%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU769^1 : 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.IsLaFYg1YM true
% Computer : n025.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 04:56:14 PM UTC 2025
% Result : Theorem 105.60s 14.49s
% Output : Refutation 106.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU769^1 : TPTP v9.2.0. Released v3.7.0.
% 0.00/0.09 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.IsLaFYg1YM true
% 0.09/0.29 % Computer : n025.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Wed Oct 1 16:04:38 EDT 2025
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % Running portfolio for 300 s
% 0.09/0.29 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.29 % Number of cores: 8
% 0.14/0.29 % Python version: Python 3.6.8
% 0.14/0.29 % Running in HO mode
% 0.14/0.57 % Total configuration time : 828
% 0.14/0.57 % Estimated wc time : 1656
% 0.14/0.57 % Estimated cpu time (8 cpus) : 207.0
% 0.97/0.65 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.97/0.67 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.97/0.67 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.97/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.97/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.97/0.71 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.97/0.71 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.30/0.73 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.48/0.96 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 105.60/14.49 % Solved by lams/40_b.comb.sh.
% 105.60/14.49 % done 0 iterations in 13.446s
% 105.60/14.49 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 105.60/14.49 % SZS output start Refutation
% 105.60/14.49 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 105.60/14.49 thf(notdexE_type, type, notdexE: $o).
% 105.60/14.49 thf(demorgan1a_type, type, demorgan1a: $o).
% 105.60/14.49 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 105.60/14.49 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 105.60/14.49 thf(setunionAx_type, type, setunionAx: $o).
% 105.60/14.49 thf(setminusELneg_type, type, setminusELneg: $o).
% 105.60/14.49 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 105.60/14.49 thf(ex1E1_type, type, ex1E1: $o).
% 105.60/14.49 thf(powersetE_type, type, powersetE: $o).
% 105.60/14.49 thf(woz13rule4_type, type, woz13rule4: $o).
% 105.60/14.49 thf(omegaSAx_type, type, omegaSAx: $o).
% 105.60/14.49 thf(exuI1_type, type, exuI1: $o).
% 105.60/14.49 thf(exuI2_type, type, exuI2: $o).
% 105.60/14.49 thf(notequalI2_type, type, notequalI2: $o).
% 105.60/14.49 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 105.60/14.49 thf(woz13rule1_type, type, woz13rule1: $o).
% 105.60/14.49 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 105.60/14.49 thf(upairsubunion_type, type, upairsubunion: $o).
% 105.60/14.49 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 105.60/14.49 thf(binunionTE_type, type, binunionTE: $o).
% 105.60/14.49 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 105.60/14.49 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 105.60/14.49 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 105.60/14.49 thf(setminusILneg_type, type, setminusILneg: $o).
% 105.60/14.49 thf('#sk21_type', type, '#sk21': $i > ($i > $o) > $i).
% 105.60/14.49 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 105.60/14.49 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 105.60/14.49 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 105.60/14.49 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 105.60/14.49 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 105.60/14.49 thf(iftrue_type, type, iftrue: $o).
% 105.60/14.49 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 105.60/14.49 thf(ifSingleton_type, type, ifSingleton: $o).
% 105.60/14.49 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 105.60/14.49 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 105.60/14.49 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 105.60/14.49 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 105.60/14.49 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 105.60/14.49 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 105.60/14.49 thf(lamProp_type, type, lamProp: $o).
% 105.60/14.49 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 105.60/14.49 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 105.60/14.49 thf(demorgan2_type, type, demorgan2: $o).
% 105.60/14.49 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 105.60/14.49 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 105.60/14.49 thf(setukpairIR_type, type, setukpairIR: $o).
% 105.60/14.49 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 105.60/14.49 thf(lam2p_type, type, lam2p: $o).
% 105.60/14.49 thf(binunionE_type, type, binunionE: $o).
% 105.60/14.49 thf(setext_type, type, setext: $o).
% 105.60/14.49 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 105.60/14.49 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 105.60/14.49 thf(descr__Cong_type, type, descr__Cong: $o).
