfstsingleton) =>
% 102.63/17.21 (((theprop) =>
% 102.63/17.21 (((kfstpairEq) =>
% 102.63/17.21 (((cartprodfstin) =>
% 102.63/17.21 (((setukpairinjL2) =>
% 102.63/17.21 (((setukpairinjL) =>
% 102.63/17.21 (((setukpairinjR11) =>
% 102.63/17.21 (((setukpairinjR12) =>
% 102.63/17.21 (((setukpairinjR1) =>
% 102.63/17.21 (((upairequniteq) =>
% 102.63/17.21 (((setukpairinjR2) =>
% 102.63/17.21 (((setukpairinjR) =>
% 102.63/17.21 (((ksndsingleton) =>
% 102.63/17.21 (((ksndpairEq) =>
% 102.63/17.21 (((kpairsurjEq) =>
% 102.63/17.21 (((cartprodsndin) =>
% 102.63/17.21 (((cartprodpairmemEL) =>
% 102.63/17.21 (((cartprodpairmemER) =>
% 102.63/17.21 (((cartprodmempaircEq) =>
% 102.63/17.21 (((cartprodfstpairEq) =>
% 102.63/17.21 (((cartprodsndpairEq) =>
% 102.63/17.21 (((cartprodpairsurjEq) =>
% 102.63/17.21 (((dpsetconstrI) =>
% 102.63/17.21 (((dpsetconstrSub) =>
% 102.63/17.21 (((setOfPairsIsBReln) =>
% 102.63/17.21 (((dpsetconstrERa) =>
% 102.63/17.21 (((dpsetconstrEL1) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrEL2) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrER) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcImageSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (apProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (app) =>
% 102.63/17.21 ((
% 102.63/17.21 (infuncsetfunc) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcinfuncset) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall1) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ex1E2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp3) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcextLem) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp4) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq1) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq2) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2lamEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifp) =>
% 102.63/17.21 ((
% 102.63/17.21 (theeq) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrue) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueorfalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setminusT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setextT) =>
% 102.63/17.21 ((
% 102.63/17.21 (subsetTI) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTELcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTERcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT1) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT2) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT3) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub2) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTnotintersectT) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementImpComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementSubsetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementInPowersetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (contraSubsetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTcontraSubset) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTILcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTIRcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion2) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (intersectInPowersetIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpNotIn1) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpInComplement1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTE) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTEcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementUnionInPowersetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule0) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_5) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all2) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1SetBreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (choice2fnsingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (setOfPairsIsBReln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all1) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compEex) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIL) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIR) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionEcases) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionCommutes) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2W) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2A) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2B) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex1) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Equiv) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1E) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1I) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncInInjFuncSet) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncInj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (leftInvIsSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjCantorThm) =>
% 102.63/17.21 ((
% 102.63/17.21 (foundation2) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself2) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSp) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSclos) =>
% 102.63/17.21 ((
% 102.63/17.21 (peano0notS) =>
% 102.63/17.21 ((
% 102.63/17.21 (peanoSinj) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (setunionTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (ordinalMinLem1) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y0 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (ordinal @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y1 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y2 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y2 @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @
% 102.63/17.21 Y2) =>
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1321])).
% 102.63/17.21 thf(zip_derived_cl1336, plain,
% 102.63/17.21 (~ (((singletonsuniq) =>
% 102.63/17.21 (((setukpairinjL1) =>
% 102.63/17.21 (((kfstsingleton) =>
% 102.63/17.21 (((theprop) =>
% 102.63/17.21 (((kfstpairEq) =>
% 102.63/17.21 (((cartprodfstin) =>
% 102.63/17.21 (((setukpairinjL2) =>
% 102.63/17.21 (((setukpairinjL) =>
% 102.63/17.21 (((setukpairinjR11) =>
% 102.63/17.21 (((setukpairinjR12) =>
% 102.63/17.21 (((setukpairinjR1) =>
% 102.63/17.21 (((upairequniteq) =>
% 102.63/17.21 (((setukpairinjR2) =>
% 102.63/17.21 (((setukpairinjR) =>
% 102.63/17.21 (((ksndsingleton) =>
% 102.63/17.21 (((ksndpairEq) =>
% 102.63/17.21 (((kpairsurjEq) =>
% 102.63/17.21 (((cartprodsndin) =>
% 102.63/17.21 (((cartprodpairmemEL) =>
% 102.63/17.21 (((cartprodpairmemER) =>
% 102.63/17.21 (((cartprodmempaircEq) =>
% 102.63/17.21 (((cartprodfstpairEq) =>
% 102.63/17.21 (((cartprodsndpairEq) =>
% 102.63/17.21 (((cartprodpairsurjEq) =>
% 102.63/17.21 (((dpsetconstrI) =>
% 102.63/17.21 (((dpsetconstrSub) =>
% 102.63/17.21 (((setOfPairsIsBReln) =>
% 102.63/17.21 (((dpsetconstrERa) =>
% 102.63/17.21 (((dpsetconstrEL1) =>
% 102.63/17.21 (((dpsetconstrEL2) =>
% 102.63/17.21 ((
% 102.63/17.21 (dpsetconstrER) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcImageSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (apProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (app) =>
% 102.63/17.21 ((
% 102.63/17.21 (infuncsetfunc) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcinfuncset) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall1) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ex1E2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp3) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcextLem) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp4) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq1) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq2) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2lamEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifp) =>
% 102.63/17.21 ((
% 102.63/17.21 (theeq) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrue) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueorfalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setminusT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setextT) =>
% 102.63/17.21 ((
% 102.63/17.21 (subsetTI) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTELcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTERcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT1) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT2) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT3) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub2) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTnotintersectT) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementImpComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementSubsetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementInPowersetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (contraSubsetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTcontraSubset) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTILcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTIRcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion2) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (intersectInPowersetIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpNotIn1) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpInComplement1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTE) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTEcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementUnionInPowersetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule0) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_5) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all2) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1SetBreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (choice2fnsingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (setOfPairsIsBReln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all1) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compEex) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIL) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIR) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionEcases) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionCommutes) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2W) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2A) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2B) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex1) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Equiv) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1E) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1I) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncInInjFuncSet) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncInj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (leftInvIsSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjCantorThm) =>
% 102.63/17.21 ((
% 102.63/17.21 (foundation2) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself2) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSp) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSclos) =>
% 102.63/17.21 ((
% 102.63/17.21 (peano0notS) =>
% 102.63/17.21 ((
% 102.63/17.21 (peanoSinj) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (setunionTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (ordinalMinLem1) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y0 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (ordinal @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y1 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y2 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y2 @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @
% 102.63/17.21 Y2) =>
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1328])).
% 102.63/17.21 thf(zip_derived_cl1344, plain,
% 102.63/17.21 (~ (((setukpairinjL1) =>
% 102.63/17.21 (((kfstsingleton) =>
% 102.63/17.21 (((theprop) =>
% 102.63/17.21 (((kfstpairEq) =>
% 102.63/17.21 (((cartprodfstin) =>
% 102.63/17.21 (((setukpairinjL2) =>
% 102.63/17.21 (((setukpairinjL) =>
% 102.63/17.21 (((setukpairinjR11) =>
% 102.63/17.21 (((setukpairinjR12) =>
% 102.63/17.21 (((setukpairinjR1) =>
% 102.63/17.21 (((upairequniteq) =>
% 102.63/17.21 (((setukpairinjR2) =>
% 102.63/17.21 (((setukpairinjR) =>
% 102.63/17.21 (((ksndsingleton) =>
% 102.63/17.21 (((ksndpairEq) =>
% 102.63/17.21 (((kpairsurjEq) =>
% 102.63/17.21 (((cartprodsndin) =>
% 102.63/17.21 (((cartprodpairmemEL) =>
% 102.63/17.21 (((cartprodpairmemER) =>
% 102.63/17.21 (((cartprodmempaircEq) =>
% 102.63/17.21 (((cartprodfstpairEq) =>
% 102.63/17.21 (((cartprodsndpairEq) =>
% 102.63/17.21 (((cartprodpairsurjEq) =>
% 102.63/17.21 (((dpsetconstrI) =>
% 102.63/17.21 (((dpsetconstrSub) =>
% 102.63/17.21 (((setOfPairsIsBReln) =>
% 102.63/17.21 (((dpsetconstrERa) =>
% 102.63/17.21 (((dpsetconstrEL1) =>
% 102.63/17.21 (((dpsetconstrEL2) =>
% 102.63/17.21 (((dpsetconstrER) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcImageSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (apProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (app) =>
% 102.63/17.21 ((
% 102.63/17.21 (infuncsetfunc) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcinfuncset) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall1) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ex1E2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp3) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcextLem) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp4) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq1) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq2) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2lamEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifp) =>
% 102.63/17.21 ((
% 102.63/17.21 (theeq) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrue) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueorfalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setminusT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setextT) =>
% 102.63/17.21 ((
% 102.63/17.21 (subsetTI) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTELcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTERcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT1) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT2) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT3) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub2) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTnotintersectT) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementImpComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementSubsetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementInPowersetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (contraSubsetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTcontraSubset) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTILcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTIRcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion2) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (intersectInPowersetIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpNotIn1) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpInComplement1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTE) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTEcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementUnionInPowersetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule0) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_5) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all2) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1SetBreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (choice2fnsingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (setOfPairsIsBReln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all1) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compEex) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIL) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIR) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionEcases) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionCommutes) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2W) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2A) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2B) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex1) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Equiv) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1E) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1I) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncInInjFuncSet) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncInj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (leftInvIsSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjCantorThm) =>
% 102.63/17.21 ((
% 102.63/17.21 (foundation2) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself2) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSp) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSclos) =>
% 102.63/17.21 ((
% 102.63/17.21 (peano0notS) =>
% 102.63/17.21 ((
% 102.63/17.21 (peanoSinj) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (setunionTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (ordinalMinLem1) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y0 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (ordinal @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y1 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y2 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y2 @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @
% 102.63/17.21 Y2) =>
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1336])).
% 102.63/17.21 thf(zip_derived_cl1352, plain,
% 102.63/17.21 (~ (((kfstsingleton) =>
% 102.63/17.21 (((theprop) =>
% 102.63/17.21 (((kfstpairEq) =>
% 102.63/17.21 (((cartprodfstin) =>
% 102.63/17.21 (((setukpairinjL2) =>
% 102.63/17.21 (((setukpairinjL) =>
% 102.63/17.21 (((setukpairinjR11) =>
% 102.63/17.21 (((setukpairinjR12) =>
% 102.63/17.21 (((setukpairinjR1) =>
% 102.63/17.21 (((upairequniteq) =>
% 102.63/17.21 (((setukpairinjR2) =>
% 102.63/17.21 (((setukpairinjR) =>
% 102.63/17.21 (((ksndsingleton) =>
% 102.63/17.21 (((ksndpairEq) =>
% 102.63/17.21 (((kpairsurjEq) =>
% 102.63/17.21 (((cartprodsndin) =>
% 102.63/17.21 (((cartprodpairmemEL) =>
% 102.63/17.21 (((cartprodpairmemER) =>
% 102.63/17.21 (((cartprodmempaircEq) =>
% 102.63/17.21 (((cartprodfstpairEq) =>
% 102.63/17.21 (((cartprodsndpairEq) =>
% 102.63/17.21 (((cartprodpairsurjEq) =>
% 102.63/17.21 (((dpsetconstrI) =>
% 102.63/17.21 (((dpsetconstrSub) =>
% 102.63/17.21 (((setOfPairsIsBReln) =>
% 102.63/17.21 (((dpsetconstrERa) =>
% 102.63/17.21 (((dpsetconstrEL1) =>
% 102.63/17.21 (((dpsetconstrEL2) =>
% 102.63/17.21 (((dpsetconstrER) =>
% 102.63/17.21 (((funcImageSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (apProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (app) =>
% 102.63/17.21 ((
% 102.63/17.21 (infuncsetfunc) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcinfuncset) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall1) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ex1E2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp3) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcextLem) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp4) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq1) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq2) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta1) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2lamEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (beta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (eta2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalseProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifSingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (ifp) =>
% 102.63/17.21 ((
% 102.63/17.21 (theeq) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrue) =>
% 102.63/17.21 ((
% 102.63/17.21 (iffalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (iftrueorfalse) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setminusT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementT_lem) =>
% 102.63/17.21 ((
% 102.63/17.21 (setextT) =>
% 102.63/17.21 ((
% 102.63/17.21 (subsetTI) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (powersetTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTELcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintersectTERcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT1) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT2) =>
% 102.63/17.21 ((
% 102.63/17.21 (contrasubsetT3) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementI1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementE1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub1) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementSub2) =>
% 102.63/17.21 ((
% 102.63/17.21 (doubleComplementEq) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTnotintersectT) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementImpComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementSubsetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementInPowersetComplementIntersect) =>
% 102.63/17.21 ((
% 102.63/17.21 (contraSubsetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementTcontraSubset) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTILcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTIRcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInUnion2) =>
% 102.63/17.21 ((
% 102.63/17.21 (inIntersectImpInIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (intersectInPowersetIntersectUnions) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpNotIn1) =>
% 102.63/17.21 ((
% 102.63/17.21 (inComplementUnionImpInComplement1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTE) =>
% 102.63/17.21 ((
% 102.63/17.21 (binunionTEcontra) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a1) =>
% 102.63/17.21 ((
% 102.63/17.21 (complementUnionInPowersetComplement) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan1) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2a) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b2) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2b) =>
% 102.63/17.21 ((
% 102.63/17.21 (demorgan2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule0) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz13rule4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_1) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_2) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_3) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_4) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz1_5) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all2) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1SetBreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (choice2fnsingleton) =>
% 102.63/17.21 ((
% 102.63/17.21 (setOfPairsIsBReln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1all1) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln1) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1invE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1compEex) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionprop) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIL) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionIR) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionI) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionE) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionEcases) =>
% 102.63/17.21 ((
% 102.63/17.21 (breln1unionCommutes) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2W) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2A) =>
% 102.63/17.21 ((
% 102.63/17.21 (woz2B) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Ex1) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1Equiv) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1E) =>
% 102.63/17.21 ((
% 102.63/17.21 (image1I) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncInInjFuncSet) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (injFuncSetFuncInj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncIn) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjFuncSetFuncSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (leftInvIsSurj) =>
% 102.63/17.21 ((
% 102.63/17.21 (surjCantorThm) =>
% 102.63/17.21 ((
% 102.63/17.21 (foundation2) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself) =>
% 102.63/17.21 ((
% 102.63/17.21 (notinself2) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSp) =>
% 102.63/17.21 ((
% 102.63/17.21 (omegaSclos) =>
% 102.63/17.21 ((
% 102.63/17.21 (peano0notS) =>
% 102.63/17.21 ((
% 102.63/17.21 (peanoSinj) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (binintTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (transitivesetOp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (setunionTransitive) =>
% 102.63/17.21 ((
% 102.63/17.21 (ordinalMinLem1) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y0 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (ordinal @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y1 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (!!) @ (
% 102.63/17.21 ^[Y2 : $i]:
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y2 @
% 102.63/17.21 Y0) =>
% 102.63/17.21 ((
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @
% 102.63/17.21 Y2) =>
% 102.63/17.21 (in @
% 102.63/17.21 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1344])).
% 102.63/17.21 thf(zip_derived_cl1361, plain,
% 102.63/17.21 (~ (((theprop) =>
% 102.63/17.21 (((kfstpairEq) =>
% 102.63/17.21 (((cartprodfstin) =>
% 102.63/17.21 (((setukpairinjL2) =>
% 102.63/17.21 (((setukpairinjL) =>
% 102.63/17.21 (((setukpairinjR11) =>
% 102.63/17.21 (((setukpairinjR12) =>
% 102.63/17.21 (((setukpairinjR1) =>
% 102.63/17.21 (((upairequniteq) =>
% 102.63/17.21 (((setukpairinjR2) =>
% 102.63/17.21 (((setukpairinjR) =>
% 102.63/17.21 (((ksndsingleton) =>
% 102.63/17.21 (((ksndpairEq) =>
% 102.63/17.21 (((kpairsurjEq) =>
% 102.63/17.21 (((cartprodsndin) =>
% 102.63/17.21 (((cartprodpairmemEL) =>
% 102.63/17.21 (((cartprodpairmemER) =>
% 102.63/17.21 (((cartprodmempaircEq) =>
% 102.63/17.21 (((cartprodfstpairEq) =>
% 102.63/17.21 (((cartprodsndpairEq) =>
% 102.63/17.21 (((cartprodpairsurjEq) =>
% 102.63/17.21 (((dpsetconstrI) =>
% 102.63/17.21 (((dpsetconstrSub) =>
% 102.63/17.21 (((setOfPairsIsBReln) =>
% 102.63/17.21 (((dpsetconstrERa) =>
% 102.63/17.21 (((dpsetconstrEL1) =>
% 102.63/17.21 (((dpsetconstrEL2) =>
% 102.63/17.21 (((dpsetconstrER) =>
% 102.63/17.21 (((funcImageSingleton) =>
% 102.63/17.21 (((apProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (app) =>
% 102.63/17.21 ((
% 102.63/17.21 (infuncsetfunc) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcinfuncset) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamProp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lamp) =>
% 102.63/17.21 ((
% 102.63/17.21 (lam2p) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall1) =>
% 102.63/17.21 ((
% 102.63/17.21 (brelnall2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ex1E2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp1) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp3) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp2) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcextLem) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcGraphProp4) =>
% 102.63/17.21 ((
% 102.63/17.21 (subbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (eqbreln) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext) =>
% 102.63/17.21 ((
% 102.63/17.21 (funcext2) =>
% 102.63/17.21 ((
% 102.63/17.21 (ap2apEq1) =>
% 102.63/17.21 ((
% 102.63/17.22 (ap2apEq2) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2lamEq) =>
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% 102.63/17.22 (beta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta2) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp2) =>
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% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (powersetTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTELcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTERcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT) =>
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% 102.63/17.22 (contrasubsetT2) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT3) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub2) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementEq) =>
% 102.63/17.22 ((
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% 102.63/17.22 (complementImpComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementSubsetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementInPowersetComplementIntersect) =>
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% 102.63/17.22 (contraSubsetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTcontraSubset) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTILcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTIRcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion2) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (intersectInPowersetIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpNotIn1) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpInComplement1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTE) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTEcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementUnionInPowersetComplement) =>
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% 102.63/17.22 (demorgan1a) =>
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% 102.63/17.22 (demorgan1b) =>
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% 102.63/17.22 (demorgan1) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule0) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_5) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all2) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1SetBreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (choice2fnsingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (setOfPairsIsBReln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all1) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compEex) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIL) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIR) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionEcases) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionCommutes) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2W) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2A) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2B) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex1) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Equiv) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1E) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1I) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncInInjFuncSet) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncInj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (leftInvIsSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjCantorThm) =>
% 102.63/17.22 ((
% 102.63/17.22 (foundation2) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself2) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSp) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSclos) =>
% 102.63/17.22 ((
% 102.63/17.22 (peano0notS) =>
% 102.63/17.22 ((
% 102.63/17.22 (peanoSinj) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (setunionTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (ordinalMinLem1) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y0 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (ordinal @
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% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y1 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y2 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y2 @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @
% 102.63/17.22 Y2) =>
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1352])).
% 102.63/17.22 thf(zip_derived_cl1371, plain,
% 102.63/17.22 (~ (((kfstpairEq) =>
% 102.63/17.22 (((cartprodfstin) =>
% 102.63/17.22 (((setukpairinjL2) =>
% 102.63/17.22 (((setukpairinjL) =>
% 102.63/17.22 (((setukpairinjR11) =>
% 102.63/17.22 (((setukpairinjR12) =>
% 102.63/17.22 (((setukpairinjR1) =>
% 102.63/17.22 (((upairequniteq) =>
% 102.63/17.22 (((setukpairinjR2) =>
% 102.63/17.22 (((setukpairinjR) =>
% 102.63/17.22 (((ksndsingleton) =>
% 102.63/17.22 (((ksndpairEq) =>
% 102.63/17.22 (((kpairsurjEq) =>
% 102.63/17.22 (((cartprodsndin) =>
% 102.63/17.22 (((cartprodpairmemEL) =>
% 102.63/17.22 (((cartprodpairmemER) =>
% 102.63/17.22 (((cartprodmempaircEq) =>
% 102.63/17.22 (((cartprodfstpairEq) =>
% 102.63/17.22 (((cartprodsndpairEq) =>
% 102.63/17.22 (((cartprodpairsurjEq) =>
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% 102.63/17.22 (((dpsetconstrSub) =>
% 102.63/17.22 (((setOfPairsIsBReln) =>
% 102.63/17.22 (((dpsetconstrERa) =>
% 102.63/17.22 (((dpsetconstrEL1) =>
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% 102.63/17.22 (((dpsetconstrER) =>
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% 102.63/17.22 (((apProp) =>
% 102.63/17.22 (((app) =>
% 102.63/17.22 ((
% 102.63/17.22 (infuncsetfunc) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2p) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcinfuncset) =>
% 102.63/17.22 ((
% 102.63/17.22 (lamProp) =>
% 102.63/17.22 ((
% 102.63/17.22 (lamp) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2p) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall1) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ex1E2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp3) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcextLem) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp4) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext2) =>
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% 102.63/17.22 (eta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2lamEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta2) =>
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% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp2) =>
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% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp2) =>
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% 102.63/17.22 (ifSingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifp) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (iftrue) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
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% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (setextT) =>
% 102.63/17.22 ((
% 102.63/17.22 (subsetTI) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTE1) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (complementTE1) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (binintersectTERcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT1) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT2) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT3) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub2) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTnotintersectT) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementImpComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementSubsetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementInPowersetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (contraSubsetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTcontraSubset) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTILcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTIRcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion2) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (intersectInPowersetIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpNotIn1) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpInComplement1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTE) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTEcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementUnionInPowersetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule0) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule4) =>
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% 102.63/17.22 ((
% 102.63/17.22 (woz1_2) =>
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% 102.63/17.22 (woz1_3) =>
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% 102.63/17.22 (woz1_4) =>
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% 102.63/17.22 (woz1_5) =>
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% 102.63/17.22 (breln1all2) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1SetBreln1) =>
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% 102.63/17.22 (choice2fnsingleton) =>
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% 102.63/17.22 ((
% 102.63/17.22 (breln1all1) =>
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% 102.63/17.22 ((
% 102.63/17.22 (breln1invE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compEex) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIL) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIR) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionEcases) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionCommutes) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2W) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (image1Equiv) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1E) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1I) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncInInjFuncSet) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (leftInvIsSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjCantorThm) =>
% 102.63/17.22 ((
% 102.63/17.22 (foundation2) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself2) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSp) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSclos) =>
% 102.63/17.22 ((
% 102.63/17.22 (peano0notS) =>
% 102.63/17.22 ((
% 102.63/17.22 (peanoSinj) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (setunionTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (ordinalMinLem1) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y0 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (ordinal @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y1 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y2 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y2 @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @
% 102.63/17.22 Y2) =>
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])).
% 102.63/17.22 thf(zip_derived_cl1382, plain,
% 102.63/17.22 (~ (((cartprodfstin) =>
% 102.63/17.22 (((setukpairinjL2) =>
% 102.63/17.22 (((setukpairinjL) =>
% 102.63/17.22 (((setukpairinjR11) =>
% 102.63/17.22 (((setukpairinjR12) =>
% 102.63/17.22 (((setukpairinjR1) =>
% 102.63/17.22 (((upairequniteq) =>
% 102.63/17.22 (((setukpairinjR2) =>
% 102.63/17.22 (((setukpairinjR) =>
% 102.63/17.22 (((ksndsingleton) =>
% 102.63/17.22 (((ksndpairEq) =>
% 102.63/17.22 (((kpairsurjEq) =>
% 102.63/17.22 (((cartprodsndin) =>
% 102.63/17.22 (((cartprodpairmemEL) =>
% 102.63/17.22 (((cartprodpairmemER) =>
% 102.63/17.22 (((cartprodmempaircEq) =>
% 102.63/17.22 (((cartprodfstpairEq) =>
% 102.63/17.22 (((cartprodsndpairEq) =>
% 102.63/17.22 (((cartprodpairsurjEq) =>
% 102.63/17.22 (((dpsetconstrI) =>
% 102.63/17.22 (((dpsetconstrSub) =>
% 102.63/17.22 (((setOfPairsIsBReln) =>
% 102.63/17.22 (((dpsetconstrERa) =>
% 102.63/17.22 (((dpsetconstrEL1) =>
% 102.63/17.22 (((dpsetconstrEL2) =>
% 102.63/17.22 (((dpsetconstrER) =>
% 102.63/17.22 (((funcImageSingleton) =>
% 102.63/17.22 (((apProp) =>
% 102.63/17.22 (((app) =>
% 102.63/17.22 (((infuncsetfunc) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2p) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcinfuncset) =>
% 102.63/17.22 ((
% 102.63/17.22 (lamProp) =>
% 102.63/17.22 ((
% 102.63/17.22 (lamp) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2p) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall1) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ex1E2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp3) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcextLem) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp4) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq1) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq2) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2lamEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifSingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifp) =>
% 102.63/17.22 ((
% 102.63/17.22 (theeq) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrue) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueorfalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setminusT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setextT) =>
% 102.63/17.22 ((
% 102.63/17.22 (subsetTI) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTELcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTERcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT1) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT2) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT3) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub2) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTnotintersectT) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementImpComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementSubsetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementInPowersetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (contraSubsetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTcontraSubset) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTILcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTIRcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion2) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (intersectInPowersetIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpNotIn1) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpInComplement1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTE) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTEcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementUnionInPowersetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule0) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_5) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all2) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1SetBreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (choice2fnsingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (setOfPairsIsBReln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all1) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compEex) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIL) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIR) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionEcases) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionCommutes) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2W) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2A) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2B) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex1) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Equiv) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1E) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1I) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncInInjFuncSet) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncInj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (leftInvIsSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjCantorThm) =>
% 102.63/17.22 ((
% 102.63/17.22 (foundation2) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself2) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSp) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSclos) =>
% 102.63/17.22 ((
% 102.63/17.22 (peano0notS) =>
% 102.63/17.22 ((
% 102.63/17.22 (peanoSinj) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (setunionTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (ordinalMinLem1) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y0 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (ordinal @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y1 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y2 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y2 @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @
% 102.63/17.22 Y2) =>
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1371])).
% 102.63/17.22 thf(zip_derived_cl1396, plain,
% 102.63/17.22 (~ (((setukpairinjL2) =>
% 102.63/17.22 (((setukpairinjL) =>
% 102.63/17.22 (((setukpairinjR11) =>
% 102.63/17.22 (((setukpairinjR12) =>
% 102.63/17.22 (((setukpairinjR1) =>
% 102.63/17.22 (((upairequniteq) =>
% 102.63/17.22 (((setukpairinjR2) =>
% 102.63/17.22 (((setukpairinjR) =>
% 102.63/17.22 (((ksndsingleton) =>
% 102.63/17.22 (((ksndpairEq) =>
% 102.63/17.22 (((kpairsurjEq) =>
% 102.63/17.22 (((cartprodsndin) =>
% 102.63/17.22 (((cartprodpairmemEL) =>
% 102.63/17.22 (((cartprodpairmemER) =>
% 102.63/17.22 (((cartprodmempaircEq) =>
% 102.63/17.22 (((cartprodfstpairEq) =>
% 102.63/17.22 (((cartprodsndpairEq) =>
% 102.63/17.22 (((cartprodpairsurjEq) =>
% 102.63/17.22 (((dpsetconstrI) =>
% 102.63/17.22 (((dpsetconstrSub) =>
% 102.63/17.22 (((setOfPairsIsBReln) =>
% 102.63/17.22 (((dpsetconstrERa) =>
% 102.63/17.22 (((dpsetconstrEL1) =>
% 102.63/17.22 (((dpsetconstrEL2) =>
% 102.63/17.22 (((dpsetconstrER) =>
% 102.63/17.22 (((funcImageSingleton) =>
% 102.63/17.22 (((apProp) =>
% 102.63/17.22 (((app) =>
% 102.63/17.22 (((infuncsetfunc) =>
% 102.63/17.22 (((ap2p) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcinfuncset) =>
% 102.63/17.22 ((
% 102.63/17.22 (lamProp) =>
% 102.63/17.22 ((
% 102.63/17.22 (lamp) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2p) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall1) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ex1E2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp3) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcextLem) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp4) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq1) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq2) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2lamEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifSingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifp) =>
% 102.63/17.22 ((
% 102.63/17.22 (theeq) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrue) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueorfalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setminusT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setextT) =>
% 102.63/17.22 ((
% 102.63/17.22 (subsetTI) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTELcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTERcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT1) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT2) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT3) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub2) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTnotintersectT) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementImpComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementSubsetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementInPowersetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (contraSubsetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTcontraSubset) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTILcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTIRcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion2) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (intersectInPowersetIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpNotIn1) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpInComplement1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTE) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTEcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementUnionInPowersetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule0) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_5) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all2) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1SetBreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (choice2fnsingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (setOfPairsIsBReln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all1) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compEex) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIL) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIR) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionEcases) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionCommutes) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2W) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2A) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2B) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex1) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Equiv) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1E) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1I) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncInInjFuncSet) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncInj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (leftInvIsSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjCantorThm) =>
% 102.63/17.22 ((
% 102.63/17.22 (foundation2) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself2) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSp) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSclos) =>
% 102.63/17.22 ((
% 102.63/17.22 (peano0notS) =>
% 102.63/17.22 ((
% 102.63/17.22 (peanoSinj) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (setunionTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (ordinalMinLem1) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y0 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (ordinal @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y1 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y2 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y2 @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @
% 102.63/17.22 Y2) =>
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1382])).
% 102.63/17.22 thf(zip_derived_cl1409, plain,
% 102.63/17.22 (~ (((setukpairinjL) =>
% 102.63/17.22 (((setukpairinjR11) =>
% 102.63/17.22 (((setukpairinjR12) =>
% 102.63/17.22 (((setukpairinjR1) =>
% 102.63/17.22 (((upairequniteq) =>
% 102.63/17.22 (((setukpairinjR2) =>
% 102.63/17.22 (((setukpairinjR) =>
% 102.63/17.22 (((ksndsingleton) =>
% 102.63/17.22 (((ksndpairEq) =>
% 102.63/17.22 (((kpairsurjEq) =>
% 102.63/17.22 (((cartprodsndin) =>
% 102.63/17.22 (((cartprodpairmemEL) =>
% 102.63/17.22 (((cartprodpairmemER) =>
% 102.63/17.22 (((cartprodmempaircEq) =>
% 102.63/17.22 (((cartprodfstpairEq) =>
% 102.63/17.22 (((cartprodsndpairEq) =>
% 102.63/17.22 (((cartprodpairsurjEq) =>
% 102.63/17.22 (((dpsetconstrI) =>
% 102.63/17.22 (((dpsetconstrSub) =>
% 102.63/17.22 (((setOfPairsIsBReln) =>
% 102.63/17.22 (((dpsetconstrERa) =>
% 102.63/17.22 (((dpsetconstrEL1) =>
% 102.63/17.22 (((dpsetconstrEL2) =>
% 102.63/17.22 (((dpsetconstrER) =>
% 102.63/17.22 (((funcImageSingleton) =>
% 102.63/17.22 (((apProp) =>
% 102.63/17.22 (((app) =>
% 102.63/17.22 (((infuncsetfunc) =>
% 102.63/17.22 (((ap2p) =>
% 102.63/17.22 (((funcinfuncset) =>
% 102.63/17.22 ((
% 102.63/17.22 (lamProp) =>
% 102.63/17.22 ((
% 102.63/17.22 (lamp) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2p) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall1) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ex1E2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp3) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcextLem) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp4) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq1) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq2) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2lamEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifSingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifp) =>
% 102.63/17.22 ((
% 102.63/17.22 (theeq) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrue) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueorfalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setminusT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setextT) =>
% 102.63/17.22 ((
% 102.63/17.22 (subsetTI) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTELcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTERcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT1) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT2) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT3) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub2) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTnotintersectT) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementImpComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementSubsetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementInPowersetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (contraSubsetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTcontraSubset) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTILcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTIRcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion2) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (intersectInPowersetIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpNotIn1) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpInComplement1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTE) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTEcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementUnionInPowersetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule0) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_5) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all2) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1SetBreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (choice2fnsingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (setOfPairsIsBReln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all1) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compEex) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIL) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIR) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionEcases) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionCommutes) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2W) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2A) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2B) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex1) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Equiv) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1E) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1I) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncInInjFuncSet) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncInj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (leftInvIsSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjCantorThm) =>
% 102.63/17.22 ((
% 102.63/17.22 (foundation2) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself2) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSp) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSclos) =>
% 102.63/17.22 ((
% 102.63/17.22 (peano0notS) =>
% 102.63/17.22 ((
% 102.63/17.22 (peanoSinj) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (setunionTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (ordinalMinLem1) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y0 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (ordinal @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y1 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y2 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y2 @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @
% 102.63/17.22 Y2) =>
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
% 102.63/17.22 thf(zip_derived_cl1425, plain,
% 102.63/17.22 (~ (((setukpairinjR11) =>
% 102.63/17.22 (((setukpairinjR12) =>
% 102.63/17.22 (((setukpairinjR1) =>
% 102.63/17.22 (((upairequniteq) =>
% 102.63/17.22 (((setukpairinjR2) =>
% 102.63/17.22 (((setukpairinjR) =>
% 102.63/17.22 (((ksndsingleton) =>
% 102.63/17.22 (((ksndpairEq) =>
% 102.63/17.22 (((kpairsurjEq) =>
% 102.63/17.22 (((cartprodsndin) =>
% 102.63/17.22 (((cartprodpairmemEL) =>
% 102.63/17.22 (((cartprodpairmemER) =>
% 102.63/17.22 (((cartprodmempaircEq) =>
% 102.63/17.22 (((cartprodfstpairEq) =>
% 102.63/17.22 (((cartprodsndpairEq) =>
% 102.63/17.22 (((cartprodpairsurjEq) =>
% 102.63/17.22 (((dpsetconstrI) =>
% 102.63/17.22 (((dpsetconstrSub) =>
% 102.63/17.22 (((setOfPairsIsBReln) =>
% 102.63/17.22 (((dpsetconstrERa) =>
% 102.63/17.22 (((dpsetconstrEL1) =>
% 102.63/17.22 (((dpsetconstrEL2) =>
% 102.63/17.22 (((dpsetconstrER) =>
% 102.63/17.22 (((funcImageSingleton) =>
% 102.63/17.22 (((apProp) =>
% 102.63/17.22 (((app) =>
% 102.63/17.22 (((infuncsetfunc) =>
% 102.63/17.22 (((ap2p) =>
% 102.63/17.22 (((funcinfuncset) =>
% 102.63/17.22 (((lamProp) =>
% 102.63/17.22 ((
% 102.63/17.22 (lamp) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2p) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall1) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ex1E2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp3) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcextLem) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp4) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq1) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq2) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2lamEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifSingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifp) =>
% 102.63/17.22 ((
% 102.63/17.22 (theeq) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrue) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueorfalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionT_lem) =>
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% 102.63/17.22 (powersetT_lem) =>
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% 102.63/17.22 ((
% 102.63/17.22 (complementT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setextT) =>
% 102.63/17.22 ((
% 102.63/17.22 (subsetTI) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTELcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTERcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT1) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT2) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT3) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub2) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTnotintersectT) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementImpComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementSubsetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementInPowersetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (contraSubsetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTcontraSubset) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTILcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTIRcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion2) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (intersectInPowersetIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpNotIn1) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpInComplement1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTE) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTEcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementUnionInPowersetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule0) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_5) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all2) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1SetBreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (choice2fnsingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (setOfPairsIsBReln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all1) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compEex) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIL) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIR) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionEcases) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionCommutes) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2W) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2A) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2B) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex1) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Equiv) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1E) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1I) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncInInjFuncSet) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncInj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (leftInvIsSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjCantorThm) =>
% 102.63/17.22 ((
% 102.63/17.22 (foundation2) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself2) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSp) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSclos) =>
% 102.63/17.22 ((
% 102.63/17.22 (peano0notS) =>
% 102.63/17.22 ((
% 102.63/17.22 (peanoSinj) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (setunionTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (ordinalMinLem1) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y0 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (ordinal @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y1 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y2 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y2 @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @
% 102.63/17.22 Y2) =>
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1409])).
% 102.63/17.22 thf(zip_derived_cl1440, plain,
% 102.63/17.22 (~ (((setukpairinjR12) =>
% 102.63/17.22 (((setukpairinjR1) =>
% 102.63/17.22 (((upairequniteq) =>
% 102.63/17.22 (((setukpairinjR2) =>
% 102.63/17.22 (((setukpairinjR) =>
% 102.63/17.22 (((ksndsingleton) =>
% 102.63/17.22 (((ksndpairEq) =>
% 102.63/17.22 (((kpairsurjEq) =>
% 102.63/17.22 (((cartprodsndin) =>
% 102.63/17.22 (((cartprodpairmemEL) =>
% 102.63/17.22 (((cartprodpairmemER) =>
% 102.63/17.22 (((cartprodmempaircEq) =>
% 102.63/17.22 (((cartprodfstpairEq) =>
% 102.63/17.22 (((cartprodsndpairEq) =>
% 102.63/17.22 (((cartprodpairsurjEq) =>
% 102.63/17.22 (((dpsetconstrI) =>
% 102.63/17.22 (((dpsetconstrSub) =>
% 102.63/17.22 (((setOfPairsIsBReln) =>
% 102.63/17.22 (((dpsetconstrERa) =>
% 102.63/17.22 (((dpsetconstrEL1) =>
% 102.63/17.22 (((dpsetconstrEL2) =>
% 102.63/17.22 (((dpsetconstrER) =>
% 102.63/17.22 (((funcImageSingleton) =>
% 102.63/17.22 (((apProp) =>
% 102.63/17.22 (((app) =>
% 102.63/17.22 (((infuncsetfunc) =>
% 102.63/17.22 (((ap2p) =>
% 102.63/17.22 (((funcinfuncset) =>
% 102.63/17.22 (((lamProp) =>
% 102.63/17.22 (((lamp) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2p) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall1) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ex1E2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp3) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcextLem) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp4) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq1) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq2) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2lamEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifSingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifp) =>
% 102.63/17.22 ((
% 102.63/17.22 (theeq) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrue) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueorfalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setminusT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setextT) =>
% 102.63/17.22 ((
% 102.63/17.22 (subsetTI) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTELcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTERcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT1) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT2) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT3) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub2) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTnotintersectT) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementImpComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementSubsetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementInPowersetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (contraSubsetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTcontraSubset) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTILcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTIRcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion2) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (intersectInPowersetIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpNotIn1) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpInComplement1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTE) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTEcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementUnionInPowersetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule0) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_5) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all2) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1SetBreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (choice2fnsingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (setOfPairsIsBReln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all1) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compEex) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIL) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIR) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionEcases) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionCommutes) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2W) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2A) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2B) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex1) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Equiv) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1E) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1I) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncInInjFuncSet) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncInj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (leftInvIsSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjCantorThm) =>
% 102.63/17.22 ((
% 102.63/17.22 (foundation2) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself2) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSp) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSclos) =>
% 102.63/17.22 ((
% 102.63/17.22 (peano0notS) =>
% 102.63/17.22 ((
% 102.63/17.22 (peanoSinj) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (setunionTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (ordinalMinLem1) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y0 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (ordinal @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y1 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y2 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y2 @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @
% 102.63/17.22 Y2) =>
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1425])).
% 102.63/17.22 thf(zip_derived_cl1453, plain,
% 102.63/17.22 (~ (((setukpairinjR1) =>
% 102.63/17.22 (((upairequniteq) =>
% 102.63/17.22 (((setukpairinjR2) =>
% 102.63/17.22 (((setukpairinjR) =>
% 102.63/17.22 (((ksndsingleton) =>
% 102.63/17.22 (((ksndpairEq) =>
% 102.63/17.22 (((kpairsurjEq) =>
% 102.63/17.22 (((cartprodsndin) =>
% 102.63/17.22 (((cartprodpairmemEL) =>
% 102.63/17.22 (((cartprodpairmemER) =>
% 102.63/17.22 (((cartprodmempaircEq) =>
% 102.63/17.22 (((cartprodfstpairEq) =>
% 102.63/17.22 (((cartprodsndpairEq) =>
% 102.63/17.22 (((cartprodpairsurjEq) =>
% 102.63/17.22 (((dpsetconstrI) =>
% 102.63/17.22 (((dpsetconstrSub) =>
% 102.63/17.22 (((setOfPairsIsBReln) =>
% 102.63/17.22 (((dpsetconstrERa) =>
% 102.63/17.22 (((dpsetconstrEL1) =>
% 102.63/17.22 (((dpsetconstrEL2) =>
% 102.63/17.22 (((dpsetconstrER) =>
% 102.63/17.22 (((funcImageSingleton) =>
% 102.63/17.22 (((apProp) =>
% 102.63/17.22 (((app) =>
% 102.63/17.22 (((infuncsetfunc) =>
% 102.63/17.22 (((ap2p) =>
% 102.63/17.22 (((funcinfuncset) =>
% 102.63/17.22 (((lamProp) =>
% 102.63/17.22 (((lamp) =>
% 102.63/17.22 (((lam2p) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall1) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ex1E2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp3) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcextLem) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp4) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq1) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq2) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2lamEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifSingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifp) =>
% 102.63/17.22 ((
% 102.63/17.22 (theeq) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrue) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueorfalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setminusT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setextT) =>
% 102.63/17.22 ((
% 102.63/17.22 (subsetTI) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTELcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTERcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT1) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT2) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT3) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub2) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTnotintersectT) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementImpComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementSubsetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementInPowersetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (contraSubsetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTcontraSubset) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTILcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTIRcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion2) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (intersectInPowersetIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpNotIn1) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpInComplement1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTE) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTEcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementUnionInPowersetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule0) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_5) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all2) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1SetBreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (choice2fnsingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (setOfPairsIsBReln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all1) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compEex) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIL) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIR) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionEcases) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionCommutes) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2W) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2A) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2B) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex1) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Equiv) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1E) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1I) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncInInjFuncSet) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncInj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (leftInvIsSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjCantorThm) =>
% 102.63/17.22 ((
% 102.63/17.22 (foundation2) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself2) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSp) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSclos) =>
% 102.63/17.22 ((
% 102.63/17.22 (peano0notS) =>
% 102.63/17.22 ((
% 102.63/17.22 (peanoSinj) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (setunionTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (ordinalMinLem1) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y0 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (ordinal @
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% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y1 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y2 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y2 @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @
% 102.63/17.22 Y2) =>
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1440])).
% 102.63/17.22 thf(zip_derived_cl1465, plain,
% 102.63/17.22 (~ (((upairequniteq) =>
% 102.63/17.22 (((setukpairinjR2) =>
% 102.63/17.22 (((setukpairinjR) =>
% 102.63/17.22 (((ksndsingleton) =>
% 102.63/17.22 (((ksndpairEq) =>
% 102.63/17.22 (((kpairsurjEq) =>
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% 102.63/17.22 (((cartprodpairmemEL) =>
% 102.63/17.22 (((cartprodpairmemER) =>
% 102.63/17.22 (((cartprodmempaircEq) =>
% 102.63/17.22 (((cartprodfstpairEq) =>
% 102.63/17.22 (((cartprodsndpairEq) =>
% 102.63/17.22 (((cartprodpairsurjEq) =>
% 102.63/17.22 (((dpsetconstrI) =>
% 102.63/17.22 (((dpsetconstrSub) =>
% 102.63/17.22 (((setOfPairsIsBReln) =>
% 102.63/17.22 (((dpsetconstrERa) =>
% 102.63/17.22 (((dpsetconstrEL1) =>
% 102.63/17.22 (((dpsetconstrEL2) =>
% 102.63/17.22 (((dpsetconstrER) =>
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% 102.63/17.22 (((apProp) =>
% 102.63/17.22 (((app) =>
% 102.63/17.22 (((infuncsetfunc) =>
% 102.63/17.22 (((ap2p) =>
% 102.63/17.22 (((funcinfuncset) =>
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% 102.63/17.22 (((lamp) =>
% 102.63/17.22 (((lam2p) =>
% 102.63/17.22 (((brelnall1) =>
% 102.63/17.22 ((
% 102.63/17.22 (brelnall2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ex1E2) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp3) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcextLem) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp4) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (funcext2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq1) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq2) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2lamEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta2) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp2) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
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% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (theeq) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (iffalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueorfalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setminusT_lem) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (setextT) =>
% 102.63/17.22 ((
% 102.63/17.22 (subsetTI) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTE1) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT1) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT2) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT3) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub2) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTnotintersectT) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementImpComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementSubsetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementInPowersetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (contraSubsetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTcontraSubset) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTILcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTIRcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion2) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (intersectInPowersetIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpNotIn1) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpInComplement1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTE) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTEcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementUnionInPowersetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule0) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_5) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all2) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1SetBreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (choice2fnsingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (setOfPairsIsBReln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all1) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compEex) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIL) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIR) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionEcases) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionCommutes) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2W) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2A) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2B) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex1) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Equiv) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1E) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1I) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncInInjFuncSet) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncInj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (leftInvIsSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjCantorThm) =>
% 102.63/17.22 ((
% 102.63/17.22 (foundation2) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself2) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSp) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSclos) =>
% 102.63/17.22 ((
% 102.63/17.22 (peano0notS) =>
% 102.63/17.22 ((
% 102.63/17.22 (peanoSinj) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (setunionTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (ordinalMinLem1) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y0 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (ordinal @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y1 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y2 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y2 @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @
% 102.63/17.22 Y2) =>
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1453])).
% 102.63/17.22 thf(zip_derived_cl1475, plain,
% 102.63/17.22 (~ (((setukpairinjR2) =>
% 102.63/17.22 (((setukpairinjR) =>
% 102.63/17.22 (((ksndsingleton) =>
% 102.63/17.22 (((ksndpairEq) =>
% 102.63/17.22 (((kpairsurjEq) =>
% 102.63/17.22 (((cartprodsndin) =>
% 102.63/17.22 (((cartprodpairmemEL) =>
% 102.63/17.22 (((cartprodpairmemER) =>
% 102.63/17.22 (((cartprodmempaircEq) =>
% 102.63/17.22 (((cartprodfstpairEq) =>
% 102.63/17.22 (((cartprodsndpairEq) =>
% 102.63/17.22 (((cartprodpairsurjEq) =>
% 102.63/17.22 (((dpsetconstrI) =>
% 102.63/17.22 (((dpsetconstrSub) =>
% 102.63/17.22 (((setOfPairsIsBReln) =>
% 102.63/17.22 (((dpsetconstrERa) =>
% 102.63/17.22 (((dpsetconstrEL1) =>
% 102.63/17.22 (((dpsetconstrEL2) =>
% 102.63/17.22 (((dpsetconstrER) =>
% 102.63/17.22 (((funcImageSingleton) =>
% 102.63/17.22 (((apProp) =>
% 102.63/17.22 (((app) =>
% 102.63/17.22 (((infuncsetfunc) =>
% 102.63/17.22 (((ap2p) =>
% 102.63/17.22 (((funcinfuncset) =>
% 102.63/17.22 (((lamProp) =>
% 102.63/17.22 (((lamp) =>
% 102.63/17.22 (((lam2p) =>
% 102.63/17.22 (((brelnall1) =>
% 102.63/17.22 (((brelnall2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ex1E2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp3) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcextLem) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp4) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq1) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq2) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2lamEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifSingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifp) =>
% 102.63/17.22 ((
% 102.63/17.22 (theeq) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrue) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueorfalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setminusT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementT_lem) =>
% 102.63/17.22 ((
% 102.63/17.22 (setextT) =>
% 102.63/17.22 ((
% 102.63/17.22 (subsetTI) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (powersetTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTELcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTERcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT1) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT2) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT3) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub2) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTnotintersectT) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementImpComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementSubsetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementInPowersetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (contraSubsetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTcontraSubset) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTILcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTIRcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion2) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (intersectInPowersetIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpNotIn1) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpInComplement1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTE) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTEcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementUnionInPowersetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule0) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_5) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all2) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1SetBreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (choice2fnsingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (setOfPairsIsBReln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all1) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compEex) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIL) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIR) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionEcases) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionCommutes) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2W) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2A) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2B) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex1) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Equiv) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1E) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1I) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncInInjFuncSet) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncInj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (leftInvIsSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjCantorThm) =>
% 102.63/17.22 ((
% 102.63/17.22 (foundation2) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself2) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSp) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSclos) =>
% 102.63/17.22 ((
% 102.63/17.22 (peano0notS) =>
% 102.63/17.22 ((
% 102.63/17.22 (peanoSinj) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (setunionTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (ordinalMinLem1) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y0 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (ordinal @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y1 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y2 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y2 @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @
% 102.63/17.22 Y2) =>
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1465])).
% 102.63/17.22 thf(zip_derived_cl1485, plain,
% 102.63/17.22 (~ (((setukpairinjR) =>
% 102.63/17.22 (((ksndsingleton) =>
% 102.63/17.22 (((ksndpairEq) =>
% 102.63/17.22 (((kpairsurjEq) =>
% 102.63/17.22 (((cartprodsndin) =>
% 102.63/17.22 (((cartprodpairmemEL) =>
% 102.63/17.22 (((cartprodpairmemER) =>
% 102.63/17.22 (((cartprodmempaircEq) =>
% 102.63/17.22 (((cartprodfstpairEq) =>
% 102.63/17.22 (((cartprodsndpairEq) =>
% 102.63/17.22 (((cartprodpairsurjEq) =>
% 102.63/17.22 (((dpsetconstrI) =>
% 102.63/17.22 (((dpsetconstrSub) =>
% 102.63/17.22 (((setOfPairsIsBReln) =>
% 102.63/17.22 (((dpsetconstrERa) =>
% 102.63/17.22 (((dpsetconstrEL1) =>
% 102.63/17.22 (((dpsetconstrEL2) =>
% 102.63/17.22 (((dpsetconstrER) =>
% 102.63/17.22 (((funcImageSingleton) =>
% 102.63/17.22 (((apProp) =>
% 102.63/17.22 (((app) =>
% 102.63/17.22 (((infuncsetfunc) =>
% 102.63/17.22 (((ap2p) =>
% 102.63/17.22 (((funcinfuncset) =>
% 102.63/17.22 (((lamProp) =>
% 102.63/17.22 (((lamp) =>
% 102.63/17.22 (((lam2p) =>
% 102.63/17.22 (((brelnall1) =>
% 102.63/17.22 (((brelnall2) =>
% 102.63/17.22 (((ex1E2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp3) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcextLem) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcGraphProp4) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext) =>
% 102.63/17.22 ((
% 102.63/17.22 (funcext2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq1) =>
% 102.63/17.22 ((
% 102.63/17.22 (ap2apEq2) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta1) =>
% 102.63/17.22 ((
% 102.63/17.22 (lam2lamEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (beta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (eta2) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalseProp2) =>
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% 102.63/17.22 (iftrueProp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueProp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifSingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (ifp) =>
% 102.63/17.22 ((
% 102.63/17.22 (theeq) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrue) =>
% 102.63/17.22 ((
% 102.63/17.22 (iffalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (iftrueorfalse) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectT_lem) =>
% 102.63/17.22 ((
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% 102.63/17.22 (powersetT_lem) =>
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% 102.63/17.22 ((
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% 102.63/17.22 ((
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% 102.63/17.22 (subsetTI) =>
% 102.63/17.22 ((
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% 102.63/17.22 ((
% 102.63/17.22 (powersetTE1) =>
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% 102.63/17.22 (complementTI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTELcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintersectTERcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT1) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT2) =>
% 102.63/17.22 ((
% 102.63/17.22 (contrasubsetT3) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementI1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementE1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub1) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementSub2) =>
% 102.63/17.22 ((
% 102.63/17.22 (doubleComplementEq) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTnotintersectT) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementImpComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementSubsetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementInPowersetComplementIntersect) =>
% 102.63/17.22 ((
% 102.63/17.22 (contraSubsetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementTcontraSubset) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTILcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTIRcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInUnion2) =>
% 102.63/17.22 ((
% 102.63/17.22 (inIntersectImpInIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (intersectInPowersetIntersectUnions) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpNotIn1) =>
% 102.63/17.22 ((
% 102.63/17.22 (inComplementUnionImpInComplement1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTE) =>
% 102.63/17.22 ((
% 102.63/17.22 (binunionTEcontra) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a1) =>
% 102.63/17.22 ((
% 102.63/17.22 (complementUnionInPowersetComplement) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan1) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2a) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b2) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2b) =>
% 102.63/17.22 ((
% 102.63/17.22 (demorgan2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule0) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz13rule4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_1) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_2) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_3) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_4) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz1_5) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all2) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1SetBreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (choice2fnsingleton) =>
% 102.63/17.22 ((
% 102.63/17.22 (setOfPairsIsBReln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1all1) =>
% 102.63/17.22 ((
% 102.63/17.22 (subbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (eqbreln1) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1invE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1compEex) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionprop) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIL) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionIR) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionI) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionE) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionEcases) =>
% 102.63/17.22 ((
% 102.63/17.22 (breln1unionCommutes) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2W) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2A) =>
% 102.63/17.22 ((
% 102.63/17.22 (woz2B) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Ex1) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1Equiv) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1E) =>
% 102.63/17.22 ((
% 102.63/17.22 (image1I) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncInInjFuncSet) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (injFuncSetFuncInj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncIn) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjFuncSetFuncSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (leftInvIsSurj) =>
% 102.63/17.22 ((
% 102.63/17.22 (surjCantorThm) =>
% 102.63/17.22 ((
% 102.63/17.22 (foundation2) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself) =>
% 102.63/17.22 ((
% 102.63/17.22 (notinself2) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSp) =>
% 102.63/17.22 ((
% 102.63/17.22 (omegaSclos) =>
% 102.63/17.22 ((
% 102.63/17.22 (peano0notS) =>
% 102.63/17.22 ((
% 102.63/17.22 (peanoSinj) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp1) =>
% 102.63/17.22 ((
% 102.63/17.22 (binintTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (transitivesetOp2) =>
% 102.63/17.22 ((
% 102.63/17.22 (setunionTransitive) =>
% 102.63/17.22 ((
% 102.63/17.22 (ordinalMinLem1) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y0 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (ordinal @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y1 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (!!) @ (
% 102.63/17.22 ^[Y2 : $i]:
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y2 @
% 102.63/17.22 Y0) =>
% 102.63/17.22 ((
% 102.63/17.22 (in @
% 102.63/17.22 Y1 @
% 102.63/17.22 Y2) =>
% 102.63/17.22 (in @
% 102.63/17.23 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1475])).