% 105.60/14.49 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 105.60/14.49 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 105.60/14.49 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 105.60/14.49 thf(eqbreln_type, type, eqbreln: $o).
% 105.60/14.49 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 105.60/14.49 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 105.60/14.49 $o).
% 105.60/14.49 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 105.60/14.49 $o).
% 105.60/14.49 thf(in_type, type, in: $i > $i > $o).
% 105.60/14.49 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 105.60/14.49 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 105.60/14.49 thf(complementT_lem_type, type, complementT_lem: $o).
% 105.60/14.49 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 105.60/14.49 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 105.60/14.49 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 105.60/14.49 thf(beta1_type, type, beta1: $o).
% 105.60/14.49 thf(breln1all2_type, type, breln1all2: $o).
% 105.60/14.49 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 105.60/14.49 thf(powersetTE1_type, type, powersetTE1: $o).
% 105.60/14.49 thf(symdiffI2_type, type, symdiffI2: $o).
% 105.60/14.49 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 105.60/14.49 thf(upairset2IR_type, type, upairset2IR: $o).
% 105.60/14.49 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 105.60/14.49 thf(subsetE_type, type, subsetE: $o).
% 105.60/14.49 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 105.60/14.49 thf(demorgan2a_type, type, demorgan2a: $o).
% 105.60/14.49 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 105.60/14.49 thf(setbeta_type, type, setbeta: $o).
% 105.60/14.49 thf(eqinunit_type, type, eqinunit: $o).
% 105.60/14.49 thf(upairsetIL_type, type, upairsetIL: $o).
% 105.60/14.49 thf(powersetI1_type, type, powersetI1: $o).
% 105.60/14.49 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 105.60/14.49 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 105.60/14.49 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 105.60/14.49 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 105.60/14.49 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 105.60/14.49 thf(powersetAx_type, type, powersetAx: $o).
% 105.60/14.49 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 105.60/14.49 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 105.60/14.49 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 105.60/14.49 thf(powersetI_type, type, powersetI: $o).
% 105.60/14.49 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 105.60/14.49 thf(upairsetIR_type, type, upairsetIR: $o).
% 105.60/14.49 thf(lamp_type, type, lamp: $o).
% 105.60/14.49 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 105.60/14.49 thf(inCongP_type, type, inCongP: $o).
% 105.60/14.49 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 105.60/14.49 thf(exuE3e_type, type, exuE3e: $o).
% 105.60/14.49 thf(emptysetE_type, type, emptysetE: $o).
% 105.60/14.49 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 105.60/14.49 thf(setunionI_type, type, setunionI: $o).
% 105.60/14.49 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 105.60/14.49 thf(prop2setI_type, type, prop2setI: $o).
% 105.60/14.49 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 105.60/14.49 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 105.60/14.49 thf(setminusER_type, type, setminusER: $o).
% 105.60/14.49 thf(exuE2_type, type, exuE2: $o).
% 105.60/14.49 thf(emptyset_type, type, emptyset: $i).
% 105.60/14.49 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 105.60/14.49 thf(ex1I_type, type, ex1I: $o).
% 105.60/14.49 thf(ex1E2_type, type, ex1E2: $o).
% 105.60/14.49 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 105.60/14.49 thf(powersetsubset_type, type, powersetsubset: $o).
% 105.60/14.49 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 105.60/14.49 thf(subPowSU_type, type, subPowSU: $o).
% 105.60/14.49 thf(notequalI1_type, type, notequalI1: $o).
% 105.60/14.49 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 105.60/14.49 thf(notinemptyset_type, type, notinemptyset: $o).
% 105.60/14.49 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 105.60/14.49 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 105.60/14.49 thf(subsetTrans_type, type, subsetTrans: $o).
% 105.60/14.49 thf(kpairp_type, type, kpairp: $o).
% 105.60/14.49 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 105.60/14.49 thf(setminusI_type, type, setminusI: $o).
% 105.60/14.49 thf(binunionIL_type, type, binunionIL: $o).