% 102.63/17.23 thf(zip_derived_cl1495, plain,
% 102.63/17.23 (~ (((ksndsingleton) =>
% 102.63/17.23 (((ksndpairEq) =>
% 102.63/17.23 (((kpairsurjEq) =>
% 102.63/17.23 (((cartprodsndin) =>
% 102.63/17.23 (((cartprodpairmemEL) =>
% 102.63/17.23 (((cartprodpairmemER) =>
% 102.63/17.23 (((cartprodmempaircEq) =>
% 102.63/17.23 (((cartprodfstpairEq) =>
% 102.63/17.23 (((cartprodsndpairEq) =>
% 102.63/17.23 (((cartprodpairsurjEq) =>
% 102.63/17.23 (((dpsetconstrI) =>
% 102.63/17.23 (((dpsetconstrSub) =>
% 102.63/17.23 (((setOfPairsIsBReln) =>
% 102.63/17.23 (((dpsetconstrERa) =>
% 102.63/17.23 (((dpsetconstrEL1) =>
% 102.63/17.23 (((dpsetconstrEL2) =>
% 102.63/17.23 (((dpsetconstrER) =>
% 102.63/17.23 (((funcImageSingleton) =>
% 102.63/17.23 (((apProp) =>
% 102.63/17.23 (((app) =>
% 102.63/17.23 (((infuncsetfunc) =>
% 102.63/17.23 (((ap2p) =>
% 102.63/17.23 (((funcinfuncset) =>
% 102.63/17.23 (((lamProp) =>
% 102.63/17.23 (((lamp) =>
% 102.63/17.23 (((lam2p) =>
% 102.63/17.23 (((brelnall1) =>
% 102.63/17.23 (((brelnall2) =>
% 102.63/17.23 (((ex1E2) =>
% 102.63/17.23 (((funcGraphProp1) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcGraphProp3) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcGraphProp2) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcextLem) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcGraphProp4) =>
% 102.63/17.23 ((
% 102.63/17.23 (subbreln) =>
% 102.63/17.23 ((
% 102.63/17.23 (eqbreln) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcext) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcext2) =>
% 102.63/17.23 ((
% 102.63/17.23 (ap2apEq1) =>
% 102.63/17.23 ((
% 102.63/17.23 (ap2apEq2) =>
% 102.63/17.23 ((
% 102.63/17.23 (beta1) =>
% 102.63/17.23 ((
% 102.63/17.23 (eta1) =>
% 102.63/17.23 ((
% 102.63/17.23 (lam2lamEq) =>
% 102.63/17.23 ((
% 102.63/17.23 (beta2) =>
% 102.63/17.23 ((
% 102.63/17.23 (eta2) =>
% 102.63/17.23 ((
% 102.63/17.23 (iffalseProp1) =>
% 102.63/17.23 ((
% 102.63/17.23 (iffalseProp2) =>
% 102.63/17.23 ((
% 102.63/17.23 (iftrueProp1) =>
% 102.63/17.23 ((
% 102.63/17.23 (iftrueProp2) =>
% 102.63/17.23 ((
% 102.63/17.23 (ifSingleton) =>
% 102.63/17.23 ((
% 102.63/17.23 (ifp) =>
% 102.63/17.23 ((
% 102.63/17.23 (theeq) =>
% 102.63/17.23 ((
% 102.63/17.23 (iftrue) =>
% 102.63/17.23 ((
% 102.63/17.23 (iffalse) =>
% 102.63/17.23 ((
% 102.63/17.23 (iftrueorfalse) =>
% 102.63/17.23 ((
% 102.63/17.23 (binintersectT_lem) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionT_lem) =>
% 102.63/17.23 ((
% 102.63/17.23 (powersetT_lem) =>
% 102.63/17.23 ((
% 102.63/17.23 (setminusT_lem) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementT_lem) =>
% 102.63/17.23 ((
% 102.63/17.23 (setextT) =>
% 102.63/17.23 ((
% 102.63/17.23 (subsetTI) =>
% 102.63/17.23 ((
% 102.63/17.23 (powersetTI1) =>
% 102.63/17.23 ((
% 102.63/17.23 (powersetTE1) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementTI1) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementTE1) =>
% 102.63/17.23 ((
% 102.63/17.23 (binintersectTELcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (binintersectTERcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT) =>
% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT1) =>
% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT2) =>
% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT3) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementI1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementE1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementSub1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementSub2) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementEq) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementTnotintersectT) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementImpComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementSubsetComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementInPowersetComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (contraSubsetComplement) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementTcontraSubset) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTILcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTIRcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (inIntersectImpInUnion) =>
% 102.63/17.23 ((
% 102.63/17.23 (inIntersectImpInUnion2) =>
% 102.63/17.23 ((
% 102.63/17.23 (inIntersectImpInIntersectUnions) =>
% 102.63/17.23 ((
% 102.63/17.23 (intersectInPowersetIntersectUnions) =>
% 102.63/17.23 ((
% 102.63/17.23 (inComplementUnionImpNotIn1) =>
% 102.63/17.23 ((
% 102.63/17.23 (inComplementUnionImpInComplement1) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTE) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTEcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2a1) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementUnionInPowersetComplement) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2a2) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan1a) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan1b) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan1) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2a) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2b2) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2b) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule0) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule1) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule2) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule3) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule4) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_1) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_2) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_3) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_4) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_5) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1all2) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1SetBreln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (choice2fnsingleton) =>
% 102.63/17.23 ((
% 102.63/17.23 (setOfPairsIsBReln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1all1) =>
% 102.63/17.23 ((
% 102.63/17.23 (subbreln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (eqbreln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1invprop) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1invI) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1invE) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1compprop) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1compI) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1compE) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1compEex) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionprop) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionIL) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionIR) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionI) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionE) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionEcases) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionCommutes) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz2Ex) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz2W) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz2A) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz2B) =>
% 102.63/17.23 ((
% 102.63/17.23 (image1Ex) =>
% 102.63/17.23 ((
% 102.63/17.23 (image1Ex1) =>
% 102.63/17.23 ((
% 102.63/17.23 (image1Equiv) =>
% 102.63/17.23 ((
% 102.63/17.23 (image1E) =>
% 102.63/17.23 ((
% 102.63/17.23 (image1I) =>
% 102.63/17.23 ((
% 102.63/17.23 (injFuncInInjFuncSet) =>
% 102.63/17.23 ((
% 102.63/17.23 (injFuncSetFuncIn) =>
% 102.63/17.23 ((
% 102.63/17.23 (injFuncSetFuncInj) =>
% 102.63/17.23 ((
% 102.63/17.23 (surjFuncSetFuncIn) =>
% 102.63/17.23 ((
% 102.63/17.23 (surjFuncSetFuncSurj) =>
% 102.63/17.23 ((
% 102.63/17.23 (leftInvIsSurj) =>
% 102.63/17.23 ((
% 102.63/17.23 (surjCantorThm) =>
% 102.63/17.23 ((
% 102.63/17.23 (foundation2) =>
% 102.63/17.23 ((
% 102.63/17.23 (notinself) =>
% 102.63/17.23 ((
% 102.63/17.23 (notinself2) =>
% 102.63/17.23 ((
% 102.63/17.23 (omegaSp) =>
% 102.63/17.23 ((
% 102.63/17.23 (omegaSclos) =>
% 102.63/17.23 ((
% 102.63/17.23 (peano0notS) =>
% 102.63/17.23 ((
% 102.63/17.23 (peanoSinj) =>
% 102.63/17.23 ((
% 102.63/17.23 (transitivesetOp1) =>
% 102.63/17.23 ((
% 102.63/17.23 (binintTransitive) =>
% 102.63/17.23 ((
% 102.63/17.23 (transitivesetOp2) =>
% 102.63/17.23 ((
% 102.63/17.23 (setunionTransitive) =>
% 102.63/17.23 ((
% 102.63/17.23 (ordinalMinLem1) =>
% 102.63/17.23 ((
% 102.63/17.23 (!!) @ (
% 102.63/17.23 ^[Y0 : $i]:
% 102.63/17.23 ((
% 102.63/17.23 (ordinal @
% 102.63/17.23 Y0) =>
% 102.63/17.23 ((
% 102.63/17.23 (!!) @ (
% 102.63/17.23 ^[Y1 : $i]:
% 102.63/17.23 ((
% 102.63/17.23 (!!) @ (
% 102.63/17.23 ^[Y2 : $i]:
% 102.63/17.23 ((
% 102.63/17.23 (in @
% 102.63/17.23 Y2 @
% 102.63/17.23 Y0) =>
% 102.63/17.23 ((
% 102.63/17.23 (in @
% 102.63/17.23 Y1 @
% 102.63/17.23 Y2) =>
% 102.63/17.23 (in @
% 102.63/17.23 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 102.63/17.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1485])).
% 102.63/17.23 thf(zip_derived_cl1504, plain,
% 102.63/17.23 (~ (((ksndpairEq) =>
% 102.63/17.23 (((kpairsurjEq) =>
% 102.63/17.23 (((cartprodsndin) =>
% 102.63/17.23 (((cartprodpairmemEL) =>
% 102.63/17.23 (((cartprodpairmemER) =>
% 102.63/17.23 (((cartprodmempaircEq) =>
% 102.63/17.23 (((cartprodfstpairEq) =>
% 102.63/17.23 (((cartprodsndpairEq) =>
% 102.63/17.23 (((cartprodpairsurjEq) =>
% 102.63/17.23 (((dpsetconstrI) =>
% 102.63/17.23 (((dpsetconstrSub) =>
% 102.63/17.23 (((setOfPairsIsBReln) =>
% 102.63/17.23 (((dpsetconstrERa) =>
% 102.63/17.23 (((dpsetconstrEL1) =>
% 102.63/17.23 (((dpsetconstrEL2) =>
% 102.63/17.23 (((dpsetconstrER) =>
% 102.63/17.23 (((funcImageSingleton) =>
% 102.63/17.23 (((apProp) =>
% 102.63/17.23 (((app) =>
% 102.63/17.23 (((infuncsetfunc) =>
% 102.63/17.23 (((ap2p) =>
% 102.63/17.23 (((funcinfuncset) =>
% 102.63/17.23 (((lamProp) =>
% 102.63/17.23 (((lamp) =>
% 102.63/17.23 (((lam2p) =>
% 102.63/17.23 (((brelnall1) =>
% 102.63/17.23 (((brelnall2) =>
% 102.63/17.23 (((ex1E2) =>
% 102.63/17.23 (((funcGraphProp1) =>
% 102.63/17.23 (((funcGraphProp3) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcGraphProp2) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcextLem) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcGraphProp4) =>
% 102.63/17.23 ((
% 102.63/17.23 (subbreln) =>
% 102.63/17.23 ((
% 102.63/17.23 (eqbreln) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcext) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcext2) =>
% 102.63/17.23 ((
% 102.63/17.23 (ap2apEq1) =>
% 102.63/17.23 ((
% 102.63/17.23 (ap2apEq2) =>
% 102.63/17.23 ((
% 102.63/17.23 (beta1) =>
% 102.63/17.23 ((
% 102.63/17.23 (eta1) =>
% 102.63/17.23 ((
% 102.63/17.23 (lam2lamEq) =>
% 102.63/17.23 ((
% 102.63/17.23 (beta2) =>
% 102.63/17.23 ((
% 102.63/17.23 (eta2) =>
% 102.63/17.23 ((
% 102.63/17.23 (iffalseProp1) =>
% 102.63/17.23 ((
% 102.63/17.23 (iffalseProp2) =>
% 102.63/17.23 ((
% 102.63/17.23 (iftrueProp1) =>
% 102.63/17.23 ((
% 102.63/17.23 (iftrueProp2) =>
% 102.63/17.23 ((
% 102.63/17.23 (ifSingleton) =>
% 102.63/17.23 ((
% 102.63/17.23 (ifp) =>
% 102.63/17.23 ((
% 102.63/17.23 (theeq) =>
% 102.63/17.23 ((
% 102.63/17.23 (iftrue) =>
% 102.63/17.23 ((
% 102.63/17.23 (iffalse) =>
% 102.63/17.23 ((
% 102.63/17.23 (iftrueorfalse) =>
% 102.63/17.23 ((
% 102.63/17.23 (binintersectT_lem) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionT_lem) =>
% 102.63/17.23 ((
% 102.63/17.23 (powersetT_lem) =>
% 102.63/17.23 ((
% 102.63/17.23 (setminusT_lem) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementT_lem) =>
% 102.63/17.23 ((
% 102.63/17.23 (setextT) =>
% 102.63/17.23 ((
% 102.63/17.23 (subsetTI) =>
% 102.63/17.23 ((
% 102.63/17.23 (powersetTI1) =>
% 102.63/17.23 ((
% 102.63/17.23 (powersetTE1) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementTI1) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementTE1) =>
% 102.63/17.23 ((
% 102.63/17.23 (binintersectTELcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (binintersectTERcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT) =>
% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT1) =>
% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT2) =>
% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT3) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementI1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementE1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementSub1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementSub2) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementEq) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementTnotintersectT) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementImpComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementSubsetComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementInPowersetComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (contraSubsetComplement) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementTcontraSubset) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTILcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTIRcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (inIntersectImpInUnion) =>
% 102.63/17.23 ((
% 102.63/17.23 (inIntersectImpInUnion2) =>
% 102.63/17.23 ((
% 102.63/17.23 (inIntersectImpInIntersectUnions) =>
% 102.63/17.23 ((
% 102.63/17.23 (intersectInPowersetIntersectUnions) =>
% 102.63/17.23 ((
% 102.63/17.23 (inComplementUnionImpNotIn1) =>
% 102.63/17.23 ((
% 102.63/17.23 (inComplementUnionImpInComplement1) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTE) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTEcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2a1) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementUnionInPowersetComplement) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2a2) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan1a) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan1b) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan1) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2a) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2b2) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2b) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule0) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule1) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule2) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule3) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule4) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_1) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_2) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_3) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_4) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_5) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1all2) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1SetBreln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (choice2fnsingleton) =>
% 102.63/17.23 ((
% 102.63/17.23 (setOfPairsIsBReln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1all1) =>
% 102.63/17.23 ((
% 102.63/17.23 (subbreln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (eqbreln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1invprop) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1invI) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1invE) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1compprop) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1compI) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1compE) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1compEex) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionprop) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionIL) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionIR) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionI) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionE) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionEcases) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionCommutes) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz2Ex) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz2W) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz2A) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz2B) =>
% 102.63/17.23 ((
% 102.63/17.23 (image1Ex) =>
% 102.63/17.23 ((
% 102.63/17.23 (image1Ex1) =>
% 102.63/17.23 ((
% 102.63/17.23 (image1Equiv) =>
% 102.63/17.23 ((
% 102.63/17.23 (image1E) =>
% 102.63/17.23 ((
% 102.63/17.23 (image1I) =>
% 102.63/17.23 ((
% 102.63/17.23 (injFuncInInjFuncSet) =>
% 102.63/17.23 ((
% 102.63/17.23 (injFuncSetFuncIn) =>
% 102.63/17.23 ((
% 102.63/17.23 (injFuncSetFuncInj) =>
% 102.63/17.23 ((
% 102.63/17.23 (surjFuncSetFuncIn) =>
% 102.63/17.23 ((
% 102.63/17.23 (surjFuncSetFuncSurj) =>
% 102.63/17.23 ((
% 102.63/17.23 (leftInvIsSurj) =>
% 102.63/17.23 ((
% 102.63/17.23 (surjCantorThm) =>
% 102.63/17.23 ((
% 102.63/17.23 (foundation2) =>
% 102.63/17.23 ((
% 102.63/17.23 (notinself) =>
% 102.63/17.23 ((
% 102.63/17.23 (notinself2) =>
% 102.63/17.23 ((
% 102.63/17.23 (omegaSp) =>
% 102.63/17.23 ((
% 102.63/17.23 (omegaSclos) =>
% 102.63/17.23 ((
% 102.63/17.23 (peano0notS) =>
% 102.63/17.23 ((
% 102.63/17.23 (peanoSinj) =>
% 102.63/17.23 ((
% 102.63/17.23 (transitivesetOp1) =>
% 102.63/17.23 ((
% 102.63/17.23 (binintTransitive) =>
% 102.63/17.23 ((
% 102.63/17.23 (transitivesetOp2) =>
% 102.63/17.23 ((
% 102.63/17.23 (setunionTransitive) =>
% 102.63/17.23 ((
% 102.63/17.23 (ordinalMinLem1) =>
% 102.63/17.23 ((
% 102.63/17.23 (!!) @ (
% 102.63/17.23 ^[Y0 : $i]:
% 102.63/17.23 ((
% 102.63/17.23 (ordinal @
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% 102.63/17.23 ((
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% 102.63/17.23 (!!) @ (
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% 102.63/17.23 ((
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% 102.63/17.23 Y0) =>
% 102.63/17.23 ((
% 102.63/17.23 (in @
% 102.63/17.23 Y1 @
% 102.63/17.23 Y2) =>
% 102.63/17.23 (in @
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% 102.63/17.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1495])).
% 102.63/17.23 thf(zip_derived_cl1511, plain,
% 102.63/17.23 (~ (((kpairsurjEq) =>
% 102.63/17.23 (((cartprodsndin) =>
% 102.63/17.23 (((cartprodpairmemEL) =>
% 102.63/17.23 (((cartprodpairmemER) =>
% 102.63/17.23 (((cartprodmempaircEq) =>
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% 102.63/17.23 (((cartprodsndpairEq) =>
% 102.63/17.23 (((cartprodpairsurjEq) =>
% 102.63/17.23 (((dpsetconstrI) =>
% 102.63/17.23 (((dpsetconstrSub) =>
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% 102.63/17.23 (((dpsetconstrEL1) =>
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% 102.63/17.23 (((funcGraphProp3) =>
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% 102.63/17.23 ((
% 102.63/17.23 (funcextLem) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcGraphProp4) =>
% 102.63/17.23 ((
% 102.63/17.23 (subbreln) =>
% 102.63/17.23 ((
% 102.63/17.23 (eqbreln) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcext) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcext2) =>
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% 102.63/17.23 ((
% 102.63/17.23 (eta1) =>
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (iffalseProp2) =>
% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (powersetT_lem) =>
% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (complementT_lem) =>
% 102.63/17.23 ((
% 102.63/17.23 (setextT) =>
% 102.63/17.23 ((
% 102.63/17.23 (subsetTI) =>
% 102.63/17.23 ((
% 102.63/17.23 (powersetTI1) =>
% 102.63/17.23 ((
% 102.63/17.23 (powersetTE1) =>
% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (complementTE1) =>
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% 102.63/17.23 ((
% 102.63/17.23 (binintersectTERcontra) =>
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% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT2) =>
% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT3) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementI1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementE1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementSub1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementSub2) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementEq) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementTnotintersectT) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementImpComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementSubsetComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementInPowersetComplementIntersect) =>
% 102.63/17.23 ((
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% 102.63/17.23 (injFuncSetFuncInj) =>
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% 102.63/17.23 ((
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% 102.63/17.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1504])).
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% 102.63/17.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1511])).
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% 102.63/17.23 ((
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% 102.63/17.23 (injFuncSetFuncInj) =>
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% 102.63/17.23 (surjFuncSetFuncSurj) =>
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% 102.63/17.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1519])).
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% 102.63/17.23 ((
% 102.63/17.23 (binintTransitive) =>
% 102.63/17.23 ((
% 102.63/17.23 (transitivesetOp2) =>
% 102.63/17.23 ((
% 102.63/17.23 (setunionTransitive) =>
% 102.63/17.23 ((
% 102.63/17.23 (ordinalMinLem1) =>
% 102.63/17.23 ((
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% 102.63/17.23 (ordinal @
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% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (!!) @ (
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% 102.63/17.23 ((
% 102.63/17.23 (in @
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% 102.63/17.23 ((
% 102.63/17.23 (in @
% 102.63/17.23 Y1 @
% 102.63/17.23 Y2) =>
% 102.63/17.23 (in @
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% 102.63/17.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1529])).
% 102.63/17.23 thf(zip_derived_cl1546, plain,
% 102.63/17.23 (~ (((cartprodmempaircEq) =>
% 102.63/17.23 (((cartprodfstpairEq) =>
% 102.63/17.23 (((cartprodsndpairEq) =>
% 102.63/17.23 (((cartprodpairsurjEq) =>
% 102.63/17.23 (((dpsetconstrI) =>
% 102.63/17.23 (((dpsetconstrSub) =>
% 102.63/17.23 (((setOfPairsIsBReln) =>
% 102.63/17.23 (((dpsetconstrERa) =>
% 102.63/17.23 (((dpsetconstrEL1) =>
% 102.63/17.23 (((dpsetconstrEL2) =>
% 102.63/17.23 (((dpsetconstrER) =>
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% 102.63/17.23 (((apProp) =>
% 102.63/17.23 (((app) =>
% 102.63/17.23 (((infuncsetfunc) =>
% 102.63/17.23 (((ap2p) =>
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% 102.63/17.23 (((lam2p) =>
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% 102.63/17.23 (((brelnall2) =>
% 102.63/17.23 (((ex1E2) =>
% 102.63/17.23 (((funcGraphProp1) =>
% 102.63/17.23 (((funcGraphProp3) =>
% 102.63/17.23 (((funcGraphProp2) =>
% 102.63/17.23 (((funcextLem) =>
% 102.63/17.23 (((funcGraphProp4) =>
% 102.63/17.23 (((subbreln) =>
% 102.63/17.23 (((eqbreln) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcext) =>
% 102.63/17.23 ((
% 102.63/17.23 (funcext2) =>
% 102.63/17.23 ((
% 102.63/17.23 (ap2apEq1) =>
% 102.63/17.23 ((
% 102.63/17.23 (ap2apEq2) =>
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (iftrue) =>
% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (iftrueorfalse) =>
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% 102.63/17.23 ((
% 102.63/17.23 (powersetT_lem) =>
% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (complementTE1) =>
% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (binintersectTERcontra) =>
% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT1) =>
% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT2) =>
% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT3) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementI1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementE1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementSub1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementSub2) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementEq) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementTnotintersectT) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementImpComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementSubsetComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementInPowersetComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (contraSubsetComplement) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementTcontraSubset) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTILcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTIRcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (inIntersectImpInUnion) =>
% 102.63/17.23 ((
% 102.63/17.23 (inIntersectImpInUnion2) =>
% 102.63/17.23 ((
% 102.63/17.23 (inIntersectImpInIntersectUnions) =>
% 102.63/17.23 ((
% 102.63/17.23 (intersectInPowersetIntersectUnions) =>
% 102.63/17.23 ((
% 102.63/17.23 (inComplementUnionImpNotIn1) =>
% 102.63/17.23 ((
% 102.63/17.23 (inComplementUnionImpInComplement1) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTE) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTEcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2a1) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementUnionInPowersetComplement) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2a2) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan1a) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan1b) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan1) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2a) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2b2) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2b) =>
% 102.63/17.23 ((
% 102.63/17.23 (demorgan2) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule0) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule1) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule2) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule3) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz13rule4) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_1) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_2) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_3) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_4) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz1_5) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1all2) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1SetBreln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (choice2fnsingleton) =>
% 102.63/17.23 ((
% 102.63/17.23 (setOfPairsIsBReln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1all1) =>
% 102.63/17.23 ((
% 102.63/17.23 (subbreln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (eqbreln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1invprop) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1invI) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1invE) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1compprop) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1compI) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1compE) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1compEex) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionprop) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionIL) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionIR) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionI) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionE) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionEcases) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1unionCommutes) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz2Ex) =>
% 102.63/17.23 ((
% 102.63/17.23 (woz2W) =>
% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (woz2B) =>
% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (image1Ex1) =>
% 102.63/17.23 ((
% 102.63/17.23 (image1Equiv) =>
% 102.63/17.23 ((
% 102.63/17.23 (image1E) =>
% 102.63/17.23 ((
% 102.63/17.23 (image1I) =>
% 102.63/17.23 ((
% 102.63/17.23 (injFuncInInjFuncSet) =>
% 102.63/17.23 ((
% 102.63/17.23 (injFuncSetFuncIn) =>
% 102.63/17.23 ((
% 102.63/17.23 (injFuncSetFuncInj) =>
% 102.63/17.23 ((
% 102.63/17.23 (surjFuncSetFuncIn) =>
% 102.63/17.23 ((
% 102.63/17.23 (surjFuncSetFuncSurj) =>
% 102.63/17.23 ((
% 102.63/17.23 (leftInvIsSurj) =>
% 102.63/17.23 ((
% 102.63/17.23 (surjCantorThm) =>
% 102.63/17.23 ((
% 102.63/17.23 (foundation2) =>
% 102.63/17.23 ((
% 102.63/17.23 (notinself) =>
% 102.63/17.23 ((
% 102.63/17.23 (notinself2) =>
% 102.63/17.23 ((
% 102.63/17.23 (omegaSp) =>
% 102.63/17.23 ((
% 102.63/17.23 (omegaSclos) =>
% 102.63/17.23 ((
% 102.63/17.23 (peano0notS) =>
% 102.63/17.23 ((
% 102.63/17.23 (peanoSinj) =>
% 102.63/17.23 ((
% 102.63/17.23 (transitivesetOp1) =>
% 102.63/17.23 ((
% 102.63/17.23 (binintTransitive) =>
% 102.63/17.23 ((
% 102.63/17.23 (transitivesetOp2) =>
% 102.63/17.23 ((
% 102.63/17.23 (setunionTransitive) =>
% 102.63/17.23 ((
% 102.63/17.23 (ordinalMinLem1) =>
% 102.63/17.23 ((
% 102.63/17.23 (!!) @ (
% 102.63/17.23 ^[Y0 : $i]:
% 102.63/17.23 ((
% 102.63/17.23 (ordinal @
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% 102.63/17.23 ((
% 102.63/17.23 (!!) @ (
% 102.63/17.23 ^[Y1 : $i]:
% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 Y1 @
% 102.63/17.23 Y2) =>
% 102.63/17.23 (in @
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% 102.63/17.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1538])).
% 102.63/17.23 thf(zip_derived_cl1553, plain,
% 102.63/17.23 (~ (((cartprodfstpairEq) =>
% 102.63/17.23 (((cartprodsndpairEq) =>
% 102.63/17.23 (((cartprodpairsurjEq) =>
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% 102.63/17.23 (((dpsetconstrEL1) =>
% 102.63/17.23 (((dpsetconstrEL2) =>
% 102.63/17.23 (((dpsetconstrER) =>
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% 102.63/17.23 (((lam2p) =>
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (binintersectTERcontra) =>
% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (contrasubsetT2) =>
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% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementE1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementSub1) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementSub2) =>
% 102.63/17.23 ((
% 102.63/17.23 (doubleComplementEq) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementTnotintersectT) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementImpComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementSubsetComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementInPowersetComplementIntersect) =>
% 102.63/17.23 ((
% 102.63/17.23 (contraSubsetComplement) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementTcontraSubset) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTILcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (binunionTIRcontra) =>
% 102.63/17.23 ((
% 102.63/17.23 (inIntersectImpInUnion) =>
% 102.63/17.23 ((
% 102.63/17.23 (inIntersectImpInUnion2) =>
% 102.63/17.23 ((
% 102.63/17.23 (inIntersectImpInIntersectUnions) =>
% 102.63/17.23 ((
% 102.63/17.23 (intersectInPowersetIntersectUnions) =>
% 102.63/17.23 ((
% 102.63/17.23 (inComplementUnionImpNotIn1) =>
% 102.63/17.23 ((
% 102.63/17.23 (inComplementUnionImpInComplement1) =>
% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (demorgan2a1) =>
% 102.63/17.23 ((
% 102.63/17.23 (complementUnionInPowersetComplement) =>
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
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% 102.63/17.23 ((
% 102.63/17.23 (woz1_5) =>
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% 102.63/17.23 (breln1all2) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1SetBreln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (choice2fnsingleton) =>
% 102.63/17.23 ((
% 102.63/17.23 (setOfPairsIsBReln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1all1) =>
% 102.63/17.23 ((
% 102.63/17.23 (subbreln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (eqbreln1) =>
% 102.63/17.23 ((
% 102.63/17.23 (breln1invprop) =>
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% 102.63/17.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1546])).
% 102.63/17.23 thf(zip_derived_cl1559, plain,
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% 103.13/17.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1572])).
% 103.13/17.24 thf(zip_derived_cl1586, plain,
% 103.13/17.24 (~ (((setOfPairsIsBReln) =>
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% 103.13/17.24 (((brelnall2) =>
% 103.13/17.24 (((ex1E2) =>
% 103.13/17.24 (((funcGraphProp1) =>
% 103.13/17.24 (((funcGraphProp3) =>
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% 103.13/17.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1579])).
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% 103.13/17.24 (((funcGraphProp2) =>
% 103.13/17.24 (((funcextLem) =>
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% 103.13/17.24 (((funcext2) =>
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% 103.13/17.24 (inComplementUnionImpInComplement1) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (woz13rule2) =>
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% 103.13/17.24 (woz13rule3) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz13rule4) =>
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% 103.13/17.24 ((
% 103.13/17.24 (woz1_2) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz1_3) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz1_4) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz1_5) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (setOfPairsIsBReln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1all1) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (breln1invI) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1invE) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (breln1compE) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1compEex) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (breln1unionIL) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionIR) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionI) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionE) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionEcases) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionCommutes) =>
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% 103.13/17.24 ((
% 103.13/17.24 (woz2W) =>
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% 103.13/17.24 (woz2B) =>
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (image1E) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1I) =>
% 103.13/17.24 ((
% 103.13/17.24 (injFuncInInjFuncSet) =>
% 103.13/17.24 ((
% 103.13/17.24 (injFuncSetFuncIn) =>
% 103.13/17.24 ((
% 103.13/17.24 (injFuncSetFuncInj) =>
% 103.13/17.24 ((
% 103.13/17.24 (surjFuncSetFuncIn) =>
% 103.13/17.24 ((
% 103.13/17.24 (surjFuncSetFuncSurj) =>
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (peanoSinj) =>
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1586])).
% 103.13/17.24 thf(zip_derived_cl1603, plain,
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% 103.13/17.24 ((
% 103.13/17.24 (breln1unionIR) =>
% 103.13/17.24 ((
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% 103.13/17.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1594])).
% 103.13/17.24 thf(zip_derived_cl1613, plain,
% 103.13/17.24 (~ (((dpsetconstrEL2) =>
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% 103.13/17.24 (((lam2p) =>
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% 103.13/17.24 (((brelnall2) =>
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% 103.13/17.24 (((funcGraphProp1) =>
% 103.13/17.24 (((funcGraphProp3) =>
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1603])).
% 103.13/17.24 thf(zip_derived_cl1624, plain,
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% 103.13/17.24 (surjFuncSetFuncSurj) =>
% 103.13/17.24 ((
% 103.13/17.24 (leftInvIsSurj) =>
% 103.13/17.24 ((
% 103.13/17.24 (surjCantorThm) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (notinself) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (omegaSclos) =>
% 103.13/17.24 ((
% 103.13/17.24 (peano0notS) =>
% 103.13/17.24 ((
% 103.13/17.24 (peanoSinj) =>
% 103.13/17.24 ((
% 103.13/17.24 (transitivesetOp1) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (setunionTransitive) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 (!!) @ (
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1613])).
% 103.13/17.24 thf(zip_derived_cl1633, plain,
% 103.13/17.24 (~ (((funcImageSingleton) =>
% 103.13/17.24 (((apProp) =>
% 103.13/17.24 (((app) =>
% 103.13/17.24 (((infuncsetfunc) =>
% 103.13/17.24 (((ap2p) =>
% 103.13/17.24 (((funcinfuncset) =>
% 103.13/17.24 (((lamProp) =>
% 103.13/17.24 (((lamp) =>
% 103.13/17.24 (((lam2p) =>
% 103.13/17.24 (((brelnall1) =>
% 103.13/17.24 (((brelnall2) =>
% 103.13/17.24 (((ex1E2) =>
% 103.13/17.24 (((funcGraphProp1) =>
% 103.13/17.24 (((funcGraphProp3) =>
% 103.13/17.24 (((funcGraphProp2) =>
% 103.13/17.24 (((funcextLem) =>
% 103.13/17.24 (((funcGraphProp4) =>
% 103.13/17.24 (((subbreln) =>
% 103.13/17.24 (((eqbreln) =>
% 103.13/17.24 (((funcext) =>
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% 103.13/17.24 (((ap2apEq2) =>
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% 103.13/17.24 (((lam2lamEq) =>
% 103.13/17.24 (((beta2) =>
% 103.13/17.24 (((eta2) =>
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (contrasubsetT2) =>
% 103.13/17.24 ((
% 103.13/17.24 (contrasubsetT3) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (doubleComplementE1) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (doubleComplementSub2) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (complementTnotintersectT) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementImpComplementIntersect) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementSubsetComplementIntersect) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementInPowersetComplementIntersect) =>
% 103.13/17.24 ((
% 103.13/17.24 (contraSubsetComplement) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementTcontraSubset) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (inIntersectImpInUnion2) =>
% 103.13/17.24 ((
% 103.13/17.24 (inIntersectImpInIntersectUnions) =>
% 103.13/17.24 ((
% 103.13/17.24 (intersectInPowersetIntersectUnions) =>
% 103.13/17.24 ((
% 103.13/17.24 (inComplementUnionImpNotIn1) =>
% 103.13/17.24 ((
% 103.13/17.24 (inComplementUnionImpInComplement1) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (complementUnionInPowersetComplement) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2a2) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (demorgan1b) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (demorgan2a) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2b2) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2b) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (breln1all2) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1SetBreln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (choice2fnsingleton) =>
% 103.13/17.24 ((
% 103.13/17.24 (setOfPairsIsBReln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1all1) =>
% 103.13/17.24 ((
% 103.13/17.24 (subbreln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (eqbreln1) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (breln1invI) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1invE) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1compprop) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1compI) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1compE) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1compEex) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionprop) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionIL) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionIR) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionI) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionE) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionEcases) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionCommutes) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2Ex) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2W) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (image1I) =>
% 103.13/17.24 ((
% 103.13/17.24 (injFuncInInjFuncSet) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (injFuncSetFuncInj) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1624])).
% 103.13/17.24 thf(zip_derived_cl1641, plain,
% 103.13/17.24 (~ (((apProp) =>
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (breln1unionE) =>
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% 103.13/17.24 (breln1unionEcases) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionCommutes) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2Ex) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2W) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2A) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2B) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1Ex) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1Ex1) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1Equiv) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1E) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1I) =>
% 103.13/17.24 ((
% 103.13/17.24 (injFuncInInjFuncSet) =>
% 103.13/17.24 ((
% 103.13/17.24 (injFuncSetFuncIn) =>
% 103.13/17.24 ((
% 103.13/17.24 (injFuncSetFuncInj) =>
% 103.13/17.24 ((
% 103.13/17.24 (surjFuncSetFuncIn) =>
% 103.13/17.24 ((
% 103.13/17.24 (surjFuncSetFuncSurj) =>
% 103.13/17.24 ((
% 103.13/17.24 (leftInvIsSurj) =>
% 103.13/17.24 ((
% 103.13/17.24 (surjCantorThm) =>
% 103.13/17.24 ((
% 103.13/17.24 (foundation2) =>
% 103.13/17.24 ((
% 103.13/17.24 (notinself) =>
% 103.13/17.24 ((
% 103.13/17.24 (notinself2) =>
% 103.13/17.24 ((
% 103.13/17.24 (omegaSp) =>
% 103.13/17.24 ((
% 103.13/17.24 (omegaSclos) =>
% 103.13/17.24 ((
% 103.13/17.24 (peano0notS) =>
% 103.13/17.24 ((
% 103.13/17.24 (peanoSinj) =>
% 103.13/17.24 ((
% 103.13/17.24 (transitivesetOp1) =>
% 103.13/17.24 ((
% 103.13/17.24 (binintTransitive) =>
% 103.13/17.24 ((
% 103.13/17.24 (transitivesetOp2) =>
% 103.13/17.24 ((
% 103.13/17.24 (setunionTransitive) =>
% 103.13/17.24 ((
% 103.13/17.24 (ordinalMinLem1) =>
% 103.13/17.24 ((
% 103.13/17.24 (!!) @ (
% 103.13/17.24 ^[Y0 : $i]:
% 103.13/17.24 ((
% 103.13/17.24 (ordinal @
% 103.13/17.24 Y0) =>
% 103.13/17.24 ((
% 103.13/17.24 (!!) @ (
% 103.13/17.24 ^[Y1 : $i]:
% 103.13/17.24 ((
% 103.13/17.24 (!!) @ (
% 103.13/17.24 ^[Y2 : $i]:
% 103.13/17.24 ((
% 103.13/17.24 (in @
% 103.13/17.24 Y2 @
% 103.13/17.24 Y0) =>
% 103.13/17.24 ((
% 103.13/17.24 (in @
% 103.13/17.24 Y1 @
% 103.13/17.24 Y2) =>
% 103.13/17.24 (in @
% 103.13/17.24 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1633])).
% 103.13/17.24 thf(zip_derived_cl1650, plain,
% 103.13/17.24 (~ (((app) =>
% 103.13/17.24 (((infuncsetfunc) =>
% 103.13/17.24 (((ap2p) =>
% 103.13/17.24 (((funcinfuncset) =>
% 103.13/17.24 (((lamProp) =>
% 103.13/17.24 (((lamp) =>
% 103.13/17.24 (((lam2p) =>
% 103.13/17.24 (((brelnall1) =>
% 103.13/17.24 (((brelnall2) =>
% 103.13/17.24 (((ex1E2) =>
% 103.13/17.24 (((funcGraphProp1) =>
% 103.13/17.24 (((funcGraphProp3) =>
% 103.13/17.24 (((funcGraphProp2) =>
% 103.13/17.24 (((funcextLem) =>
% 103.13/17.24 (((funcGraphProp4) =>
% 103.13/17.24 (((subbreln) =>
% 103.13/17.24 (((eqbreln) =>
% 103.13/17.24 (((funcext) =>
% 103.13/17.24 (((funcext2) =>
% 103.13/17.24 (((ap2apEq1) =>
% 103.13/17.24 (((ap2apEq2) =>
% 103.13/17.24 (((beta1) =>
% 103.13/17.24 (((eta1) =>
% 103.13/17.24 (((lam2lamEq) =>
% 103.13/17.24 (((beta2) =>
% 103.13/17.24 (((eta2) =>
% 103.13/17.24 (((iffalseProp1) =>
% 103.13/17.24 (((iffalseProp2) =>
% 103.13/17.24 (((iftrueProp1) =>
% 103.13/17.24 (((iftrueProp2) =>
% 103.13/17.24 ((
% 103.13/17.24 (ifSingleton) =>
% 103.13/17.24 ((
% 103.13/17.24 (ifp) =>
% 103.13/17.24 ((
% 103.13/17.24 (theeq) =>
% 103.13/17.24 ((
% 103.13/17.24 (iftrue) =>
% 103.13/17.24 ((
% 103.13/17.24 (iffalse) =>
% 103.13/17.24 ((
% 103.13/17.24 (iftrueorfalse) =>
% 103.13/17.24 ((
% 103.13/17.24 (binintersectT_lem) =>
% 103.13/17.24 ((
% 103.13/17.24 (binunionT_lem) =>
% 103.13/17.24 ((
% 103.13/17.24 (powersetT_lem) =>
% 103.13/17.24 ((
% 103.13/17.24 (setminusT_lem) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementT_lem) =>
% 103.13/17.24 ((
% 103.13/17.24 (setextT) =>
% 103.13/17.24 ((
% 103.13/17.24 (subsetTI) =>
% 103.13/17.24 ((
% 103.13/17.24 (powersetTI1) =>
% 103.13/17.24 ((
% 103.13/17.24 (powersetTE1) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementTI1) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementTE1) =>
% 103.13/17.24 ((
% 103.13/17.24 (binintersectTELcontra) =>
% 103.13/17.24 ((
% 103.13/17.24 (binintersectTERcontra) =>
% 103.13/17.24 ((
% 103.13/17.24 (contrasubsetT) =>
% 103.13/17.24 ((
% 103.13/17.24 (contrasubsetT1) =>
% 103.13/17.24 ((
% 103.13/17.24 (contrasubsetT2) =>
% 103.13/17.24 ((
% 103.13/17.24 (contrasubsetT3) =>
% 103.13/17.24 ((
% 103.13/17.24 (doubleComplementI1) =>
% 103.13/17.24 ((
% 103.13/17.24 (doubleComplementE1) =>
% 103.13/17.24 ((
% 103.13/17.24 (doubleComplementSub1) =>
% 103.13/17.24 ((
% 103.13/17.24 (doubleComplementSub2) =>
% 103.13/17.24 ((
% 103.13/17.24 (doubleComplementEq) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementTnotintersectT) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementImpComplementIntersect) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementSubsetComplementIntersect) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementInPowersetComplementIntersect) =>
% 103.13/17.24 ((
% 103.13/17.24 (contraSubsetComplement) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementTcontraSubset) =>
% 103.13/17.24 ((
% 103.13/17.24 (binunionTILcontra) =>
% 103.13/17.24 ((
% 103.13/17.24 (binunionTIRcontra) =>
% 103.13/17.24 ((
% 103.13/17.24 (inIntersectImpInUnion) =>
% 103.13/17.24 ((
% 103.13/17.24 (inIntersectImpInUnion2) =>
% 103.13/17.24 ((
% 103.13/17.24 (inIntersectImpInIntersectUnions) =>
% 103.13/17.24 ((
% 103.13/17.24 (intersectInPowersetIntersectUnions) =>
% 103.13/17.24 ((
% 103.13/17.24 (inComplementUnionImpNotIn1) =>
% 103.13/17.24 ((
% 103.13/17.24 (inComplementUnionImpInComplement1) =>
% 103.13/17.24 ((
% 103.13/17.24 (binunionTE) =>
% 103.13/17.24 ((
% 103.13/17.24 (binunionTEcontra) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2a1) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementUnionInPowersetComplement) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2a2) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan1a) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan1b) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan1) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2a) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2b2) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2b) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz13rule0) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz13rule1) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz13rule2) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz13rule3) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz13rule4) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz1_1) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz1_2) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz1_3) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz1_4) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz1_5) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1all2) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1SetBreln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (choice2fnsingleton) =>
% 103.13/17.24 ((
% 103.13/17.24 (setOfPairsIsBReln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1all1) =>
% 103.13/17.24 ((
% 103.13/17.24 (subbreln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (eqbreln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1invprop) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1invI) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1invE) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1compprop) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1compI) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1compE) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1compEex) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionprop) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionIL) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionIR) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionI) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionE) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionEcases) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionCommutes) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2Ex) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2W) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2A) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2B) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1Ex) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1Ex1) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1Equiv) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1E) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1I) =>
% 103.13/17.24 ((
% 103.13/17.24 (injFuncInInjFuncSet) =>
% 103.13/17.24 ((
% 103.13/17.24 (injFuncSetFuncIn) =>
% 103.13/17.24 ((
% 103.13/17.24 (injFuncSetFuncInj) =>
% 103.13/17.24 ((
% 103.13/17.24 (surjFuncSetFuncIn) =>
% 103.13/17.24 ((
% 103.13/17.24 (surjFuncSetFuncSurj) =>
% 103.13/17.24 ((
% 103.13/17.24 (leftInvIsSurj) =>
% 103.13/17.24 ((
% 103.13/17.24 (surjCantorThm) =>
% 103.13/17.24 ((
% 103.13/17.24 (foundation2) =>
% 103.13/17.24 ((
% 103.13/17.24 (notinself) =>
% 103.13/17.24 ((
% 103.13/17.24 (notinself2) =>
% 103.13/17.24 ((
% 103.13/17.24 (omegaSp) =>
% 103.13/17.24 ((
% 103.13/17.24 (omegaSclos) =>
% 103.13/17.24 ((
% 103.13/17.24 (peano0notS) =>
% 103.13/17.24 ((
% 103.13/17.24 (peanoSinj) =>
% 103.13/17.24 ((
% 103.13/17.24 (transitivesetOp1) =>
% 103.13/17.24 ((
% 103.13/17.24 (binintTransitive) =>
% 103.13/17.24 ((
% 103.13/17.24 (transitivesetOp2) =>
% 103.13/17.24 ((
% 103.13/17.24 (setunionTransitive) =>
% 103.13/17.24 ((
% 103.13/17.24 (ordinalMinLem1) =>
% 103.13/17.24 ((
% 103.13/17.24 (!!) @ (
% 103.13/17.24 ^[Y0 : $i]:
% 103.13/17.24 ((
% 103.13/17.24 (ordinal @
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% 103.13/17.24 ((
% 103.13/17.24 (!!) @ (
% 103.13/17.24 ^[Y1 : $i]:
% 103.13/17.24 ((
% 103.13/17.24 (!!) @ (
% 103.13/17.24 ^[Y2 : $i]:
% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (in @
% 103.13/17.24 Y1 @
% 103.13/17.24 Y2) =>
% 103.13/17.24 (in @
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% 103.13/17.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1641])).
% 103.13/17.24 thf(zip_derived_cl1659, plain,
% 103.13/17.24 (~ (((infuncsetfunc) =>
% 103.13/17.24 (((ap2p) =>
% 103.13/17.24 (((funcinfuncset) =>
% 103.13/17.24 (((lamProp) =>
% 103.13/17.24 (((lamp) =>
% 103.13/17.24 (((lam2p) =>
% 103.13/17.24 (((brelnall1) =>
% 103.13/17.24 (((brelnall2) =>
% 103.13/17.24 (((ex1E2) =>
% 103.13/17.24 (((funcGraphProp1) =>
% 103.13/17.24 (((funcGraphProp3) =>
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% 103.13/17.24 (((funcextLem) =>
% 103.13/17.24 (((funcGraphProp4) =>
% 103.13/17.24 (((subbreln) =>
% 103.13/17.24 (((eqbreln) =>
% 103.13/17.24 (((funcext) =>
% 103.13/17.24 (((funcext2) =>
% 103.13/17.24 (((ap2apEq1) =>
% 103.13/17.24 (((ap2apEq2) =>
% 103.13/17.24 (((beta1) =>
% 103.13/17.24 (((eta1) =>
% 103.13/17.24 (((lam2lamEq) =>
% 103.13/17.24 (((beta2) =>
% 103.13/17.24 (((eta2) =>
% 103.13/17.24 (((iffalseProp1) =>
% 103.13/17.24 (((iffalseProp2) =>
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (setextT) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (powersetTE1) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementTI1) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementTE1) =>
% 103.13/17.24 ((
% 103.13/17.24 (binintersectTELcontra) =>
% 103.13/17.24 ((
% 103.13/17.24 (binintersectTERcontra) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (contrasubsetT2) =>
% 103.13/17.24 ((
% 103.13/17.24 (contrasubsetT3) =>
% 103.13/17.24 ((
% 103.13/17.24 (doubleComplementI1) =>
% 103.13/17.24 ((
% 103.13/17.24 (doubleComplementE1) =>
% 103.13/17.24 ((
% 103.13/17.24 (doubleComplementSub1) =>
% 103.13/17.24 ((
% 103.13/17.24 (doubleComplementSub2) =>
% 103.13/17.24 ((
% 103.13/17.24 (doubleComplementEq) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementTnotintersectT) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementImpComplementIntersect) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementSubsetComplementIntersect) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementInPowersetComplementIntersect) =>
% 103.13/17.24 ((
% 103.13/17.24 (contraSubsetComplement) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementTcontraSubset) =>
% 103.13/17.24 ((
% 103.13/17.24 (binunionTILcontra) =>
% 103.13/17.24 ((
% 103.13/17.24 (binunionTIRcontra) =>
% 103.13/17.24 ((
% 103.13/17.24 (inIntersectImpInUnion) =>
% 103.13/17.24 ((
% 103.13/17.24 (inIntersectImpInUnion2) =>
% 103.13/17.24 ((
% 103.13/17.24 (inIntersectImpInIntersectUnions) =>
% 103.13/17.24 ((
% 103.13/17.24 (intersectInPowersetIntersectUnions) =>
% 103.13/17.24 ((
% 103.13/17.24 (inComplementUnionImpNotIn1) =>
% 103.13/17.24 ((
% 103.13/17.24 (inComplementUnionImpInComplement1) =>
% 103.13/17.24 ((
% 103.13/17.24 (binunionTE) =>
% 103.13/17.24 ((
% 103.13/17.24 (binunionTEcontra) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2a1) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementUnionInPowersetComplement) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2a2) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan1a) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan1b) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan1) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2a) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2b2) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2b) =>
% 103.13/17.24 ((
% 103.13/17.24 (demorgan2) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz13rule0) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz13rule1) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz13rule2) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz13rule3) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz13rule4) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (woz1_2) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz1_3) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz1_4) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz1_5) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1all2) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1SetBreln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (choice2fnsingleton) =>
% 103.13/17.24 ((
% 103.13/17.24 (setOfPairsIsBReln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1all1) =>
% 103.13/17.24 ((
% 103.13/17.24 (subbreln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (eqbreln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1invprop) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1invI) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1invE) =>
% 103.13/17.24 ((
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% 103.13/17.24 (breln1compEex) =>
% 103.13/17.24 ((
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% 103.13/17.24 (breln1unionEcases) =>
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% 103.13/17.24 (injFuncInInjFuncSet) =>
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% 103.13/17.24 (injFuncSetFuncIn) =>
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% 103.13/17.24 ((
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% 103.13/17.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1650])).
% 103.13/17.24 thf(zip_derived_cl1668, plain,
% 103.13/17.24 (~ (((ap2p) =>
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% 103.13/17.24 ((
% 103.13/17.24 (complementSubsetComplementIntersect) =>
% 103.13/17.24 ((
% 103.13/17.24 (complementInPowersetComplementIntersect) =>
% 103.13/17.24 ((
% 103.13/17.24 (contraSubsetComplement) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (demorgan2a) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (demorgan2b) =>
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (setOfPairsIsBReln1) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (breln1invE) =>
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
% 103.13/17.24 (breln1unionIR) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionI) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionE) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionEcases) =>
% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 ((
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% 103.13/17.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1659])).