% 105.60/14.49 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 105.60/14.49 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 105.60/14.49 thf(subsetE2_type, type, subsetE2: $o).
% 105.60/14.49 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 105.60/14.49 thf(breln1Set_type, type, breln1Set: $i > $i).
% 105.60/14.49 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 105.60/14.49 thf(beta2_type, type, beta2: $o).
% 105.60/14.49 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 105.60/14.49 thf(setextsub_type, type, setextsub: $o).
% 105.60/14.49 thf(binunionLsub_type, type, binunionLsub: $o).
% 105.60/14.49 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 105.60/14.49 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 105.60/14.49 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 105.60/14.49 $o).
% 105.60/14.49 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 105.60/14.49 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 105.60/14.49 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 105.60/14.49 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 105.60/14.49 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 105.60/14.49 thf(setunionE_type, type, setunionE: $o).
% 105.60/14.49 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 105.60/14.49 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 105.60/14.49 thf(woz13rule0_type, type, woz13rule0: $o).
% 105.60/14.49 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 105.60/14.49 thf(woz1_5_type, type, woz1_5: $o).
% 105.60/14.49 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 105.60/14.49 thf(binunionIR_type, type, binunionIR: $o).
% 105.60/14.49 thf(theeq_type, type, theeq: $o).
% 105.60/14.49 thf(setadjoinE_type, type, setadjoinE: $o).
% 105.60/14.49 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 105.60/14.49 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 105.60/14.49 thf(woz13rule3_type, type, woz13rule3: $o).
% 105.60/14.49 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 105.60/14.49 thf(ap2p_type, type, ap2p: $o).
% 105.60/14.49 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 105.60/14.49 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 105.60/14.49 thf(exuE1_type, type, exuE1: $o).
% 105.60/14.49 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 105.60/14.49 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 105.60/14.49 thf(setminusLsub_type, type, setminusLsub: $o).
% 105.60/14.49 thf(funcextLem_type, type, funcextLem: $o).
% 105.60/14.49 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 105.60/14.49 thf(notinsingleton_type, type, notinsingleton: $o).
% 105.60/14.49 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 105.60/14.49 $o).
% 105.60/14.49 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 105.60/14.49 thf(exuEu_type, type, exuEu: $o).
% 105.60/14.49 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 105.60/14.49 thf(upairsetE_type, type, upairsetE: $o).
% 105.60/14.49 thf(omega0Ax_type, type, omega0Ax: $o).
% 105.60/14.49 thf(subsetTI_type, type, subsetTI: $o).
% 105.60/14.49 thf(notsubsetI_type, type, notsubsetI: $o).
% 105.60/14.49 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 105.60/14.49 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 105.60/14.49 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 105.60/14.49 thf(setextAx_type, type, setextAx: $o).
% 105.60/14.49 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 105.60/14.49 thf(powersetE1_type, type, powersetE1: $o).
% 105.60/14.49 thf(bs114d_type, type, bs114d: $o).
% 105.60/14.49 thf(breln1_type, type, breln1: $i > $i > $o).
% 105.60/14.49 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 105.60/14.49 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 105.60/14.49 thf(breln_type, type, breln: $i > $i > $i > $o).
% 105.60/14.49 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 105.60/14.49 thf(woz1_3_type, type, woz1_3: $o).
% 105.60/14.49 thf(ifp_type, type, ifp: $o).
% 105.60/14.49 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 105.60/14.49 thf(powersetTI1_type, type, powersetTI1: $o).
% 105.60/14.49 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 105.60/14.49 thf(subsetI1_type, type, subsetI1: $o).
% 105.60/14.49 thf(symdiffE_type, type, symdiffE: $o).
% 105.60/14.49 thf(descrp_type, type, descrp: $o).
% 105.60/14.49 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 105.60/14.49 thf(foundationAx_type, type, foundationAx: $o).
% 105.60/14.49 thf(emptysetAx_type, type, emptysetAx: $o).
% 105.60/14.49 thf(emptyI_type, type, emptyI: $o).
% 105.60/14.49 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 105.60/14.49 thf(eta2_type, type, eta2: $o).
% 105.60/14.49 thf(binintersectEL_type, type, binintersectEL: $o).
% 105.60/14.49 thf(emptyE1_type, type, emptyE1: $o).
% 105.60/14.49 thf(woz1_2_type, type, woz1_2: $o).
% 105.60/14.49 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 105.60/14.49 thf(complementTI1_type, type, complementTI1: $o).
% 105.60/14.49 thf(vacuousDall_type, type, vacuousDall: $o).
% 105.60/14.49 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 105.60/14.49 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 105.60/14.49 thf(binintersectI_type, type, binintersectI: $o).
% 105.60/14.49 thf(woz1_4_type, type, woz1_4: $o).
% 105.60/14.49 thf(funcext_type, type, funcext: $o).
% 105.60/14.49 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 105.60/14.49 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 105.60/14.49 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 105.60/14.49 thf(woz13rule2_type, type, woz13rule2: $o).
% 105.60/14.49 thf(brelnall2_type, type, brelnall2: $o).
% 105.60/14.49 thf(setextT_type, type, setextT: $o).
% 105.60/14.49 thf(ex1I2_type, type, ex1I2: $o).
% 105.60/14.49 thf(symdiffI1_type, type, symdiffI1: $o).
% 105.60/14.49 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 105.60/14.49 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 105.60/14.49 thf(theprop_type, type, theprop: $o).
% 105.60/14.49 thf(subsetI2_type, type, subsetI2: $o).
% 105.60/14.49 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 105.60/14.49 $o).
% 105.60/14.49 thf(demorgan1_type, type, demorgan1: $o).
% 105.60/14.49 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 105.60/14.49 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 105.60/14.49 thf(setminusERneg_type, type, setminusERneg: $o).
% 105.60/14.49 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 105.60/14.49 thf(omega__Cong_type, type, omega__Cong: $o).
% 105.60/14.49 thf(subsetRefl_type, type, subsetRefl: $o).
% 105.60/14.49 thf(uniqinunit_type, type, uniqinunit: $o).
% 105.60/14.49 thf('#sk42_type', type, '#sk42': $i).
% 105.60/14.49 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 105.60/14.49 $o).
% 105.60/14.49 thf(demorgan2b_type, type, demorgan2b: $o).
% 105.60/14.49 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 105.60/14.49 thf(prop2setE_type, type, prop2setE: $o).
% 105.60/14.49 thf(binunionEcases_type, type, binunionEcases: $o).
% 105.60/14.49 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 105.60/14.49 thf(complementTE1_type, type, complementTE1: $o).
% 105.60/14.49 thf(omega_type, type, omega: $i).
% 105.60/14.49 thf(nonemptyI_type, type, nonemptyI: $o).
% 105.60/14.49 thf(app_type, type, app: $o).
% 105.60/14.49 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 105.60/14.49 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 105.60/14.49 thf(exuE3u_type, type, exuE3u: $o).
% 105.60/14.49 thf(eta1_type, type, eta1: $o).
% 105.60/14.49 thf(setminusEL_type, type, setminusEL: $o).
% 105.60/14.49 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 105.60/14.49 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 105.60/14.49 thf(sepSubset_type, type, sepSubset: $o).
% 105.60/14.49 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 105.60/14.49 thf(upairset2E_type, type, upairset2E: $o).
% 105.60/14.49 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 105.60/14.49 thf(exuI3_type, type, exuI3: $o).
% 105.60/14.49 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 105.60/14.49 thf(apProp_type, type, apProp: $o).
% 105.60/14.49 thf(notdallE_type, type, notdallE: $o).
% 105.60/14.49 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 105.60/14.49 thf(binintersectER_type, type, binintersectER: $o).
% 105.60/14.49 thf(brelnall1_type, type, brelnall1: $o).
% 105.60/14.49 thf(powerset_type, type, powerset: $i > $i).