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% 103.13/17.24 (setOfPairsIsBReln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1all1) =>
% 103.13/17.24 ((
% 103.13/17.24 (subbreln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (eqbreln1) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1invprop) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1invI) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1invE) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1compprop) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1compI) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1compE) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1compEex) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionprop) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionIL) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionIR) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionI) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionE) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionEcases) =>
% 103.13/17.24 ((
% 103.13/17.24 (breln1unionCommutes) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2Ex) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2W) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2A) =>
% 103.13/17.24 ((
% 103.13/17.24 (woz2B) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1Ex) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1Ex1) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1Equiv) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1E) =>
% 103.13/17.24 ((
% 103.13/17.24 (image1I) =>
% 103.13/17.24 ((
% 103.13/17.24 (injFuncInInjFuncSet) =>
% 103.13/17.24 ((
% 103.13/17.24 (injFuncSetFuncIn) =>
% 103.13/17.24 ((
% 103.13/17.24 (injFuncSetFuncInj) =>
% 103.13/17.24 ((
% 103.13/17.24 (surjFuncSetFuncIn) =>
% 103.13/17.24 ((
% 103.13/17.24 (surjFuncSetFuncSurj) =>
% 103.13/17.24 ((
% 103.13/17.24 (leftInvIsSurj) =>
% 103.13/17.24 ((
% 103.13/17.24 (surjCantorThm) =>
% 103.13/17.24 ((
% 103.13/17.24 (foundation2) =>
% 103.13/17.24 ((
% 103.13/17.24 (notinself) =>
% 103.13/17.24 ((
% 103.13/17.24 (notinself2) =>
% 103.13/17.24 ((
% 103.13/17.24 (omegaSp) =>
% 103.13/17.24 ((
% 103.13/17.24 (omegaSclos) =>
% 103.13/17.24 ((
% 103.13/17.24 (peano0notS) =>
% 103.13/17.25 ((
% 103.13/17.25 (peanoSinj) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp2) =>
% 103.13/17.25 ((
% 103.13/17.25 (setunionTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (ordinalMinLem1) =>
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y0 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (ordinal @
% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y1 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y2 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y2 @
% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @
% 103.13/17.25 Y2) =>
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1668])).
% 103.13/17.25 thf(zip_derived_cl1688, plain,
% 103.13/17.25 (~ (((lamProp) =>
% 103.13/17.25 (((lamp) =>
% 103.13/17.25 (((lam2p) =>
% 103.13/17.25 (((brelnall1) =>
% 103.13/17.25 (((brelnall2) =>
% 103.13/17.25 (((ex1E2) =>
% 103.13/17.25 (((funcGraphProp1) =>
% 103.13/17.25 (((funcGraphProp3) =>
% 103.13/17.25 (((funcGraphProp2) =>
% 103.13/17.25 (((funcextLem) =>
% 103.13/17.25 (((funcGraphProp4) =>
% 103.13/17.25 (((subbreln) =>
% 103.13/17.25 (((eqbreln) =>
% 103.13/17.25 (((funcext) =>
% 103.13/17.25 (((funcext2) =>
% 103.13/17.25 (((ap2apEq1) =>
% 103.13/17.25 (((ap2apEq2) =>
% 103.13/17.25 (((beta1) =>
% 103.13/17.25 (((eta1) =>
% 103.13/17.25 (((lam2lamEq) =>
% 103.13/17.25 (((beta2) =>
% 103.13/17.25 (((eta2) =>
% 103.13/17.25 (((iffalseProp1) =>
% 103.13/17.25 (((iffalseProp2) =>
% 103.13/17.25 (((iftrueProp1) =>
% 103.13/17.25 (((iftrueProp2) =>
% 103.13/17.25 (((ifSingleton) =>
% 103.13/17.25 (((ifp) =>
% 103.13/17.25 (((theeq) =>
% 103.13/17.25 (((iftrue) =>
% 103.13/17.25 ((
% 103.13/17.25 (iffalse) =>
% 103.13/17.25 ((
% 103.13/17.25 (iftrueorfalse) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (setminusT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (setextT) =>
% 103.13/17.25 ((
% 103.13/17.25 (subsetTI) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTELcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTERcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT1) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT2) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT3) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub2) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementEq) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTnotintersectT) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementImpComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementSubsetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementInPowersetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (contraSubsetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTcontraSubset) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTILcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTIRcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpNotIn1) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTE) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTEcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule0) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_5) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all2) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1SetBreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (choice2fnsingleton) =>
% 103.13/17.25 ((
% 103.13/17.25 (setOfPairsIsBReln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all1) =>
% 103.13/17.25 ((
% 103.13/17.25 (subbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (eqbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compEex) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIL) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIR) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionEcases) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionCommutes) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2W) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2A) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2B) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex1) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Equiv) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1E) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1I) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncInInjFuncSet) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncInj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (leftInvIsSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjCantorThm) =>
% 103.13/17.25 ((
% 103.13/17.25 (foundation2) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself2) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSp) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSclos) =>
% 103.13/17.25 ((
% 103.13/17.25 (peano0notS) =>
% 103.13/17.25 ((
% 103.13/17.25 (peanoSinj) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp2) =>
% 103.13/17.25 ((
% 103.13/17.25 (setunionTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (ordinalMinLem1) =>
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y0 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (ordinal @
% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y1 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y2 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y2 @
% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @
% 103.13/17.25 Y2) =>
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1678])).
% 103.13/17.25 thf(zip_derived_cl1697, plain,
% 103.13/17.25 (~ (((lamp) =>
% 103.13/17.25 (((lam2p) =>
% 103.13/17.25 (((brelnall1) =>
% 103.13/17.25 (((brelnall2) =>
% 103.13/17.25 (((ex1E2) =>
% 103.13/17.25 (((funcGraphProp1) =>
% 103.13/17.25 (((funcGraphProp3) =>
% 103.13/17.25 (((funcGraphProp2) =>
% 103.13/17.25 (((funcextLem) =>
% 103.13/17.25 (((funcGraphProp4) =>
% 103.13/17.25 (((subbreln) =>
% 103.13/17.25 (((eqbreln) =>
% 103.13/17.25 (((funcext) =>
% 103.13/17.25 (((funcext2) =>
% 103.13/17.25 (((ap2apEq1) =>
% 103.13/17.25 (((ap2apEq2) =>
% 103.13/17.25 (((beta1) =>
% 103.13/17.25 (((eta1) =>
% 103.13/17.25 (((lam2lamEq) =>
% 103.13/17.25 (((beta2) =>
% 103.13/17.25 (((eta2) =>
% 103.13/17.25 (((iffalseProp1) =>
% 103.13/17.25 (((iffalseProp2) =>
% 103.13/17.25 (((iftrueProp1) =>
% 103.13/17.25 (((iftrueProp2) =>
% 103.13/17.25 (((ifSingleton) =>
% 103.13/17.25 (((ifp) =>
% 103.13/17.25 (((theeq) =>
% 103.13/17.25 (((iftrue) =>
% 103.13/17.25 (((iffalse) =>
% 103.13/17.25 ((
% 103.13/17.25 (iftrueorfalse) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (setminusT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (setextT) =>
% 103.13/17.25 ((
% 103.13/17.25 (subsetTI) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTELcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTERcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT1) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT2) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT3) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub2) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementEq) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTnotintersectT) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementImpComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementSubsetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementInPowersetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (contraSubsetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTcontraSubset) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTILcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTIRcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpNotIn1) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTE) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTEcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule0) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_5) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all2) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1SetBreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (choice2fnsingleton) =>
% 103.13/17.25 ((
% 103.13/17.25 (setOfPairsIsBReln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all1) =>
% 103.13/17.25 ((
% 103.13/17.25 (subbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (eqbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compEex) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIL) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIR) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionEcases) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionCommutes) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2W) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2A) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2B) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex1) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Equiv) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1E) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1I) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncInInjFuncSet) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncInj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (leftInvIsSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjCantorThm) =>
% 103.13/17.25 ((
% 103.13/17.25 (foundation2) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself2) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSp) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSclos) =>
% 103.13/17.25 ((
% 103.13/17.25 (peano0notS) =>
% 103.13/17.25 ((
% 103.13/17.25 (peanoSinj) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp2) =>
% 103.13/17.25 ((
% 103.13/17.25 (setunionTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (ordinalMinLem1) =>
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y0 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (ordinal @
% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y1 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y2 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y2 @
% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @
% 103.13/17.25 Y2) =>
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1688])).
% 103.13/17.25 thf(zip_derived_cl1706, plain,
% 103.13/17.25 (~ (((lam2p) =>
% 103.13/17.25 (((brelnall1) =>
% 103.13/17.25 (((brelnall2) =>
% 103.13/17.25 (((ex1E2) =>
% 103.13/17.25 (((funcGraphProp1) =>
% 103.13/17.25 (((funcGraphProp3) =>
% 103.13/17.25 (((funcGraphProp2) =>
% 103.13/17.25 (((funcextLem) =>
% 103.13/17.25 (((funcGraphProp4) =>
% 103.13/17.25 (((subbreln) =>
% 103.13/17.25 (((eqbreln) =>
% 103.13/17.25 (((funcext) =>
% 103.13/17.25 (((funcext2) =>
% 103.13/17.25 (((ap2apEq1) =>
% 103.13/17.25 (((ap2apEq2) =>
% 103.13/17.25 (((beta1) =>
% 103.13/17.25 (((eta1) =>
% 103.13/17.25 (((lam2lamEq) =>
% 103.13/17.25 (((beta2) =>
% 103.13/17.25 (((eta2) =>
% 103.13/17.25 (((iffalseProp1) =>
% 103.13/17.25 (((iffalseProp2) =>
% 103.13/17.25 (((iftrueProp1) =>
% 103.13/17.25 (((iftrueProp2) =>
% 103.13/17.25 (((ifSingleton) =>
% 103.13/17.25 (((ifp) =>
% 103.13/17.25 (((theeq) =>
% 103.13/17.25 (((iftrue) =>
% 103.13/17.25 (((iffalse) =>
% 103.13/17.25 (((iftrueorfalse) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (setminusT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (setextT) =>
% 103.13/17.25 ((
% 103.13/17.25 (subsetTI) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTELcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTERcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT1) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT2) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT3) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub2) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementEq) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTnotintersectT) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementImpComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementSubsetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementInPowersetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (contraSubsetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTcontraSubset) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTILcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTIRcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpNotIn1) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTE) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTEcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule0) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_5) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all2) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1SetBreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (choice2fnsingleton) =>
% 103.13/17.25 ((
% 103.13/17.25 (setOfPairsIsBReln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all1) =>
% 103.13/17.25 ((
% 103.13/17.25 (subbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (eqbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compEex) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIL) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIR) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionEcases) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionCommutes) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2W) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2A) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2B) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex1) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Equiv) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1E) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1I) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncInInjFuncSet) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncInj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (leftInvIsSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjCantorThm) =>
% 103.13/17.25 ((
% 103.13/17.25 (foundation2) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself2) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSp) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSclos) =>
% 103.13/17.25 ((
% 103.13/17.25 (peano0notS) =>
% 103.13/17.25 ((
% 103.13/17.25 (peanoSinj) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp2) =>
% 103.13/17.25 ((
% 103.13/17.25 (setunionTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (ordinalMinLem1) =>
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y0 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (ordinal @
% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y1 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y2 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y2 @
% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @
% 103.13/17.25 Y2) =>
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1697])).
% 103.13/17.25 thf(zip_derived_cl1716, plain,
% 103.13/17.25 (~ (((brelnall1) =>
% 103.13/17.25 (((brelnall2) =>
% 103.13/17.25 (((ex1E2) =>
% 103.13/17.25 (((funcGraphProp1) =>
% 103.13/17.25 (((funcGraphProp3) =>
% 103.13/17.25 (((funcGraphProp2) =>
% 103.13/17.25 (((funcextLem) =>
% 103.13/17.25 (((funcGraphProp4) =>
% 103.13/17.25 (((subbreln) =>
% 103.13/17.25 (((eqbreln) =>
% 103.13/17.25 (((funcext) =>
% 103.13/17.25 (((funcext2) =>
% 103.13/17.25 (((ap2apEq1) =>
% 103.13/17.25 (((ap2apEq2) =>
% 103.13/17.25 (((beta1) =>
% 103.13/17.25 (((eta1) =>
% 103.13/17.25 (((lam2lamEq) =>
% 103.13/17.25 (((beta2) =>
% 103.13/17.25 (((eta2) =>
% 103.13/17.25 (((iffalseProp1) =>
% 103.13/17.25 (((iffalseProp2) =>
% 103.13/17.25 (((iftrueProp1) =>
% 103.13/17.25 (((iftrueProp2) =>
% 103.13/17.25 (((ifSingleton) =>
% 103.13/17.25 (((ifp) =>
% 103.13/17.25 (((theeq) =>
% 103.13/17.25 (((iftrue) =>
% 103.13/17.25 (((iffalse) =>
% 103.13/17.25 (((iftrueorfalse) =>
% 103.13/17.25 (((binintersectT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (setminusT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (setextT) =>
% 103.13/17.25 ((
% 103.13/17.25 (subsetTI) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTELcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTERcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT1) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT2) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT3) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub2) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementEq) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTnotintersectT) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementImpComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementSubsetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementInPowersetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (contraSubsetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTcontraSubset) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTILcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTIRcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpNotIn1) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTE) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTEcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule0) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_5) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all2) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1SetBreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (choice2fnsingleton) =>
% 103.13/17.25 ((
% 103.13/17.25 (setOfPairsIsBReln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all1) =>
% 103.13/17.25 ((
% 103.13/17.25 (subbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (eqbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compEex) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIL) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIR) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionEcases) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionCommutes) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2W) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2A) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2B) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex1) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Equiv) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1E) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1I) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncInInjFuncSet) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncInj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (leftInvIsSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjCantorThm) =>
% 103.13/17.25 ((
% 103.13/17.25 (foundation2) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself2) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSp) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSclos) =>
% 103.13/17.25 ((
% 103.13/17.25 (peano0notS) =>
% 103.13/17.25 ((
% 103.13/17.25 (peanoSinj) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp2) =>
% 103.13/17.25 ((
% 103.13/17.25 (setunionTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (ordinalMinLem1) =>
% 103.13/17.25 ((
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% 103.13/17.25 ^[Y0 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (ordinal @
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% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y1 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y2 : $i]:
% 103.13/17.25 ((
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% 103.13/17.25 Y2 @
% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @
% 103.13/17.25 Y2) =>
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1706])).
% 103.13/17.25 thf(zip_derived_cl1725, plain,
% 103.13/17.25 (~ (((brelnall2) =>
% 103.13/17.25 (((ex1E2) =>
% 103.13/17.25 (((funcGraphProp1) =>
% 103.13/17.25 (((funcGraphProp3) =>
% 103.13/17.25 (((funcGraphProp2) =>
% 103.13/17.25 (((funcextLem) =>
% 103.13/17.25 (((funcGraphProp4) =>
% 103.13/17.25 (((subbreln) =>
% 103.13/17.25 (((eqbreln) =>
% 103.13/17.25 (((funcext) =>
% 103.13/17.25 (((funcext2) =>
% 103.13/17.25 (((ap2apEq1) =>
% 103.13/17.25 (((ap2apEq2) =>
% 103.13/17.25 (((beta1) =>
% 103.13/17.25 (((eta1) =>
% 103.13/17.25 (((lam2lamEq) =>
% 103.13/17.25 (((beta2) =>
% 103.13/17.25 (((eta2) =>
% 103.13/17.25 (((iffalseProp1) =>
% 103.13/17.25 (((iffalseProp2) =>
% 103.13/17.25 (((iftrueProp1) =>
% 103.13/17.25 (((iftrueProp2) =>
% 103.13/17.25 (((ifSingleton) =>
% 103.13/17.25 (((ifp) =>
% 103.13/17.25 (((theeq) =>
% 103.13/17.25 (((iftrue) =>
% 103.13/17.25 (((iffalse) =>
% 103.13/17.25 (((iftrueorfalse) =>
% 103.13/17.25 (((binintersectT_lem) =>
% 103.13/17.25 (((binunionT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (setminusT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementT_lem) =>
% 103.13/17.25 ((
% 103.13/17.25 (setextT) =>
% 103.13/17.25 ((
% 103.13/17.25 (subsetTI) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTELcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTERcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT1) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT2) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT3) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub2) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementEq) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTnotintersectT) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementImpComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementSubsetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementInPowersetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (contraSubsetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTcontraSubset) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTILcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTIRcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpNotIn1) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTE) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTEcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule0) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_5) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all2) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1SetBreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (choice2fnsingleton) =>
% 103.13/17.25 ((
% 103.13/17.25 (setOfPairsIsBReln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all1) =>
% 103.13/17.25 ((
% 103.13/17.25 (subbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (eqbreln1) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (breln1invI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compEex) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIL) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIR) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionEcases) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionCommutes) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2W) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2A) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2B) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex1) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Equiv) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1E) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1I) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncInInjFuncSet) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncInj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (leftInvIsSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjCantorThm) =>
% 103.13/17.25 ((
% 103.13/17.25 (foundation2) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself2) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSp) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSclos) =>
% 103.13/17.25 ((
% 103.13/17.25 (peano0notS) =>
% 103.13/17.25 ((
% 103.13/17.25 (peanoSinj) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp1) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (setunionTransitive) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ^[Y0 : $i]:
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 (in @
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% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1716])).
% 103.13/17.25 thf(zip_derived_cl1734, plain,
% 103.13/17.25 (~ (((ex1E2) =>
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% 103.13/17.25 (((beta2) =>
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (binintersectTERcontra) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT1) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT2) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT3) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub2) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementEq) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTnotintersectT) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementImpComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementSubsetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementInPowersetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (contraSubsetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTcontraSubset) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (binunionTIRcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpNotIn1) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTE) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTEcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule0) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_5) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all2) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1SetBreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (choice2fnsingleton) =>
% 103.13/17.25 ((
% 103.13/17.25 (setOfPairsIsBReln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all1) =>
% 103.13/17.25 ((
% 103.13/17.25 (subbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (eqbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compEex) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIL) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIR) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionEcases) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionCommutes) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2W) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (image1E) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1I) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncInInjFuncSet) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncInj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (leftInvIsSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjCantorThm) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (notinself) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself2) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSp) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSclos) =>
% 103.13/17.25 ((
% 103.13/17.25 (peano0notS) =>
% 103.13/17.25 ((
% 103.13/17.25 (peanoSinj) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp1) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 (!!) @ (
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% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @
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% 103.13/17.25 (in @
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% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1725])).
% 103.13/17.25 thf(zip_derived_cl1742, plain,
% 103.13/17.25 (~ (((funcGraphProp1) =>
% 103.13/17.25 (((funcGraphProp3) =>
% 103.13/17.25 (((funcGraphProp2) =>
% 103.13/17.25 (((funcextLem) =>
% 103.13/17.25 (((funcGraphProp4) =>
% 103.13/17.25 (((subbreln) =>
% 103.13/17.25 (((eqbreln) =>
% 103.13/17.25 (((funcext) =>
% 103.13/17.25 (((funcext2) =>
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% 103.13/17.25 (((ap2apEq2) =>
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% 103.13/17.25 (((eta1) =>
% 103.13/17.25 (((lam2lamEq) =>
% 103.13/17.25 (((beta2) =>
% 103.13/17.25 (((eta2) =>
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% 103.13/17.25 (((iffalseProp2) =>
% 103.13/17.25 (((iftrueProp1) =>
% 103.13/17.25 (((iftrueProp2) =>
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% 103.13/17.25 (((iftrue) =>
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% 103.13/17.25 (((binintersectT_lem) =>
% 103.13/17.25 (((binunionT_lem) =>
% 103.13/17.25 (((powersetT_lem) =>
% 103.13/17.25 (((setminusT_lem) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (setextT) =>
% 103.13/17.25 ((
% 103.13/17.25 (subsetTI) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTE1) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (binintersectTERcontra) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT1) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT2) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT3) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub2) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementEq) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTnotintersectT) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementImpComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementSubsetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementInPowersetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (contraSubsetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTcontraSubset) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTILcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTIRcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpNotIn1) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTE) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTEcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule0) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_5) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all2) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1SetBreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (choice2fnsingleton) =>
% 103.13/17.25 ((
% 103.13/17.25 (setOfPairsIsBReln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all1) =>
% 103.13/17.25 ((
% 103.13/17.25 (subbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (eqbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compEex) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIL) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIR) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionEcases) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionCommutes) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2W) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2A) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2B) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex1) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Equiv) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1E) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1I) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncInInjFuncSet) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncInj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (leftInvIsSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjCantorThm) =>
% 103.13/17.25 ((
% 103.13/17.25 (foundation2) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (notinself2) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (peanoSinj) =>
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1734])).
% 103.13/17.25 thf(zip_derived_cl1750, plain,
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub2) =>
% 103.13/17.25 ((
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% 103.13/17.25 (complementInPowersetComplementIntersect) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (binunionTIRcontra) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpNotIn1) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b2) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (woz1_5) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (breln1compEex) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIL) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIR) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionEcases) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionCommutes) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2W) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (image1Ex1) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Equiv) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1E) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1I) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncInInjFuncSet) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncInj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (leftInvIsSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjCantorThm) =>
% 103.13/17.25 ((
% 103.13/17.25 (foundation2) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself2) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSp) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSclos) =>
% 103.13/17.25 ((
% 103.13/17.25 (peano0notS) =>
% 103.13/17.25 ((
% 103.13/17.25 (peanoSinj) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp2) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y2 : $i]:
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @
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% 103.13/17.25 (in @
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% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1742])).
% 103.13/17.25 thf(zip_derived_cl1761, plain,
% 103.13/17.25 (~ (((funcGraphProp2) =>
% 103.13/17.25 (((funcextLem) =>
% 103.13/17.25 (((funcGraphProp4) =>
% 103.13/17.25 (((subbreln) =>
% 103.13/17.25 (((eqbreln) =>
% 103.13/17.25 (((funcext) =>
% 103.13/17.25 (((funcext2) =>
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% 103.13/17.25 (((ap2apEq2) =>
% 103.13/17.25 (((beta1) =>
% 103.13/17.25 (((eta1) =>
% 103.13/17.25 (((lam2lamEq) =>
% 103.13/17.25 (((beta2) =>
% 103.13/17.25 (((eta2) =>
% 103.13/17.25 (((iffalseProp1) =>
% 103.13/17.25 (((iffalseProp2) =>
% 103.13/17.25 (((iftrueProp1) =>
% 103.13/17.25 (((iftrueProp2) =>
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% 103.13/17.25 (((binunionT_lem) =>
% 103.13/17.25 (((powersetT_lem) =>
% 103.13/17.25 (((setminusT_lem) =>
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (powersetTI1) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (binintersectTERcontra) =>
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT2) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT3) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub2) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementEq) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTnotintersectT) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementImpComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementSubsetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementInPowersetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (contraSubsetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTcontraSubset) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTILcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTIRcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpNotIn1) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTE) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTEcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule0) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_5) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all2) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1SetBreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (choice2fnsingleton) =>
% 103.13/17.25 ((
% 103.13/17.25 (setOfPairsIsBReln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all1) =>
% 103.13/17.25 ((
% 103.13/17.25 (subbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (eqbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compEex) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIL) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIR) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionEcases) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionCommutes) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2W) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2A) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2B) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex1) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Equiv) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1E) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1I) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncInInjFuncSet) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncInj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (leftInvIsSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjCantorThm) =>
% 103.13/17.25 ((
% 103.13/17.25 (foundation2) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself2) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (omegaSclos) =>
% 103.13/17.25 ((
% 103.13/17.25 (peano0notS) =>
% 103.13/17.25 ((
% 103.13/17.25 (peanoSinj) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1750])).
% 103.13/17.25 thf(zip_derived_cl1771, plain,
% 103.13/17.25 (~ (((funcextLem) =>
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% 103.13/17.25 (((eta1) =>
% 103.13/17.25 (((lam2lamEq) =>
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementEq) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTnotintersectT) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (breln1all2) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1SetBreln1) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIL) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIR) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionEcases) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionCommutes) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (image1I) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncInInjFuncSet) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncInj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (leftInvIsSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjCantorThm) =>
% 103.13/17.25 ((
% 103.13/17.25 (foundation2) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself2) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSp) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSclos) =>
% 103.13/17.25 ((
% 103.13/17.25 (peano0notS) =>
% 103.13/17.25 ((
% 103.13/17.25 (peanoSinj) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp2) =>
% 103.13/17.25 ((
% 103.13/17.25 (setunionTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (ordinalMinLem1) =>
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y0 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (ordinal @
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% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y1 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y2 : $i]:
% 103.13/17.25 ((
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% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @
% 103.13/17.25 Y2) =>
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1761])).
% 103.13/17.25 thf(zip_derived_cl1781, plain,
% 103.13/17.25 (~ (((funcGraphProp4) =>
% 103.13/17.25 (((subbreln) =>
% 103.13/17.25 (((eqbreln) =>
% 103.13/17.25 (((funcext) =>
% 103.13/17.25 (((funcext2) =>
% 103.13/17.25 (((ap2apEq1) =>
% 103.13/17.25 (((ap2apEq2) =>
% 103.13/17.25 (((beta1) =>
% 103.13/17.25 (((eta1) =>
% 103.13/17.25 (((lam2lamEq) =>
% 103.13/17.25 (((beta2) =>
% 103.13/17.25 (((eta2) =>
% 103.13/17.25 (((iffalseProp1) =>
% 103.13/17.25 (((iffalseProp2) =>
% 103.13/17.25 (((iftrueProp1) =>
% 103.13/17.25 (((iftrueProp2) =>
% 103.13/17.25 (((ifSingleton) =>
% 103.13/17.25 (((ifp) =>
% 103.13/17.25 (((theeq) =>
% 103.13/17.25 (((iftrue) =>
% 103.13/17.25 (((iffalse) =>
% 103.13/17.25 (((iftrueorfalse) =>
% 103.13/17.25 (((binintersectT_lem) =>
% 103.13/17.25 (((binunionT_lem) =>
% 103.13/17.25 (((powersetT_lem) =>
% 103.13/17.25 (((setminusT_lem) =>
% 103.13/17.25 (((complementT_lem) =>
% 103.13/17.25 (((setextT) =>
% 103.13/17.25 (((subsetTI) =>
% 103.13/17.25 (((powersetTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (powersetTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTELcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTERcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT1) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT2) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT3) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub2) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementEq) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTnotintersectT) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementImpComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementSubsetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementInPowersetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (contraSubsetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTcontraSubset) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTILcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTIRcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpNotIn1) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTE) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTEcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule0) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_5) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all2) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1SetBreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (choice2fnsingleton) =>
% 103.13/17.25 ((
% 103.13/17.25 (setOfPairsIsBReln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all1) =>
% 103.13/17.25 ((
% 103.13/17.25 (subbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (eqbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compEex) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIL) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIR) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionEcases) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionCommutes) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2W) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2A) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2B) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex1) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Equiv) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1E) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1I) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncInInjFuncSet) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncInj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (leftInvIsSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjCantorThm) =>
% 103.13/17.25 ((
% 103.13/17.25 (foundation2) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself2) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSp) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSclos) =>
% 103.13/17.25 ((
% 103.13/17.25 (peano0notS) =>
% 103.13/17.25 ((
% 103.13/17.25 (peanoSinj) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp2) =>
% 103.13/17.25 ((
% 103.13/17.25 (setunionTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (ordinalMinLem1) =>
% 103.13/17.25 ((
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% 103.13/17.25 ^[Y0 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (ordinal @
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% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y1 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y2 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (in @
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% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @
% 103.13/17.25 Y2) =>
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1771])).