% 105.60/14.49 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 105.60/14.49 thf(demorgan1b_type, type, demorgan1b: $o).
% 105.60/14.49 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 105.60/14.49 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 105.60/14.49 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 105.60/14.49 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 105.60/14.49 thf(exu__Cong_type, type, exu__Cong: $o).
% 105.60/14.49 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 105.60/14.49 $o).
% 105.60/14.49 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 105.60/14.49 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 105.60/14.49 thf(secondinupair_type, type, secondinupair: $o).
% 105.60/14.49 thf(singletonprop_type, type, singletonprop: $o).
% 105.60/14.49 thf(singletonsubset_type, type, singletonsubset: $o).
% 105.60/14.49 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 105.60/14.49 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 105.60/14.49 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 105.60/14.49 thf(replAx_type, type, replAx: $o).
% 105.60/14.49 thf(upairequniteq_type, type, upairequniteq: $o).
% 105.60/14.49 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 105.60/14.49 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 105.60/14.49 thf(setukpairIL_type, type, setukpairIL: $o).
% 105.60/14.49 thf(setunionE2_type, type, setunionE2: $o).
% 105.60/14.49 thf(inPowerset_type, type, inPowerset: $o).
% 105.60/14.49 thf(iffalse_type, type, iffalse: $o).
% 105.60/14.49 thf(funcext2_type, type, funcext2: $o).
% 105.60/14.49 thf(cartprod_type, type, cartprod: $i > $i > $i).
% 105.60/14.49 thf(subset_type, type, subset: $i > $i > $o).
% 105.60/14.49 thf(woz1_1_type, type, woz1_1: $o).
% 105.60/14.49 thf(subbreln_type, type, subbreln: $o).
% 105.60/14.49 thf(in__Cong_type, type, in__Cong: $o).
% 105.60/14.49 thf(binunionRsub_type, type, binunionRsub: $o).
% 105.60/14.49 thf(subset2powerset_type, type, subset2powerset: $o).
% 105.60/14.49 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 105.60/14.49 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 105.60/14.49 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 105.60/14.49 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 105.60/14.49 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 105.60/14.49 thf(breln1SetBreln1, conjecture,
% 105.60/14.49 (( setextAx ) =>
% 105.60/14.49 ( ( emptysetAx ) =>
% 105.60/14.49 ( ( setadjoinAx ) =>
% 105.60/14.49 ( ( powersetAx ) =>
% 105.60/14.49 ( ( setunionAx ) =>
% 105.60/14.49 ( ( omega0Ax ) =>
% 105.60/14.49 ( ( omegaSAx ) =>
% 105.60/14.49 ( ( omegaIndAx ) =>
% 105.60/14.49 ( ( replAx ) =>
% 105.60/14.49 ( ( foundationAx ) =>
% 105.60/14.49 ( ( wellorderingAx ) =>
% 105.60/14.49 ( ( descrp ) =>
% 105.60/14.49 ( ( dsetconstrI ) =>
% 105.60/14.49 ( ( dsetconstrEL ) =>
% 105.60/14.49 ( ( dsetconstrER ) =>
% 105.60/14.49 ( ( exuE1 ) =>
% 105.60/14.49 ( ( prop2setE ) =>
% 105.60/14.49 ( ( emptysetE ) =>
% 105.60/14.49 ( ( emptysetimpfalse ) =>
% 105.60/14.49 ( ( notinemptyset ) =>
% 105.60/14.49 ( ( exuE3e ) =>
% 105.60/14.49 ( ( setext ) =>
% 105.60/14.49 ( ( emptyI ) =>
% 105.60/14.49 ( ( noeltsimpempty ) =>
% 105.60/14.49 ( ( setbeta ) =>
% 105.60/14.49 ( ( nonemptyE1 ) =>
% 105.60/14.49 ( ( nonemptyI ) =>
% 105.60/14.49 ( ( nonemptyI1 ) =>
% 105.60/14.49 ( ( setadjoinIL ) =>
% 105.60/14.49 ( ( emptyinunitempty ) =>
% 105.60/14.49 ( ( setadjoinIR ) =>
% 105.60/14.49 ( ( setadjoinE ) =>
% 105.60/14.49 ( (
% 105.60/14.49 setadjoinOr ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setoftrueEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 emptyinPowerset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 emptyInPowerset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunionI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunionE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subPowSU ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exuE2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 nonemptyImpWitness ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 uniqinunit ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 notinsingleton ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 eqinunit ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 singletonsswitch ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairsetE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairsetIL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairsetIR ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 emptyE1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 vacuousDall ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 quantDeMorgan1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 quantDeMorgan2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 quantDeMorgan3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 quantDeMorgan4 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 prop2setI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 prop2set2propI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 notdexE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 notdallE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exuI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exuI3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exuI2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inCongP ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 in__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exuE3u ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exu__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 emptyset__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setadjoin__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powerset__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunion__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 omega__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exuEu ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 descr__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dsetconstr__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 eqimpsubset2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 eqimpsubset1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetI2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 emptysetsubset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetE2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 notsubsetI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 notequalI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 notequalI2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetRefl ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetTrans ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setadjoinSub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setadjoinSub2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subset2powerset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setextsub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetemptysetimpeq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetE1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inPowerset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetsubset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 sepInPowerset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 sepSubset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionIL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairset2IR ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionIR ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionEcases ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionLsub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionRsub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectSubset5 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectEL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectLsub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectSubset2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectSubset3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectER ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 disjointsetsI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectRsub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectSubset4 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectSubset1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 