% 103.13/17.25 thf(zip_derived_cl1790, plain,
% 103.13/17.25 (~ (((subbreln) =>
% 103.13/17.25 (((eqbreln) =>
% 103.13/17.25 (((funcext) =>
% 103.13/17.25 (((funcext2) =>
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% 103.13/17.25 (((ap2apEq2) =>
% 103.13/17.25 (((beta1) =>
% 103.13/17.25 (((eta1) =>
% 103.13/17.25 (((lam2lamEq) =>
% 103.13/17.25 (((beta2) =>
% 103.13/17.25 (((eta2) =>
% 103.13/17.25 (((iffalseProp1) =>
% 103.13/17.25 (((iffalseProp2) =>
% 103.13/17.25 (((iftrueProp1) =>
% 103.13/17.25 (((iftrueProp2) =>
% 103.13/17.25 (((ifSingleton) =>
% 103.13/17.25 (((ifp) =>
% 103.13/17.25 (((theeq) =>
% 103.13/17.25 (((iftrue) =>
% 103.13/17.25 (((iffalse) =>
% 103.13/17.25 (((iftrueorfalse) =>
% 103.13/17.25 (((binintersectT_lem) =>
% 103.13/17.25 (((binunionT_lem) =>
% 103.13/17.25 (((powersetT_lem) =>
% 103.13/17.25 (((setminusT_lem) =>
% 103.13/17.25 (((complementT_lem) =>
% 103.13/17.25 (((setextT) =>
% 103.13/17.25 (((subsetTI) =>
% 103.13/17.25 (((powersetTI1) =>
% 103.13/17.25 (((powersetTE1) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT2) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT3) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub2) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementEq) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTnotintersectT) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementImpComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementSubsetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementInPowersetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (contraSubsetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTcontraSubset) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (binunionTIRcontra) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpNotIn1) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTE) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTEcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1b) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (woz1_4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_5) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all2) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1SetBreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (choice2fnsingleton) =>
% 103.13/17.25 ((
% 103.13/17.25 (setOfPairsIsBReln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all1) =>
% 103.13/17.25 ((
% 103.13/17.25 (subbreln1) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (breln1invE) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (breln1compE) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIL) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIR) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionEcases) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionCommutes) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2W) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (image1Ex1) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Equiv) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1E) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1I) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncInInjFuncSet) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncInj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (leftInvIsSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjCantorThm) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (notinself2) =>
% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
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% 103.13/17.25 ((
% 103.13/17.25 (setunionTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (ordinalMinLem1) =>
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y0 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (ordinal @
% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y1 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y2 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y2 @
% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @
% 103.13/17.25 Y2) =>
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1781])).
% 103.13/17.25 thf(zip_derived_cl1800, plain,
% 103.13/17.25 (~ (((eqbreln) =>
% 103.13/17.25 (((funcext) =>
% 103.13/17.25 (((funcext2) =>
% 103.13/17.25 (((ap2apEq1) =>
% 103.13/17.25 (((ap2apEq2) =>
% 103.13/17.25 (((beta1) =>
% 103.13/17.25 (((eta1) =>
% 103.13/17.25 (((lam2lamEq) =>
% 103.13/17.25 (((beta2) =>
% 103.13/17.25 (((eta2) =>
% 103.13/17.25 (((iffalseProp1) =>
% 103.13/17.25 (((iffalseProp2) =>
% 103.13/17.25 (((iftrueProp1) =>
% 103.13/17.25 (((iftrueProp2) =>
% 103.13/17.25 (((ifSingleton) =>
% 103.13/17.25 (((ifp) =>
% 103.13/17.25 (((theeq) =>
% 103.13/17.25 (((iftrue) =>
% 103.13/17.25 (((iffalse) =>
% 103.13/17.25 (((iftrueorfalse) =>
% 103.13/17.25 (((binintersectT_lem) =>
% 103.13/17.25 (((binunionT_lem) =>
% 103.13/17.25 (((powersetT_lem) =>
% 103.13/17.25 (((setminusT_lem) =>
% 103.13/17.25 (((complementT_lem) =>
% 103.13/17.25 (((setextT) =>
% 103.13/17.25 (((subsetTI) =>
% 103.13/17.25 (((powersetTI1) =>
% 103.13/17.25 (((powersetTE1) =>
% 103.13/17.25 (((complementTI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTELcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTERcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT1) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT2) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT3) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub2) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementEq) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTnotintersectT) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementImpComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementSubsetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementInPowersetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (contraSubsetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTcontraSubset) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTILcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTIRcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpNotIn1) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTE) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTEcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule0) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_5) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all2) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1SetBreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (choice2fnsingleton) =>
% 103.13/17.25 ((
% 103.13/17.25 (setOfPairsIsBReln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1all1) =>
% 103.13/17.25 ((
% 103.13/17.25 (subbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (eqbreln1) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1invE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1compEex) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionprop) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIL) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionIR) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionI) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionE) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionEcases) =>
% 103.13/17.25 ((
% 103.13/17.25 (breln1unionCommutes) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2W) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2A) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz2B) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Ex1) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1Equiv) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1E) =>
% 103.13/17.25 ((
% 103.13/17.25 (image1I) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncInInjFuncSet) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (injFuncSetFuncInj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncIn) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjFuncSetFuncSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (leftInvIsSurj) =>
% 103.13/17.25 ((
% 103.13/17.25 (surjCantorThm) =>
% 103.13/17.25 ((
% 103.13/17.25 (foundation2) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself) =>
% 103.13/17.25 ((
% 103.13/17.25 (notinself2) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSp) =>
% 103.13/17.25 ((
% 103.13/17.25 (omegaSclos) =>
% 103.13/17.25 ((
% 103.13/17.25 (peano0notS) =>
% 103.13/17.25 ((
% 103.13/17.25 (peanoSinj) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (transitivesetOp2) =>
% 103.13/17.25 ((
% 103.13/17.25 (setunionTransitive) =>
% 103.13/17.25 ((
% 103.13/17.25 (ordinalMinLem1) =>
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y0 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (ordinal @
% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y1 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (!!) @ (
% 103.13/17.25 ^[Y2 : $i]:
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y2 @
% 103.13/17.25 Y0) =>
% 103.13/17.25 ((
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @
% 103.13/17.25 Y2) =>
% 103.13/17.25 (in @
% 103.13/17.25 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1790])).
% 103.13/17.25 thf(zip_derived_cl1812, plain,
% 103.13/17.25 (~ (((funcext) =>
% 103.13/17.25 (((funcext2) =>
% 103.13/17.25 (((ap2apEq1) =>
% 103.13/17.25 (((ap2apEq2) =>
% 103.13/17.25 (((beta1) =>
% 103.13/17.25 (((eta1) =>
% 103.13/17.25 (((lam2lamEq) =>
% 103.13/17.25 (((beta2) =>
% 103.13/17.25 (((eta2) =>
% 103.13/17.25 (((iffalseProp1) =>
% 103.13/17.25 (((iffalseProp2) =>
% 103.13/17.25 (((iftrueProp1) =>
% 103.13/17.25 (((iftrueProp2) =>
% 103.13/17.25 (((ifSingleton) =>
% 103.13/17.25 (((ifp) =>
% 103.13/17.25 (((theeq) =>
% 103.13/17.25 (((iftrue) =>
% 103.13/17.25 (((iffalse) =>
% 103.13/17.25 (((iftrueorfalse) =>
% 103.13/17.25 (((binintersectT_lem) =>
% 103.13/17.25 (((binunionT_lem) =>
% 103.13/17.25 (((powersetT_lem) =>
% 103.13/17.25 (((setminusT_lem) =>
% 103.13/17.25 (((complementT_lem) =>
% 103.13/17.25 (((setextT) =>
% 103.13/17.25 (((subsetTI) =>
% 103.13/17.25 (((powersetTI1) =>
% 103.13/17.25 (((powersetTE1) =>
% 103.13/17.25 (((complementTI1) =>
% 103.13/17.25 (((complementTE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTELcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binintersectTERcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT1) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT2) =>
% 103.13/17.25 ((
% 103.13/17.25 (contrasubsetT3) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementI1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementE1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub1) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementSub2) =>
% 103.13/17.25 ((
% 103.13/17.25 (doubleComplementEq) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTnotintersectT) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementImpComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementSubsetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementInPowersetComplementIntersect) =>
% 103.13/17.25 ((
% 103.13/17.25 (contraSubsetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementTcontraSubset) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTILcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTIRcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInUnion2) =>
% 103.13/17.25 ((
% 103.13/17.25 (inIntersectImpInIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (intersectInPowersetIntersectUnions) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpNotIn1) =>
% 103.13/17.25 ((
% 103.13/17.25 (inComplementUnionImpInComplement1) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTE) =>
% 103.13/17.25 ((
% 103.13/17.25 (binunionTEcontra) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a1) =>
% 103.13/17.25 ((
% 103.13/17.25 (complementUnionInPowersetComplement) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan1) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2a) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b2) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2b) =>
% 103.13/17.25 ((
% 103.13/17.25 (demorgan2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule0) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule1) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule2) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule3) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz13rule4) =>
% 103.13/17.25 ((
% 103.13/17.25 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (ordinalMinLem1) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y1 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y2 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y2 @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @
% 103.13/17.26 Y2) =>
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1800])).
% 103.13/17.26 thf(zip_derived_cl1826, plain,
% 103.13/17.26 (~ (((funcext2) =>
% 103.13/17.26 (((ap2apEq1) =>
% 103.13/17.26 (((ap2apEq2) =>
% 103.13/17.26 (((beta1) =>
% 103.13/17.26 (((eta1) =>
% 103.13/17.26 (((lam2lamEq) =>
% 103.13/17.26 (((beta2) =>
% 103.13/17.26 (((eta2) =>
% 103.13/17.26 (((iffalseProp1) =>
% 103.13/17.26 (((iffalseProp2) =>
% 103.13/17.26 (((iftrueProp1) =>
% 103.13/17.26 (((iftrueProp2) =>
% 103.13/17.26 (((ifSingleton) =>
% 103.13/17.26 (((ifp) =>
% 103.13/17.26 (((theeq) =>
% 103.13/17.26 (((iftrue) =>
% 103.13/17.26 (((iffalse) =>
% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintersectTERcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT1) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT2) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT3) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementI1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementE1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub2) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementEq) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTnotintersectT) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementImpComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTILcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (ordinalMinLem1) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y1 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y2 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y2 @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @
% 103.13/17.26 Y2) =>
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1812])).
% 103.13/17.26 thf(zip_derived_cl1841, plain,
% 103.13/17.26 (~ (((ap2apEq1) =>
% 103.13/17.26 (((ap2apEq2) =>
% 103.13/17.26 (((beta1) =>
% 103.13/17.26 (((eta1) =>
% 103.13/17.26 (((lam2lamEq) =>
% 103.13/17.26 (((beta2) =>
% 103.13/17.26 (((eta2) =>
% 103.13/17.26 (((iffalseProp1) =>
% 103.13/17.26 (((iffalseProp2) =>
% 103.13/17.26 (((iftrueProp1) =>
% 103.13/17.26 (((iftrueProp2) =>
% 103.13/17.26 (((ifSingleton) =>
% 103.13/17.26 (((ifp) =>
% 103.13/17.26 (((theeq) =>
% 103.13/17.26 (((iftrue) =>
% 103.13/17.26 (((iffalse) =>
% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT1) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT2) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT3) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementI1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementE1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub2) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementEq) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTnotintersectT) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementImpComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTILcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (ordinalMinLem1) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y1 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y2 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y2 @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @
% 103.13/17.26 Y2) =>
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1826])).
% 103.13/17.26 thf(zip_derived_cl1857, plain,
% 103.13/17.26 (~ (((ap2apEq2) =>
% 103.13/17.26 (((beta1) =>
% 103.13/17.26 (((eta1) =>
% 103.13/17.26 (((lam2lamEq) =>
% 103.13/17.26 (((beta2) =>
% 103.13/17.26 (((eta2) =>
% 103.13/17.26 (((iffalseProp1) =>
% 103.13/17.26 (((iffalseProp2) =>
% 103.13/17.26 (((iftrueProp1) =>
% 103.13/17.26 (((iftrueProp2) =>
% 103.13/17.26 (((ifSingleton) =>
% 103.13/17.26 (((ifp) =>
% 103.13/17.26 (((theeq) =>
% 103.13/17.26 (((iftrue) =>
% 103.13/17.26 (((iffalse) =>
% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 (((contrasubsetT) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT1) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT2) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT3) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementI1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementE1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub2) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementEq) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTnotintersectT) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementImpComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTILcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (ordinalMinLem1) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y1 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y2 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y2 @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @
% 103.13/17.26 Y2) =>
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1841])).
% 103.13/17.26 thf(zip_derived_cl1874, plain,
% 103.13/17.26 (~ (((beta1) =>
% 103.13/17.26 (((eta1) =>
% 103.13/17.26 (((lam2lamEq) =>
% 103.13/17.26 (((beta2) =>
% 103.13/17.26 (((eta2) =>
% 103.13/17.26 (((iffalseProp1) =>
% 103.13/17.26 (((iffalseProp2) =>
% 103.13/17.26 (((iftrueProp1) =>
% 103.13/17.26 (((iftrueProp2) =>
% 103.13/17.26 (((ifSingleton) =>
% 103.13/17.26 (((ifp) =>
% 103.13/17.26 (((theeq) =>
% 103.13/17.26 (((iftrue) =>
% 103.13/17.26 (((iffalse) =>
% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 (((contrasubsetT) =>
% 103.13/17.26 (((contrasubsetT1) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT2) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT3) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementI1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementE1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub2) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementEq) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTnotintersectT) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementImpComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTILcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (ordinalMinLem1) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y1 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y2 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y2 @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @
% 103.13/17.26 Y2) =>
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1857])).
% 103.13/17.26 thf(zip_derived_cl1890, plain,
% 103.13/17.26 (~ (((eta1) =>
% 103.13/17.26 (((lam2lamEq) =>
% 103.13/17.26 (((beta2) =>
% 103.13/17.26 (((eta2) =>
% 103.13/17.26 (((iffalseProp1) =>
% 103.13/17.26 (((iffalseProp2) =>
% 103.13/17.26 (((iftrueProp1) =>
% 103.13/17.26 (((iftrueProp2) =>
% 103.13/17.26 (((ifSingleton) =>
% 103.13/17.26 (((ifp) =>
% 103.13/17.26 (((theeq) =>
% 103.13/17.26 (((iftrue) =>
% 103.13/17.26 (((iffalse) =>
% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 (((contrasubsetT) =>
% 103.13/17.26 (((contrasubsetT1) =>
% 103.13/17.26 (((contrasubsetT2) =>
% 103.13/17.26 ((
% 103.13/17.26 (contrasubsetT3) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementI1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementE1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub2) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementEq) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTnotintersectT) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementImpComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTILcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (ordinalMinLem1) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y1 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y2 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y2 @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @
% 103.13/17.26 Y2) =>
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1874])).
% 103.13/17.26 thf(zip_derived_cl1903, plain,
% 103.13/17.26 (~ (((lam2lamEq) =>
% 103.13/17.26 (((beta2) =>
% 103.13/17.26 (((eta2) =>
% 103.13/17.26 (((iffalseProp1) =>
% 103.13/17.26 (((iffalseProp2) =>
% 103.13/17.26 (((iftrueProp1) =>
% 103.13/17.26 (((iftrueProp2) =>
% 103.13/17.26 (((ifSingleton) =>
% 103.13/17.26 (((ifp) =>
% 103.13/17.26 (((theeq) =>
% 103.13/17.26 (((iftrue) =>
% 103.13/17.26 (((iffalse) =>
% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 (((contrasubsetT) =>
% 103.13/17.26 (((contrasubsetT1) =>
% 103.13/17.26 (((contrasubsetT2) =>
% 103.13/17.26 (((contrasubsetT3) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementI1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementE1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub2) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementEq) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTnotintersectT) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementImpComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTILcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (ordinalMinLem1) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y1 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y2 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y2 @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @
% 103.13/17.26 Y2) =>
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1890])).
% 103.13/17.26 thf(zip_derived_cl1916, plain,
% 103.13/17.26 (~ (((beta2) =>
% 103.13/17.26 (((eta2) =>
% 103.13/17.26 (((iffalseProp1) =>
% 103.13/17.26 (((iffalseProp2) =>
% 103.13/17.26 (((iftrueProp1) =>
% 103.13/17.26 (((iftrueProp2) =>
% 103.13/17.26 (((ifSingleton) =>
% 103.13/17.26 (((ifp) =>
% 103.13/17.26 (((theeq) =>
% 103.13/17.26 (((iftrue) =>
% 103.13/17.26 (((iffalse) =>
% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 (((contrasubsetT) =>
% 103.13/17.26 (((contrasubsetT1) =>
% 103.13/17.26 (((contrasubsetT2) =>
% 103.13/17.26 (((contrasubsetT3) =>
% 103.13/17.26 (((doubleComplementI1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementE1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub2) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementEq) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTnotintersectT) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementImpComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTILcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
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% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y1 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y2 : $i]:
% 103.13/17.26 ((
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% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @
% 103.13/17.26 Y2) =>
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1903])).
% 103.13/17.26 thf(zip_derived_cl1930, plain,
% 103.13/17.26 (~ (((eta2) =>
% 103.13/17.26 (((iffalseProp1) =>
% 103.13/17.26 (((iffalseProp2) =>
% 103.13/17.26 (((iftrueProp1) =>
% 103.13/17.26 (((iftrueProp2) =>
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% 103.13/17.26 (((ifp) =>
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% 103.13/17.26 (((iffalse) =>
% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 (((contrasubsetT) =>
% 103.13/17.26 (((contrasubsetT1) =>
% 103.13/17.26 (((contrasubsetT2) =>
% 103.13/17.26 (((contrasubsetT3) =>
% 103.13/17.26 (((doubleComplementI1) =>
% 103.13/17.26 (((doubleComplementE1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub2) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementEq) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTnotintersectT) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementImpComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
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% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1916])).
% 103.13/17.26 thf(zip_derived_cl1945, plain,
% 103.13/17.26 (~ (((iffalseProp1) =>
% 103.13/17.26 (((iffalseProp2) =>
% 103.13/17.26 (((iftrueProp1) =>
% 103.13/17.26 (((iftrueProp2) =>
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% 103.13/17.26 (((ifp) =>
% 103.13/17.26 (((theeq) =>
% 103.13/17.26 (((iftrue) =>
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% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 (((contrasubsetT) =>
% 103.13/17.26 (((contrasubsetT1) =>
% 103.13/17.26 (((contrasubsetT2) =>
% 103.13/17.26 (((contrasubsetT3) =>
% 103.13/17.26 (((doubleComplementI1) =>
% 103.13/17.26 (((doubleComplementE1) =>
% 103.13/17.26 (((doubleComplementSub1) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementSub2) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementEq) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTnotintersectT) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementImpComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
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% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
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% 103.13/17.26 ((
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% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
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% 103.13/17.26 ((
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% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
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% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
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% 103.13/17.26 ((
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% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1930])).
% 103.13/17.26 thf(zip_derived_cl1960, plain,
% 103.13/17.26 (~ (((iffalseProp2) =>
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% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 (((contrasubsetT) =>
% 103.13/17.26 (((contrasubsetT1) =>
% 103.13/17.26 (((contrasubsetT2) =>
% 103.13/17.26 (((contrasubsetT3) =>
% 103.13/17.26 (((doubleComplementI1) =>
% 103.13/17.26 (((doubleComplementE1) =>
% 103.13/17.26 (((doubleComplementSub1) =>
% 103.13/17.26 (((doubleComplementSub2) =>
% 103.13/17.26 ((
% 103.13/17.26 (doubleComplementEq) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTnotintersectT) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementImpComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTILcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (ordinalMinLem1) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y1 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y2 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y2 @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @
% 103.13/17.26 Y2) =>
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1945])).
% 103.13/17.26 thf(zip_derived_cl1982, plain,
% 103.13/17.26 (~ (((iftrueProp1) =>
% 103.13/17.26 (((iftrueProp2) =>
% 103.13/17.26 (((ifSingleton) =>
% 103.13/17.26 (((ifp) =>
% 103.13/17.26 (((theeq) =>
% 103.13/17.26 (((iftrue) =>
% 103.13/17.26 (((iffalse) =>
% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 (((contrasubsetT) =>
% 103.13/17.26 (((contrasubsetT1) =>
% 103.13/17.26 (((contrasubsetT2) =>
% 103.13/17.26 (((contrasubsetT3) =>
% 103.13/17.26 (((doubleComplementI1) =>
% 103.13/17.26 (((doubleComplementE1) =>
% 103.13/17.26 (((doubleComplementSub1) =>
% 103.13/17.26 (((doubleComplementSub2) =>
% 103.13/17.26 (((doubleComplementEq) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTnotintersectT) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementImpComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTILcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (ordinalMinLem1) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y1 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y2 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y2 @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @
% 103.13/17.26 Y2) =>
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1960])).
% 103.13/17.26 thf(zip_derived_cl2001, plain,
% 103.13/17.26 (~ (((iftrueProp2) =>
% 103.13/17.26 (((ifSingleton) =>
% 103.13/17.26 (((ifp) =>
% 103.13/17.26 (((theeq) =>
% 103.13/17.26 (((iftrue) =>
% 103.13/17.26 (((iffalse) =>
% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 (((contrasubsetT) =>
% 103.13/17.26 (((contrasubsetT1) =>
% 103.13/17.26 (((contrasubsetT2) =>
% 103.13/17.26 (((contrasubsetT3) =>
% 103.13/17.26 (((doubleComplementI1) =>
% 103.13/17.26 (((doubleComplementE1) =>
% 103.13/17.26 (((doubleComplementSub1) =>
% 103.13/17.26 (((doubleComplementSub2) =>
% 103.13/17.26 (((doubleComplementEq) =>
% 103.13/17.26 (((complementTnotintersectT) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementImpComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTILcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (ordinalMinLem1) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y1 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y2 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y2 @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @
% 103.13/17.26 Y2) =>
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1982])).
% 103.13/17.26 thf(zip_derived_cl2017, plain,
% 103.13/17.26 (~ (((ifSingleton) =>
% 103.13/17.26 (((ifp) =>
% 103.13/17.26 (((theeq) =>
% 103.13/17.26 (((iftrue) =>
% 103.13/17.26 (((iffalse) =>
% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 (((contrasubsetT) =>
% 103.13/17.26 (((contrasubsetT1) =>
% 103.13/17.26 (((contrasubsetT2) =>
% 103.13/17.26 (((contrasubsetT3) =>
% 103.13/17.26 (((doubleComplementI1) =>
% 103.13/17.26 (((doubleComplementE1) =>
% 103.13/17.26 (((doubleComplementSub1) =>
% 103.13/17.26 (((doubleComplementSub2) =>
% 103.13/17.26 (((doubleComplementEq) =>
% 103.13/17.26 (((complementTnotintersectT) =>
% 103.13/17.26 (((complementImpComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTILcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (ordinalMinLem1) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y1 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y2 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y2 @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @
% 103.13/17.26 Y2) =>
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2001])).
% 103.13/17.26 thf(zip_derived_cl2029, plain,
% 103.13/17.26 (~ (((ifp) =>
% 103.13/17.26 (((theeq) =>
% 103.13/17.26 (((iftrue) =>
% 103.13/17.26 (((iffalse) =>
% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 (((contrasubsetT) =>
% 103.13/17.26 (((contrasubsetT1) =>
% 103.13/17.26 (((contrasubsetT2) =>
% 103.13/17.26 (((contrasubsetT3) =>
% 103.13/17.26 (((doubleComplementI1) =>
% 103.13/17.26 (((doubleComplementE1) =>
% 103.13/17.26 (((doubleComplementSub1) =>
% 103.13/17.26 (((doubleComplementSub2) =>
% 103.13/17.26 (((doubleComplementEq) =>
% 103.13/17.26 (((complementTnotintersectT) =>
% 103.13/17.26 (((complementImpComplementIntersect) =>
% 103.13/17.26 (((complementSubsetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTILcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.26 (foundation2) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself) =>
% 103.13/17.26 ((
% 103.13/17.26 (notinself2) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSp) =>
% 103.13/17.26 ((
% 103.13/17.26 (omegaSclos) =>
% 103.13/17.26 ((
% 103.13/17.26 (peano0notS) =>
% 103.13/17.26 ((
% 103.13/17.26 (peanoSinj) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binintTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (transitivesetOp2) =>
% 103.13/17.26 ((
% 103.13/17.26 (setunionTransitive) =>
% 103.13/17.26 ((
% 103.13/17.26 (ordinalMinLem1) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y0 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (ordinal @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y1 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (!!) @ (
% 103.13/17.26 ^[Y2 : $i]:
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y2 @
% 103.13/17.26 Y0) =>
% 103.13/17.26 ((
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @
% 103.13/17.26 Y2) =>
% 103.13/17.26 (in @
% 103.13/17.26 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2017])).
% 103.13/17.26 thf(zip_derived_cl2041, plain,
% 103.13/17.26 (~ (((theeq) =>
% 103.13/17.26 (((iftrue) =>
% 103.13/17.26 (((iffalse) =>
% 103.13/17.26 (((iftrueorfalse) =>
% 103.13/17.26 (((binintersectT_lem) =>
% 103.13/17.26 (((binunionT_lem) =>
% 103.13/17.26 (((powersetT_lem) =>
% 103.13/17.26 (((setminusT_lem) =>
% 103.13/17.26 (((complementT_lem) =>
% 103.13/17.26 (((setextT) =>
% 103.13/17.26 (((subsetTI) =>
% 103.13/17.26 (((powersetTI1) =>
% 103.13/17.26 (((powersetTE1) =>
% 103.13/17.26 (((complementTI1) =>
% 103.13/17.26 (((complementTE1) =>
% 103.13/17.26 (((binintersectTELcontra) =>
% 103.13/17.26 (((binintersectTERcontra) =>
% 103.13/17.26 (((contrasubsetT) =>
% 103.13/17.26 (((contrasubsetT1) =>
% 103.13/17.26 (((contrasubsetT2) =>
% 103.13/17.26 (((contrasubsetT3) =>
% 103.13/17.26 (((doubleComplementI1) =>
% 103.13/17.26 (((doubleComplementE1) =>
% 103.13/17.26 (((doubleComplementSub1) =>
% 103.13/17.26 (((doubleComplementSub2) =>
% 103.13/17.26 (((doubleComplementEq) =>
% 103.13/17.26 (((complementTnotintersectT) =>
% 103.13/17.26 (((complementImpComplementIntersect) =>
% 103.13/17.26 (((complementSubsetComplementIntersect) =>
% 103.13/17.26 (((complementInPowersetComplementIntersect) =>
% 103.13/17.26 ((
% 103.13/17.26 (contraSubsetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementTcontraSubset) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTILcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTIRcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInUnion2) =>
% 103.13/17.26 ((
% 103.13/17.26 (inIntersectImpInIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (intersectInPowersetIntersectUnions) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpNotIn1) =>
% 103.13/17.26 ((
% 103.13/17.26 (inComplementUnionImpInComplement1) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTE) =>
% 103.13/17.26 ((
% 103.13/17.26 (binunionTEcontra) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a1) =>
% 103.13/17.26 ((
% 103.13/17.26 (complementUnionInPowersetComplement) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan1) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2a) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b2) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2b) =>
% 103.13/17.26 ((
% 103.13/17.26 (demorgan2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule0) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz13rule4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_1) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_2) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_3) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_4) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz1_5) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all2) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1SetBreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (choice2fnsingleton) =>
% 103.13/17.26 ((
% 103.13/17.26 (setOfPairsIsBReln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1all1) =>
% 103.13/17.26 ((
% 103.13/17.26 (subbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (eqbreln1) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1invE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1compEex) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionprop) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIL) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionIR) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionI) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionE) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionEcases) =>
% 103.13/17.26 ((
% 103.13/17.26 (breln1unionCommutes) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2W) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2A) =>
% 103.13/17.26 ((
% 103.13/17.26 (woz2B) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Ex1) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1Equiv) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1E) =>
% 103.13/17.26 ((
% 103.13/17.26 (image1I) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncInInjFuncSet) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (injFuncSetFuncInj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncIn) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjFuncSetFuncSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (leftInvIsSurj) =>
% 103.13/17.26 ((
% 103.13/17.26 (surjCantorThm) =>
% 103.13/17.26 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2029])).
% 103.13/17.27 thf(zip_derived_cl2053, plain,
% 103.13/17.27 (~ (((iftrue) =>
% 103.13/17.27 (((iffalse) =>
% 103.13/17.27 (((iftrueorfalse) =>
% 103.13/17.27 (((binintersectT_lem) =>
% 103.13/17.27 (((binunionT_lem) =>
% 103.13/17.27 (((powersetT_lem) =>
% 103.13/17.27 (((setminusT_lem) =>
% 103.13/17.27 (((complementT_lem) =>
% 103.13/17.27 (((setextT) =>
% 103.13/17.27 (((subsetTI) =>
% 103.13/17.27 (((powersetTI1) =>
% 103.13/17.27 (((powersetTE1) =>
% 103.13/17.27 (((complementTI1) =>
% 103.13/17.27 (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementTcontraSubset) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTILcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTIRcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInUnion) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInUnion2) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (intersectInPowersetIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpNotIn1) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpInComplement1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTE) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTEcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a1) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2041])).
% 103.13/17.27 thf(zip_derived_cl2062, plain,
% 103.13/17.27 (~ (((iffalse) =>
% 103.13/17.27 (((iftrueorfalse) =>
% 103.13/17.27 (((binintersectT_lem) =>
% 103.13/17.27 (((binunionT_lem) =>
% 103.13/17.27 (((powersetT_lem) =>
% 103.13/17.27 (((setminusT_lem) =>
% 103.13/17.27 (((complementT_lem) =>
% 103.13/17.27 (((setextT) =>
% 103.13/17.27 (((subsetTI) =>
% 103.13/17.27 (((powersetTI1) =>
% 103.13/17.27 (((powersetTE1) =>
% 103.13/17.27 (((complementTI1) =>
% 103.13/17.27 (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTILcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTIRcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInUnion) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInUnion2) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (intersectInPowersetIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpNotIn1) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpInComplement1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTE) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTEcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a1) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2053])).
% 103.13/17.27 thf(zip_derived_cl2072, plain,
% 103.13/17.27 (~ (((iftrueorfalse) =>
% 103.13/17.27 (((binintersectT_lem) =>
% 103.13/17.27 (((binunionT_lem) =>
% 103.13/17.27 (((powersetT_lem) =>
% 103.13/17.27 (((setminusT_lem) =>
% 103.13/17.27 (((complementT_lem) =>
% 103.13/17.27 (((setextT) =>
% 103.13/17.27 (((subsetTI) =>
% 103.13/17.27 (((powersetTI1) =>
% 103.13/17.27 (((powersetTE1) =>
% 103.13/17.27 (((complementTI1) =>
% 103.13/17.27 (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTIRcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInUnion) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInUnion2) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (intersectInPowersetIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpNotIn1) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpInComplement1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTE) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTEcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a1) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2062])).
% 103.13/17.27 thf(zip_derived_cl2082, plain,
% 103.13/17.27 (~ (((binintersectT_lem) =>
% 103.13/17.27 (((binunionT_lem) =>
% 103.13/17.27 (((powersetT_lem) =>
% 103.13/17.27 (((setminusT_lem) =>
% 103.13/17.27 (((complementT_lem) =>
% 103.13/17.27 (((setextT) =>
% 103.13/17.27 (((subsetTI) =>
% 103.13/17.27 (((powersetTI1) =>
% 103.13/17.27 (((powersetTE1) =>
% 103.13/17.27 (((complementTI1) =>
% 103.13/17.27 (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInUnion) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInUnion2) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (intersectInPowersetIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpNotIn1) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpInComplement1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTE) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTEcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a1) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2072])).
% 103.13/17.27 thf(zip_derived_cl2093, plain,
% 103.13/17.27 (~ (((binunionT_lem) =>
% 103.13/17.27 (((powersetT_lem) =>
% 103.13/17.27 (((setminusT_lem) =>
% 103.13/17.27 (((complementT_lem) =>
% 103.13/17.27 (((setextT) =>
% 103.13/17.27 (((subsetTI) =>
% 103.13/17.27 (((powersetTI1) =>
% 103.13/17.27 (((powersetTE1) =>
% 103.13/17.27 (((complementTI1) =>
% 103.13/17.27 (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInUnion2) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (intersectInPowersetIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpNotIn1) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpInComplement1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTE) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTEcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a1) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2082])).
% 103.13/17.27 thf(zip_derived_cl2103, plain,
% 103.13/17.27 (~ (((powersetT_lem) =>
% 103.13/17.27 (((setminusT_lem) =>
% 103.13/17.27 (((complementT_lem) =>
% 103.13/17.27 (((setextT) =>
% 103.13/17.27 (((subsetTI) =>
% 103.13/17.27 (((powersetTI1) =>
% 103.13/17.27 (((powersetTE1) =>
% 103.13/17.27 (((complementTI1) =>
% 103.13/17.27 (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 (((inIntersectImpInUnion2) =>
% 103.13/17.27 ((
% 103.13/17.27 (inIntersectImpInIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (intersectInPowersetIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpNotIn1) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpInComplement1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTE) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTEcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a1) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2093])).
% 103.13/17.27 thf(zip_derived_cl2113, plain,
% 103.13/17.27 (~ (((setminusT_lem) =>
% 103.13/17.27 (((complementT_lem) =>
% 103.13/17.27 (((setextT) =>
% 103.13/17.27 (((subsetTI) =>
% 103.13/17.27 (((powersetTI1) =>
% 103.13/17.27 (((powersetTE1) =>
% 103.13/17.27 (((complementTI1) =>
% 103.13/17.27 (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 (((inIntersectImpInUnion2) =>
% 103.13/17.27 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (intersectInPowersetIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpNotIn1) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpInComplement1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTE) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTEcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a1) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2103])).
% 103.13/17.27 thf(zip_derived_cl2121, plain,
% 103.13/17.27 (~ (((complementT_lem) =>
% 103.13/17.27 (((setextT) =>
% 103.13/17.27 (((subsetTI) =>
% 103.13/17.27 (((powersetTI1) =>
% 103.13/17.27 (((powersetTE1) =>
% 103.13/17.27 (((complementTI1) =>
% 103.13/17.27 (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 (((inIntersectImpInUnion2) =>
% 103.13/17.27 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.27 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpNotIn1) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpInComplement1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTE) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTEcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a1) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2113])).
% 103.13/17.27 thf(zip_derived_cl2130, plain,
% 103.13/17.27 (~ (((setextT) =>
% 103.13/17.27 (((subsetTI) =>
% 103.13/17.27 (((powersetTI1) =>
% 103.13/17.27 (((powersetTE1) =>
% 103.13/17.27 (((complementTI1) =>
% 103.13/17.27 (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 (((inIntersectImpInUnion2) =>
% 103.13/17.27 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.27 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.27 (((inComplementUnionImpNotIn1) =>
% 103.13/17.27 ((
% 103.13/17.27 (inComplementUnionImpInComplement1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTE) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTEcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a1) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2121])).
% 103.13/17.27 thf(zip_derived_cl2140, plain,
% 103.13/17.27 (~ (((subsetTI) =>
% 103.13/17.27 (((powersetTI1) =>
% 103.13/17.27 (((powersetTE1) =>
% 103.13/17.27 (((complementTI1) =>
% 103.13/17.27 (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 (((inIntersectImpInUnion2) =>
% 103.13/17.27 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.27 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.27 (((inComplementUnionImpNotIn1) =>
% 103.13/17.27 (((inComplementUnionImpInComplement1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTE) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTEcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a1) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2130])).
% 103.13/17.27 thf(zip_derived_cl2151, plain,
% 103.13/17.27 (~ (((powersetTI1) =>
% 103.13/17.27 (((powersetTE1) =>
% 103.13/17.27 (((complementTI1) =>
% 103.13/17.27 (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 (((inIntersectImpInUnion2) =>
% 103.13/17.27 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.27 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.27 (((inComplementUnionImpNotIn1) =>
% 103.13/17.27 (((inComplementUnionImpInComplement1) =>
% 103.13/17.27 (((binunionTE) =>
% 103.13/17.27 ((
% 103.13/17.27 (binunionTEcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a1) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2140])).
% 103.13/17.27 thf(zip_derived_cl2159, plain,
% 103.13/17.27 (~ (((powersetTE1) =>
% 103.13/17.27 (((complementTI1) =>
% 103.13/17.27 (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 (((inIntersectImpInUnion2) =>
% 103.13/17.27 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.27 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.27 (((inComplementUnionImpNotIn1) =>
% 103.13/17.27 (((inComplementUnionImpInComplement1) =>
% 103.13/17.27 (((binunionTE) =>
% 103.13/17.27 (((binunionTEcontra) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a1) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2151])).
% 103.13/17.27 thf(zip_derived_cl2166, plain,
% 103.13/17.27 (~ (((complementTI1) =>
% 103.13/17.27 (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 (((inIntersectImpInUnion2) =>
% 103.13/17.27 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.27 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.27 (((inComplementUnionImpNotIn1) =>
% 103.13/17.27 (((inComplementUnionImpInComplement1) =>
% 103.13/17.27 (((binunionTE) =>
% 103.13/17.27 (((binunionTEcontra) =>
% 103.13/17.27 (((demorgan2a1) =>
% 103.13/17.27 ((
% 103.13/17.27 (complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2159])).
% 103.13/17.27 thf(zip_derived_cl2173, plain,
% 103.13/17.27 (~ (((complementTE1) =>
% 103.13/17.27 (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 (((inIntersectImpInUnion2) =>
% 103.13/17.27 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.27 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.27 (((inComplementUnionImpNotIn1) =>
% 103.13/17.27 (((inComplementUnionImpInComplement1) =>
% 103.13/17.27 (((binunionTE) =>
% 103.13/17.27 (((binunionTEcontra) =>
% 103.13/17.27 (((demorgan2a1) =>
% 103.13/17.27 (((complementUnionInPowersetComplement) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2166])).
% 103.13/17.27 thf(zip_derived_cl2180, plain,
% 103.13/17.27 (~ (((binintersectTELcontra) =>
% 103.13/17.27 (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 (((inIntersectImpInUnion2) =>
% 103.13/17.27 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.27 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.27 (((inComplementUnionImpNotIn1) =>
% 103.13/17.27 (((inComplementUnionImpInComplement1) =>
% 103.13/17.27 (((binunionTE) =>
% 103.13/17.27 (((binunionTEcontra) =>
% 103.13/17.27 (((demorgan2a1) =>
% 103.13/17.27 (((complementUnionInPowersetComplement) =>
% 103.13/17.27 (((demorgan2a2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2173])).
% 103.13/17.27 thf(zip_derived_cl2188, plain,
% 103.13/17.27 (~ (((binintersectTERcontra) =>
% 103.13/17.27 (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 (((inIntersectImpInUnion2) =>
% 103.13/17.27 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.27 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.27 (((inComplementUnionImpNotIn1) =>
% 103.13/17.27 (((inComplementUnionImpInComplement1) =>
% 103.13/17.27 (((binunionTE) =>
% 103.13/17.27 (((binunionTEcontra) =>
% 103.13/17.27 (((demorgan2a1) =>
% 103.13/17.27 (((complementUnionInPowersetComplement) =>
% 103.13/17.27 (((demorgan2a2) =>
% 103.13/17.27 (((demorgan1a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2180])).
% 103.13/17.27 thf(zip_derived_cl2197, plain,
% 103.13/17.27 (~ (((contrasubsetT) =>
% 103.13/17.27 (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 (((inIntersectImpInUnion2) =>
% 103.13/17.27 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.27 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.27 (((inComplementUnionImpNotIn1) =>
% 103.13/17.27 (((inComplementUnionImpInComplement1) =>
% 103.13/17.27 (((binunionTE) =>
% 103.13/17.27 (((binunionTEcontra) =>
% 103.13/17.27 (((demorgan2a1) =>
% 103.13/17.27 (((complementUnionInPowersetComplement) =>
% 103.13/17.27 (((demorgan2a2) =>
% 103.13/17.27 (((demorgan1a) =>
% 103.13/17.27 (((demorgan1b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2A) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2B) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Ex1) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1Equiv) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1E) =>
% 103.13/17.27 ((
% 103.13/17.27 (image1I) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncInInjFuncSet) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (injFuncSetFuncInj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncIn) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjFuncSetFuncSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (leftInvIsSurj) =>
% 103.13/17.27 ((
% 103.13/17.27 (surjCantorThm) =>
% 103.13/17.27 ((
% 103.13/17.27 (foundation2) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself) =>
% 103.13/17.27 ((
% 103.13/17.27 (notinself2) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSp) =>
% 103.13/17.27 ((
% 103.13/17.27 (omegaSclos) =>
% 103.13/17.27 ((
% 103.13/17.27 (peano0notS) =>
% 103.13/17.27 ((
% 103.13/17.27 (peanoSinj) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp1) =>
% 103.13/17.27 ((
% 103.13/17.27 (binintTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (transitivesetOp2) =>
% 103.13/17.27 ((
% 103.13/17.27 (setunionTransitive) =>
% 103.13/17.27 ((
% 103.13/17.27 (ordinalMinLem1) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y0 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (ordinal @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y1 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (!!) @ (
% 103.13/17.27 ^[Y2 : $i]:
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y2 @
% 103.13/17.27 Y0) =>
% 103.13/17.27 ((
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @
% 103.13/17.27 Y2) =>
% 103.13/17.27 (in @
% 103.13/17.27 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2188])).
% 103.13/17.27 thf(zip_derived_cl2207, plain,
% 103.13/17.27 (~ (((contrasubsetT1) =>
% 103.13/17.27 (((contrasubsetT2) =>
% 103.13/17.27 (((contrasubsetT3) =>
% 103.13/17.27 (((doubleComplementI1) =>
% 103.13/17.27 (((doubleComplementE1) =>
% 103.13/17.27 (((doubleComplementSub1) =>
% 103.13/17.27 (((doubleComplementSub2) =>
% 103.13/17.27 (((doubleComplementEq) =>
% 103.13/17.27 (((complementTnotintersectT) =>
% 103.13/17.27 (((complementImpComplementIntersect) =>
% 103.13/17.27 (((complementSubsetComplementIntersect) =>
% 103.13/17.27 (((complementInPowersetComplementIntersect) =>
% 103.13/17.27 (((contraSubsetComplement) =>
% 103.13/17.27 (((complementTcontraSubset) =>
% 103.13/17.27 (((binunionTILcontra) =>
% 103.13/17.27 (((binunionTIRcontra) =>
% 103.13/17.27 (((inIntersectImpInUnion) =>
% 103.13/17.27 (((inIntersectImpInUnion2) =>
% 103.13/17.27 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.27 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.27 (((inComplementUnionImpNotIn1) =>
% 103.13/17.27 (((inComplementUnionImpInComplement1) =>
% 103.13/17.27 (((binunionTE) =>
% 103.13/17.27 (((binunionTEcontra) =>
% 103.13/17.27 (((demorgan2a1) =>
% 103.13/17.27 (((complementUnionInPowersetComplement) =>
% 103.13/17.27 (((demorgan2a2) =>
% 103.13/17.27 (((demorgan1a) =>
% 103.13/17.27 (((demorgan1b) =>
% 103.13/17.27 (((demorgan1) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2a) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b2) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2b) =>
% 103.13/17.27 ((
% 103.13/17.27 (demorgan2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule0) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz13rule4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_1) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_2) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_3) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_4) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz1_5) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all2) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1SetBreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (choice2fnsingleton) =>
% 103.13/17.27 ((
% 103.13/17.27 (setOfPairsIsBReln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1all1) =>
% 103.13/17.27 ((
% 103.13/17.27 (subbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (eqbreln1) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1invE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1compEex) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionprop) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIL) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionIR) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionI) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionE) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionEcases) =>
% 103.13/17.27 ((
% 103.13/17.27 (breln1unionCommutes) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2Ex) =>
% 103.13/17.27 ((
% 103.13/17.27 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2197])).
% 103.13/17.28 thf(zip_derived_cl2219, plain,
% 103.13/17.28 (~ (((contrasubsetT2) =>
% 103.13/17.28 (((contrasubsetT3) =>
% 103.13/17.28 (((doubleComplementI1) =>
% 103.13/17.28 (((doubleComplementE1) =>
% 103.13/17.28 (((doubleComplementSub1) =>
% 103.13/17.28 (((doubleComplementSub2) =>
% 103.13/17.28 (((doubleComplementEq) =>
% 103.13/17.28 (((complementTnotintersectT) =>
% 103.13/17.28 (((complementImpComplementIntersect) =>
% 103.13/17.28 (((complementSubsetComplementIntersect) =>
% 103.13/17.28 (((complementInPowersetComplementIntersect) =>
% 103.13/17.28 (((contraSubsetComplement) =>
% 103.13/17.28 (((complementTcontraSubset) =>
% 103.13/17.28 (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 ((
% 103.13/17.28 (demorgan2b2) =>
% 103.13/17.28 ((
% 103.13/17.28 (demorgan2b) =>
% 103.13/17.28 ((
% 103.13/17.28 (demorgan2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule0) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2207])).
% 103.13/17.28 thf(zip_derived_cl2235, plain,
% 103.13/17.28 (~ (((contrasubsetT3) =>
% 103.13/17.28 (((doubleComplementI1) =>
% 103.13/17.28 (((doubleComplementE1) =>
% 103.13/17.28 (((doubleComplementSub1) =>
% 103.13/17.28 (((doubleComplementSub2) =>
% 103.13/17.28 (((doubleComplementEq) =>
% 103.13/17.28 (((complementTnotintersectT) =>
% 103.13/17.28 (((complementImpComplementIntersect) =>
% 103.13/17.28 (((complementSubsetComplementIntersect) =>
% 103.13/17.28 (((complementInPowersetComplementIntersect) =>
% 103.13/17.28 (((contraSubsetComplement) =>
% 103.13/17.28 (((complementTcontraSubset) =>
% 103.13/17.28 (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 ((
% 103.13/17.28 (demorgan2b) =>
% 103.13/17.28 ((
% 103.13/17.28 (demorgan2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule0) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2219])).
% 103.13/17.28 thf(zip_derived_cl2254, plain,
% 103.13/17.28 (~ (((doubleComplementI1) =>
% 103.13/17.28 (((doubleComplementE1) =>
% 103.13/17.28 (((doubleComplementSub1) =>
% 103.13/17.28 (((doubleComplementSub2) =>
% 103.13/17.28 (((doubleComplementEq) =>
% 103.13/17.28 (((complementTnotintersectT) =>
% 103.13/17.28 (((complementImpComplementIntersect) =>
% 103.13/17.28 (((complementSubsetComplementIntersect) =>
% 103.13/17.28 (((complementInPowersetComplementIntersect) =>
% 103.13/17.28 (((contraSubsetComplement) =>
% 103.13/17.28 (((complementTcontraSubset) =>
% 103.13/17.28 (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 ((
% 103.13/17.28 (demorgan2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule0) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2235])).
% 103.13/17.28 thf(zip_derived_cl2267, plain,
% 103.13/17.28 (~ (((doubleComplementE1) =>
% 103.13/17.28 (((doubleComplementSub1) =>
% 103.13/17.28 (((doubleComplementSub2) =>
% 103.13/17.28 (((doubleComplementEq) =>
% 103.13/17.28 (((complementTnotintersectT) =>
% 103.13/17.28 (((complementImpComplementIntersect) =>
% 103.13/17.28 (((complementSubsetComplementIntersect) =>
% 103.13/17.28 (((complementInPowersetComplementIntersect) =>
% 103.13/17.28 (((contraSubsetComplement) =>
% 103.13/17.28 (((complementTcontraSubset) =>
% 103.13/17.28 (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule0) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2254])).
% 103.13/17.28 thf(zip_derived_cl2278, plain,
% 103.13/17.28 (~ (((doubleComplementSub1) =>
% 103.13/17.28 (((doubleComplementSub2) =>
% 103.13/17.28 (((doubleComplementEq) =>
% 103.13/17.28 (((complementTnotintersectT) =>
% 103.13/17.28 (((complementImpComplementIntersect) =>
% 103.13/17.28 (((complementSubsetComplementIntersect) =>
% 103.13/17.28 (((complementInPowersetComplementIntersect) =>
% 103.13/17.28 (((contraSubsetComplement) =>
% 103.13/17.28 (((complementTcontraSubset) =>
% 103.13/17.28 (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2267])).
% 103.13/17.28 thf(zip_derived_cl2288, plain,
% 103.13/17.28 (~ (((doubleComplementSub2) =>
% 103.13/17.28 (((doubleComplementEq) =>
% 103.13/17.28 (((complementTnotintersectT) =>
% 103.13/17.28 (((complementImpComplementIntersect) =>
% 103.13/17.28 (((complementSubsetComplementIntersect) =>
% 103.13/17.28 (((complementInPowersetComplementIntersect) =>
% 103.13/17.28 (((contraSubsetComplement) =>
% 103.13/17.28 (((complementTcontraSubset) =>
% 103.13/17.28 (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2278])).
% 103.13/17.28 thf(zip_derived_cl2299, plain,
% 103.13/17.28 (~ (((doubleComplementEq) =>
% 103.13/17.28 (((complementTnotintersectT) =>
% 103.13/17.28 (((complementImpComplementIntersect) =>
% 103.13/17.28 (((complementSubsetComplementIntersect) =>
% 103.13/17.28 (((complementInPowersetComplementIntersect) =>
% 103.13/17.28 (((contraSubsetComplement) =>
% 103.13/17.28 (((complementTcontraSubset) =>
% 103.13/17.28 (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2288])).
% 103.13/17.28 thf(zip_derived_cl2310, plain,
% 103.13/17.28 (~ (((complementTnotintersectT) =>
% 103.13/17.28 (((complementImpComplementIntersect) =>
% 103.13/17.28 (((complementSubsetComplementIntersect) =>
% 103.13/17.28 (((complementInPowersetComplementIntersect) =>
% 103.13/17.28 (((contraSubsetComplement) =>
% 103.13/17.28 (((complementTcontraSubset) =>
% 103.13/17.28 (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz13rule4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2299])).
% 103.13/17.28 thf(zip_derived_cl2321, plain,
% 103.13/17.28 (~ (((complementImpComplementIntersect) =>
% 103.13/17.28 (((complementSubsetComplementIntersect) =>
% 103.13/17.28 (((complementInPowersetComplementIntersect) =>
% 103.13/17.28 (((contraSubsetComplement) =>
% 103.13/17.28 (((complementTcontraSubset) =>
% 103.13/17.28 (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2310])).
% 103.13/17.28 thf(zip_derived_cl2332, plain,
% 103.13/17.28 (~ (((complementSubsetComplementIntersect) =>
% 103.13/17.28 (((complementInPowersetComplementIntersect) =>
% 103.13/17.28 (((contraSubsetComplement) =>
% 103.13/17.28 (((complementTcontraSubset) =>
% 103.13/17.28 (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2321])).
% 103.13/17.28 thf(zip_derived_cl2341, plain,
% 103.13/17.28 (~ (((complementInPowersetComplementIntersect) =>
% 103.13/17.28 (((contraSubsetComplement) =>
% 103.13/17.28 (((complementTcontraSubset) =>
% 103.13/17.28 (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 (((woz1_2) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2332])).
% 103.13/17.28 thf(zip_derived_cl2348, plain,
% 103.13/17.28 (~ (((contraSubsetComplement) =>
% 103.13/17.28 (((complementTcontraSubset) =>
% 103.13/17.28 (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 (((woz1_2) =>
% 103.13/17.28 (((woz1_3) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2341])).
% 103.13/17.28 thf(zip_derived_cl2355, plain,
% 103.13/17.28 (~ (((complementTcontraSubset) =>
% 103.13/17.28 (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 (((woz1_2) =>
% 103.13/17.28 (((woz1_3) =>
% 103.13/17.28 (((woz1_4) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2348])).
% 103.13/17.28 thf(zip_derived_cl2362, plain,
% 103.13/17.28 (~ (((binunionTILcontra) =>
% 103.13/17.28 (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 (((woz1_2) =>
% 103.13/17.28 (((woz1_3) =>
% 103.13/17.28 (((woz1_4) =>
% 103.13/17.28 (((woz1_5) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2355])).
% 103.13/17.28 thf(zip_derived_cl2370, plain,
% 103.13/17.28 (~ (((binunionTIRcontra) =>
% 103.13/17.28 (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 (((woz1_2) =>
% 103.13/17.28 (((woz1_3) =>
% 103.13/17.28 (((woz1_4) =>
% 103.13/17.28 (((woz1_5) =>
% 103.13/17.28 (((breln1all2) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2362])).
% 103.13/17.28 thf(zip_derived_cl2379, plain,
% 103.13/17.28 (~ (((inIntersectImpInUnion) =>
% 103.13/17.28 (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 (((woz1_2) =>
% 103.13/17.28 (((woz1_3) =>
% 103.13/17.28 (((woz1_4) =>
% 103.13/17.28 (((woz1_5) =>
% 103.13/17.28 (((breln1all2) =>
% 103.13/17.28 (((breln1SetBreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2370])).
% 103.13/17.28 thf(zip_derived_cl2389, plain,
% 103.13/17.28 (~ (((inIntersectImpInUnion2) =>
% 103.13/17.28 (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 (((woz1_2) =>
% 103.13/17.28 (((woz1_3) =>
% 103.13/17.28 (((woz1_4) =>
% 103.13/17.28 (((woz1_5) =>
% 103.13/17.28 (((breln1all2) =>
% 103.13/17.28 (((breln1SetBreln1) =>
% 103.13/17.28 (((choice2fnsingleton) =>
% 103.13/17.28 ((
% 103.13/17.28 (setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2379])).
% 103.13/17.28 thf(zip_derived_cl2399, plain,
% 103.13/17.28 (~ (((inIntersectImpInIntersectUnions) =>
% 103.13/17.28 (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 (((woz1_2) =>
% 103.13/17.28 (((woz1_3) =>
% 103.13/17.28 (((woz1_4) =>
% 103.13/17.28 (((woz1_5) =>
% 103.13/17.28 (((breln1all2) =>
% 103.13/17.28 (((breln1SetBreln1) =>
% 103.13/17.28 (((choice2fnsingleton) =>
% 103.13/17.28 (((setOfPairsIsBReln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2389])).
% 103.13/17.28 thf(zip_derived_cl2408, plain,
% 103.13/17.28 (~ (((intersectInPowersetIntersectUnions) =>
% 103.13/17.28 (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 (((woz1_2) =>
% 103.13/17.28 (((woz1_3) =>
% 103.13/17.28 (((woz1_4) =>
% 103.13/17.28 (((woz1_5) =>
% 103.13/17.28 (((breln1all2) =>
% 103.13/17.28 (((breln1SetBreln1) =>
% 103.13/17.28 (((choice2fnsingleton) =>
% 103.13/17.28 (((setOfPairsIsBReln1) =>
% 103.13/17.28 (((breln1all1) =>
% 103.13/17.28 ((
% 103.13/17.28 (subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2399])).
% 103.13/17.28 thf(zip_derived_cl2417, plain,
% 103.13/17.28 (~ (((inComplementUnionImpNotIn1) =>
% 103.13/17.28 (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 (((woz1_2) =>
% 103.13/17.28 (((woz1_3) =>
% 103.13/17.28 (((woz1_4) =>
% 103.13/17.28 (((woz1_5) =>
% 103.13/17.28 (((breln1all2) =>
% 103.13/17.28 (((breln1SetBreln1) =>
% 103.13/17.28 (((choice2fnsingleton) =>
% 103.13/17.28 (((setOfPairsIsBReln1) =>
% 103.13/17.28 (((breln1all1) =>
% 103.13/17.28 (((subbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2408])).
% 103.13/17.28 thf(zip_derived_cl2427, plain,
% 103.13/17.28 (~ (((inComplementUnionImpInComplement1) =>
% 103.13/17.28 (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 (((woz1_2) =>
% 103.13/17.28 (((woz1_3) =>
% 103.13/17.28 (((woz1_4) =>
% 103.13/17.28 (((woz1_5) =>
% 103.13/17.28 (((breln1all2) =>
% 103.13/17.28 (((breln1SetBreln1) =>
% 103.13/17.28 (((choice2fnsingleton) =>
% 103.13/17.28 (((setOfPairsIsBReln1) =>
% 103.13/17.28 (((breln1all1) =>
% 103.13/17.28 (((subbreln1) =>
% 103.13/17.28 (((eqbreln1) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2417])).
% 103.13/17.28 thf(zip_derived_cl2437, plain,
% 103.13/17.28 (~ (((binunionTE) =>
% 103.13/17.28 (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 (((woz1_2) =>
% 103.13/17.28 (((woz1_3) =>
% 103.13/17.28 (((woz1_4) =>
% 103.13/17.28 (((woz1_5) =>
% 103.13/17.28 (((breln1all2) =>
% 103.13/17.28 (((breln1SetBreln1) =>
% 103.13/17.28 (((choice2fnsingleton) =>
% 103.13/17.28 (((setOfPairsIsBReln1) =>
% 103.13/17.28 (((breln1all1) =>
% 103.13/17.28 (((subbreln1) =>
% 103.13/17.28 (((eqbreln1) =>
% 103.13/17.28 (((breln1invprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1invE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1compEex) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionprop) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIL) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionIR) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionI) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionE) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionEcases) =>
% 103.13/17.28 ((
% 103.13/17.28 (breln1unionCommutes) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2W) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2A) =>
% 103.13/17.28 ((
% 103.13/17.28 (woz2B) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Ex1) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1Equiv) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1E) =>
% 103.13/17.28 ((
% 103.13/17.28 (image1I) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncInInjFuncSet) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (injFuncSetFuncInj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncIn) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjFuncSetFuncSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (leftInvIsSurj) =>
% 103.13/17.28 ((
% 103.13/17.28 (surjCantorThm) =>
% 103.13/17.28 ((
% 103.13/17.28 (foundation2) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself) =>
% 103.13/17.28 ((
% 103.13/17.28 (notinself2) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSp) =>
% 103.13/17.28 ((
% 103.13/17.28 (omegaSclos) =>
% 103.13/17.28 ((
% 103.13/17.28 (peano0notS) =>
% 103.13/17.28 ((
% 103.13/17.28 (peanoSinj) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp1) =>
% 103.13/17.28 ((
% 103.13/17.28 (binintTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (transitivesetOp2) =>
% 103.13/17.28 ((
% 103.13/17.28 (setunionTransitive) =>
% 103.13/17.28 ((
% 103.13/17.28 (ordinalMinLem1) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y0 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (ordinal @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y1 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (!!) @ (
% 103.13/17.28 ^[Y2 : $i]:
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y2 @
% 103.13/17.28 Y0) =>
% 103.13/17.28 ((
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @
% 103.13/17.28 Y2) =>
% 103.13/17.28 (in @
% 103.13/17.28 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2427])).
% 103.13/17.28 thf(zip_derived_cl2448, plain,
% 103.13/17.28 (~ (((binunionTEcontra) =>
% 103.13/17.28 (((demorgan2a1) =>
% 103.13/17.28 (((complementUnionInPowersetComplement) =>
% 103.13/17.28 (((demorgan2a2) =>
% 103.13/17.28 (((demorgan1a) =>
% 103.13/17.28 (((demorgan1b) =>
% 103.13/17.28 (((demorgan1) =>
% 103.13/17.28 (((demorgan2a) =>
% 103.13/17.28 (((demorgan2b2) =>
% 103.13/17.28 (((demorgan2b) =>
% 103.13/17.28 (((demorgan2) =>
% 103.13/17.28 (((woz13rule0) =>
% 103.13/17.28 (((woz13rule1) =>
% 103.13/17.28 (((woz13rule2) =>
% 103.13/17.28 (((woz13rule3) =>
% 103.13/17.28 (((woz13rule4) =>
% 103.13/17.28 (((woz1_1) =>
% 103.13/17.28 (((woz1_2) =>
% 103.13/17.28 (((woz1_3) =>
% 103.13/17.28 (((woz1_4) =>
% 103.13/17.28 (((woz1_5) =>
% 103.13/17.28 (((breln1all2) =>
% 103.13/17.28 (((breln1SetBreln1) =>
% 103.13/17.28 (((choice2fnsingleton) =>
% 103.13/17.28 (((setOfPairsIsBReln1) =>
% 103.13/17.28 (((breln1all1) =>
% 103.13/17.28 (((subbreln1) =>
% 103.13/17.28 (((eqbreln1) =>
% 103.13/17.28 (((breln1invprop) =>
% 103.13/17.29 (((breln1invI) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1invE) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1compprop) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1compI) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1compE) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1compEex) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionprop) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionIL) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionIR) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionI) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionE) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionEcases) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionCommutes) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2Ex) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2W) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2A) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2B) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1Ex) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1Ex1) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1Equiv) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1E) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1I) =>
% 103.13/17.29 ((
% 103.13/17.29 (injFuncInInjFuncSet) =>
% 103.13/17.29 ((
% 103.13/17.29 (injFuncSetFuncIn) =>
% 103.13/17.29 ((
% 103.13/17.29 (injFuncSetFuncInj) =>
% 103.13/17.29 ((
% 103.13/17.29 (surjFuncSetFuncIn) =>
% 103.13/17.29 ((
% 103.13/17.29 (surjFuncSetFuncSurj) =>
% 103.13/17.29 ((
% 103.13/17.29 (leftInvIsSurj) =>
% 103.13/17.29 ((
% 103.13/17.29 (surjCantorThm) =>
% 103.13/17.29 ((
% 103.13/17.29 (foundation2) =>
% 103.13/17.29 ((
% 103.13/17.29 (notinself) =>
% 103.13/17.29 ((
% 103.13/17.29 (notinself2) =>
% 103.13/17.29 ((
% 103.13/17.29 (omegaSp) =>
% 103.13/17.29 ((
% 103.13/17.29 (omegaSclos) =>
% 103.13/17.29 ((
% 103.13/17.29 (peano0notS) =>
% 103.13/17.29 ((
% 103.13/17.29 (peanoSinj) =>
% 103.13/17.29 ((
% 103.13/17.29 (transitivesetOp1) =>
% 103.13/17.29 ((
% 103.13/17.29 (binintTransitive) =>
% 103.13/17.29 ((
% 103.13/17.29 (transitivesetOp2) =>
% 103.13/17.29 ((
% 103.13/17.29 (setunionTransitive) =>
% 103.13/17.29 ((
% 103.13/17.29 (ordinalMinLem1) =>
% 103.13/17.29 ((
% 103.13/17.29 (!!) @ (
% 103.13/17.29 ^[Y0 : $i]:
% 103.13/17.29 ((
% 103.13/17.29 (ordinal @
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% 103.13/17.29 ((
% 103.13/17.29 (!!) @ (
% 103.13/17.29 ^[Y1 : $i]:
% 103.13/17.29 ((
% 103.13/17.29 (!!) @ (
% 103.13/17.29 ^[Y2 : $i]:
% 103.13/17.29 ((
% 103.13/17.29 (in @
% 103.13/17.29 Y2 @
% 103.13/17.29 Y0) =>
% 103.13/17.29 ((
% 103.13/17.29 (in @
% 103.13/17.29 Y1 @
% 103.13/17.29 Y2) =>
% 103.13/17.29 (in @
% 103.13/17.29 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2437])).
% 103.13/17.29 thf(zip_derived_cl2459, plain,
% 103.13/17.29 (~ (((demorgan2a1) =>
% 103.13/17.29 (((complementUnionInPowersetComplement) =>
% 103.13/17.29 (((demorgan2a2) =>
% 103.13/17.29 (((demorgan1a) =>
% 103.13/17.29 (((demorgan1b) =>
% 103.13/17.29 (((demorgan1) =>
% 103.13/17.29 (((demorgan2a) =>
% 103.13/17.29 (((demorgan2b2) =>
% 103.13/17.29 (((demorgan2b) =>
% 103.13/17.29 (((demorgan2) =>
% 103.13/17.29 (((woz13rule0) =>
% 103.13/17.29 (((woz13rule1) =>
% 103.13/17.29 (((woz13rule2) =>
% 103.13/17.29 (((woz13rule3) =>
% 103.13/17.29 (((woz13rule4) =>
% 103.13/17.29 (((woz1_1) =>
% 103.13/17.29 (((woz1_2) =>
% 103.13/17.29 (((woz1_3) =>
% 103.13/17.29 (((woz1_4) =>
% 103.13/17.29 (((woz1_5) =>
% 103.13/17.29 (((breln1all2) =>
% 103.13/17.29 (((breln1SetBreln1) =>
% 103.13/17.29 (((choice2fnsingleton) =>
% 103.13/17.29 (((setOfPairsIsBReln1) =>
% 103.13/17.29 (((breln1all1) =>
% 103.13/17.29 (((subbreln1) =>
% 103.13/17.29 (((eqbreln1) =>
% 103.13/17.29 (((breln1invprop) =>
% 103.13/17.29 (((breln1invI) =>
% 103.13/17.29 (((breln1invE) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1compprop) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1compI) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1compE) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1compEex) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionprop) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionIL) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionIR) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionI) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionE) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionEcases) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionCommutes) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2Ex) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2W) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2A) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2B) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1Ex) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1Ex1) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1Equiv) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1E) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1I) =>
% 103.13/17.29 ((
% 103.13/17.29 (injFuncInInjFuncSet) =>
% 103.13/17.29 ((
% 103.13/17.29 (injFuncSetFuncIn) =>
% 103.13/17.29 ((
% 103.13/17.29 (injFuncSetFuncInj) =>
% 103.13/17.29 ((
% 103.13/17.29 (surjFuncSetFuncIn) =>
% 103.13/17.29 ((
% 103.13/17.29 (surjFuncSetFuncSurj) =>
% 103.13/17.29 ((
% 103.13/17.29 (leftInvIsSurj) =>
% 103.13/17.29 ((
% 103.13/17.29 (surjCantorThm) =>
% 103.13/17.29 ((
% 103.13/17.29 (foundation2) =>
% 103.13/17.29 ((
% 103.13/17.29 (notinself) =>
% 103.13/17.29 ((
% 103.13/17.29 (notinself2) =>
% 103.13/17.29 ((
% 103.13/17.29 (omegaSp) =>
% 103.13/17.29 ((
% 103.13/17.29 (omegaSclos) =>
% 103.13/17.29 ((
% 103.13/17.29 (peano0notS) =>
% 103.13/17.29 ((
% 103.13/17.29 (peanoSinj) =>
% 103.13/17.29 ((
% 103.13/17.29 (transitivesetOp1) =>
% 103.13/17.29 ((
% 103.13/17.29 (binintTransitive) =>
% 103.13/17.29 ((
% 103.13/17.29 (transitivesetOp2) =>
% 103.13/17.29 ((
% 103.13/17.29 (setunionTransitive) =>
% 103.13/17.29 ((
% 103.13/17.29 (ordinalMinLem1) =>
% 103.13/17.29 ((
% 103.13/17.29 (!!) @ (
% 103.13/17.29 ^[Y0 : $i]:
% 103.13/17.29 ((
% 103.13/17.29 (ordinal @
% 103.13/17.29 Y0) =>
% 103.13/17.29 ((
% 103.13/17.29 (!!) @ (
% 103.13/17.29 ^[Y1 : $i]:
% 103.13/17.29 ((
% 103.13/17.29 (!!) @ (
% 103.13/17.29 ^[Y2 : $i]:
% 103.13/17.29 ((
% 103.13/17.29 (in @
% 103.13/17.29 Y2 @
% 103.13/17.29 Y0) =>
% 103.13/17.29 ((
% 103.13/17.29 (in @
% 103.13/17.29 Y1 @
% 103.13/17.29 Y2) =>
% 103.13/17.29 (in @
% 103.13/17.29 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2448])).
% 103.13/17.29 thf(zip_derived_cl2470, plain,
% 103.13/17.29 (~ (((complementUnionInPowersetComplement) =>
% 103.13/17.29 (((demorgan2a2) =>
% 103.13/17.29 (((demorgan1a) =>
% 103.13/17.29 (((demorgan1b) =>
% 103.13/17.29 (((demorgan1) =>
% 103.13/17.29 (((demorgan2a) =>
% 103.13/17.29 (((demorgan2b2) =>
% 103.13/17.29 (((demorgan2b) =>
% 103.13/17.29 (((demorgan2) =>
% 103.13/17.29 (((woz13rule0) =>
% 103.13/17.29 (((woz13rule1) =>
% 103.13/17.29 (((woz13rule2) =>
% 103.13/17.29 (((woz13rule3) =>
% 103.13/17.29 (((woz13rule4) =>
% 103.13/17.29 (((woz1_1) =>
% 103.13/17.29 (((woz1_2) =>
% 103.13/17.29 (((woz1_3) =>
% 103.13/17.29 (((woz1_4) =>
% 103.13/17.29 (((woz1_5) =>
% 103.13/17.29 (((breln1all2) =>
% 103.13/17.29 (((breln1SetBreln1) =>
% 103.13/17.29 (((choice2fnsingleton) =>
% 103.13/17.29 (((setOfPairsIsBReln1) =>
% 103.13/17.29 (((breln1all1) =>
% 103.13/17.29 (((subbreln1) =>
% 103.13/17.29 (((eqbreln1) =>
% 103.13/17.29 (((breln1invprop) =>
% 103.13/17.29 (((breln1invI) =>
% 103.13/17.29 (((breln1invE) =>
% 103.13/17.29 (((breln1compprop) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1compI) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1compE) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1compEex) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionprop) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionIL) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionIR) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionI) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionE) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionEcases) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionCommutes) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2Ex) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2W) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2A) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2B) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1Ex) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1Ex1) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1Equiv) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1E) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1I) =>
% 103.13/17.29 ((
% 103.13/17.29 (injFuncInInjFuncSet) =>
% 103.13/17.29 ((
% 103.13/17.29 (injFuncSetFuncIn) =>
% 103.13/17.29 ((
% 103.13/17.29 (injFuncSetFuncInj) =>
% 103.13/17.29 ((
% 103.13/17.29 (surjFuncSetFuncIn) =>
% 103.13/17.29 ((
% 103.13/17.29 (surjFuncSetFuncSurj) =>
% 103.13/17.29 ((
% 103.13/17.29 (leftInvIsSurj) =>
% 103.13/17.29 ((
% 103.13/17.29 (surjCantorThm) =>
% 103.13/17.29 ((
% 103.13/17.29 (foundation2) =>
% 103.13/17.29 ((
% 103.13/17.29 (notinself) =>
% 103.13/17.29 ((
% 103.13/17.29 (notinself2) =>
% 103.13/17.29 ((
% 103.13/17.29 (omegaSp) =>
% 103.13/17.29 ((
% 103.13/17.29 (omegaSclos) =>
% 103.13/17.29 ((
% 103.13/17.29 (peano0notS) =>
% 103.13/17.29 ((
% 103.13/17.29 (peanoSinj) =>
% 103.13/17.29 ((
% 103.13/17.29 (transitivesetOp1) =>
% 103.13/17.29 ((
% 103.13/17.29 (binintTransitive) =>
% 103.13/17.29 ((
% 103.13/17.29 (transitivesetOp2) =>
% 103.13/17.29 ((
% 103.13/17.29 (setunionTransitive) =>
% 103.13/17.29 ((
% 103.13/17.29 (ordinalMinLem1) =>
% 103.13/17.29 ((
% 103.13/17.29 (!!) @ (
% 103.13/17.29 ^[Y0 : $i]:
% 103.13/17.29 ((
% 103.13/17.29 (ordinal @
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% 103.13/17.29 ((
% 103.13/17.29 (!!) @ (
% 103.13/17.29 ^[Y1 : $i]:
% 103.13/17.29 ((
% 103.13/17.29 (!!) @ (
% 103.13/17.29 ^[Y2 : $i]:
% 103.13/17.29 ((
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% 103.13/17.29 Y2 @
% 103.13/17.29 Y0) =>
% 103.13/17.29 ((
% 103.13/17.29 (in @
% 103.13/17.29 Y1 @
% 103.13/17.29 Y2) =>
% 103.13/17.29 (in @
% 103.13/17.29 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2459])).
% 103.13/17.29 thf(zip_derived_cl2481, plain,
% 103.13/17.29 (~ (((demorgan2a2) =>
% 103.13/17.29 (((demorgan1a) =>
% 103.13/17.29 (((demorgan1b) =>
% 103.13/17.29 (((demorgan1) =>
% 103.13/17.29 (((demorgan2a) =>
% 103.13/17.29 (((demorgan2b2) =>
% 103.13/17.29 (((demorgan2b) =>
% 103.13/17.29 (((demorgan2) =>
% 103.13/17.29 (((woz13rule0) =>
% 103.13/17.29 (((woz13rule1) =>
% 103.13/17.29 (((woz13rule2) =>
% 103.13/17.29 (((woz13rule3) =>
% 103.13/17.29 (((woz13rule4) =>
% 103.13/17.29 (((woz1_1) =>
% 103.13/17.29 (((woz1_2) =>
% 103.13/17.29 (((woz1_3) =>
% 103.13/17.29 (((woz1_4) =>
% 103.13/17.29 (((woz1_5) =>
% 103.13/17.29 (((breln1all2) =>
% 103.13/17.29 (((breln1SetBreln1) =>
% 103.13/17.29 (((choice2fnsingleton) =>
% 103.13/17.29 (((setOfPairsIsBReln1) =>
% 103.13/17.29 (((breln1all1) =>
% 103.13/17.29 (((subbreln1) =>
% 103.13/17.29 (((eqbreln1) =>
% 103.13/17.29 (((breln1invprop) =>
% 103.13/17.29 (((breln1invI) =>
% 103.13/17.29 (((breln1invE) =>
% 103.13/17.29 (((breln1compprop) =>
% 103.13/17.29 (((breln1compI) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1compE) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1compEex) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionprop) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionIL) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionIR) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionI) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionE) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionEcases) =>
% 103.13/17.29 ((
% 103.13/17.29 (breln1unionCommutes) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2Ex) =>
% 103.13/17.29 ((
% 103.13/17.29 (woz2W) =>
% 103.13/17.29 ((
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% 103.13/17.29 ((
% 103.13/17.29 (woz2B) =>
% 103.13/17.29 ((
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% 103.13/17.29 ((
% 103.13/17.29 (image1Ex1) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1Equiv) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1E) =>
% 103.13/17.29 ((
% 103.13/17.29 (image1I) =>
% 103.13/17.29 ((
% 103.13/17.29 (injFuncInInjFuncSet) =>
% 103.13/17.29 ((
% 103.13/17.29 (injFuncSetFuncIn) =>
% 103.13/17.29 ((
% 103.13/17.29 (injFuncSetFuncInj) =>
% 103.13/17.29 ((
% 103.13/17.29 (surjFuncSetFuncIn) =>
% 103.13/17.29 ((
% 103.13/17.29 (surjFuncSetFuncSurj) =>
% 103.13/17.29 ((
% 103.13/17.29 (leftInvIsSurj) =>
% 103.13/17.29 ((
% 103.13/17.29 (surjCantorThm) =>
% 103.13/17.29 ((
% 103.13/17.29 (foundation2) =>
% 103.13/17.29 ((
% 103.13/17.29 (notinself) =>
% 103.13/17.29 ((
% 103.13/17.29 (notinself2) =>
% 103.13/17.29 ((
% 103.13/17.29 (omegaSp) =>
% 103.13/17.29 ((
% 103.13/17.29 (omegaSclos) =>
% 103.13/17.29 ((
% 103.13/17.29 (peano0notS) =>
% 103.13/17.29 ((
% 103.13/17.29 (peanoSinj) =>
% 103.13/17.29 ((
% 103.13/17.29 (transitivesetOp1) =>
% 103.13/17.29 ((
% 103.13/17.29 (binintTransitive) =>
% 103.13/17.29 ((
% 103.13/17.29 (transitivesetOp2) =>
% 103.13/17.29 ((
% 103.13/17.29 (setunionTransitive) =>
% 103.13/17.29 ((
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% 103.13/17.29 ((
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% 103.13/17.29 ^[Y0 : $i]:
% 103.13/17.29 ((
% 103.13/17.29 (ordinal @
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% 103.13/17.29 ((
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% 103.13/17.29 ^[Y1 : $i]:
% 103.13/17.29 ((
% 103.13/17.29 (!!) @ (
% 103.13/17.29 ^[Y2 : $i]:
% 103.13/17.29 ((
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% 103.13/17.29 Y2 @
% 103.13/17.29 Y0) =>
% 103.13/17.29 ((
% 103.13/17.29 (in @
% 103.13/17.29 Y1 @
% 103.13/17.29 Y2) =>
% 103.13/17.29 (in @
% 103.13/17.29 Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 103.13/17.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2470])).
% 103.13/17.29 thf(zip_derived_cl2493, plain,
% 103.13/17.29 (~ (((demorgan1a) =>
% 103.13/17.29 (((demorgan1b) =>
% 103.13/17.29 (((demorgan1) =>
% 103.13/17.29 (((demorgan2a) =>
% 103.13/17.29 (((demorgan2b2) =>
% 103.13/17.29 (((demorgan2b) =>
% 103.13/17.29 (((demorgan2) =>
% 103.13/17.29 (((woz13rule0) =>
% 103.13/17.29 (((woz13rule1) =>
% 103.13/17.29 (((woz13rule2) =>
% 103.13/17.29 (((woz13rule3) =>
% 103.13/17.29 (((woz13rule4) =>
% 103.13/17.29 (((woz1_1) =>
% 103.13/17.29 (((woz1_2) =>
% 103.13/17.29 (((woz1_3) =>
% 103.13/17.29 (((woz1_4) =>
% 103.13/17.29 (((woz1_5) =>
% 103.13/17.29 (((breln1all2) =>
% 103.13/17.29 (((breln1SetBreln1) =>
% 103.13/17.29 (((choice2fnsingleton) =>
% 103.13/17.29 (((setOfPairsIsBReln1) =>
% 103.13/17.29 (((breln1all1) =>
% 103.13/17.29 (((subbreln1) =>
% 103.13/17.29 (((eqbreln1) =>
% 103.13/17.29 (((breln1invprop) =>
% 103.13/17.29 (((breln1invI) =>
% 103.13/17.29 (((breln1invE) =>
% 103.13/17.29 (((breln1compprop) =>