bs114d ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusEL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusER ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusSubset2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusERneg ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusELneg ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusILneg ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusIRneg ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusLsub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusSubset1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 symdiffE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 symdiffI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 symdiffI2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 symdiffIneg1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 symdiffIneg2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 secondinupair ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairIL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairIR ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 kpairiskpair ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 kpairp ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 singletonsubset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 singletoninpowerset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 singletoninpowunion ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairset2E ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairsubunion ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairinpowunion ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ubforcartprodlem1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ubforcartprodlem2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ubforcartprodlem3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodpairin ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodmempair1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodmempair ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunionE2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunionsingleton1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunionsingleton2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunionsingleton ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 singletonprop ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ex1E1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ex1I ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ex1I2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 singletonsuniq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjL1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 kfstsingleton ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 theprop ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 kfstpairEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodfstin ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjL2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjR11 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjR12 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjR1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairequniteq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjR2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjR ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ksndsingleton ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ksndpairEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 kpairsurjEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodsndin ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodpairmemEL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodpairmemER ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodmempaircEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodfstpairEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodsndpairEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodpairsurjEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dpsetconstrI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dpsetconstrSub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setOfPairsIsBReln ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dpsetconstrERa ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dpsetconstrEL1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dpsetconstrEL2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dpsetconstrER ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcImageSingleton ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 apProp ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 app ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 infuncsetfunc ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ap2p ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcinfuncset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 lamProp ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 lamp ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 lam2p ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 brelnall1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 brelnall2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ex1E2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcGraphProp1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcGraphProp3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcGraphProp2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcextLem ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcGraphProp4 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subbreln ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 eqbreln ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcext ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcext2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ap2apEq1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ap2apEq2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 beta1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 eta1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 lam2lamEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 beta2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 eta2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iffalseProp1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iffalseProp2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iftrueProp1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iftrueProp2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ifSingleton ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ifp ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 theeq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iftrue ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iffalse ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iftrueorfalse ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectT_lem ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionT_lem ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetT_lem ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusT_lem ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementT_lem ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setextT ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetTI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetTI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetTE1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementTI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementTE1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectTELcontra ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectTERcontra ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 contrasubsetT ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 contrasubsetT1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 contrasubsetT2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 contrasubsetT3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 doubleComplementI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 doubleComplementE1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 doubleComplementSub1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 doubleComplementSub2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 doubleComplementEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementTnotintersectT ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementImpComplementIntersect ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementSubsetComplementIntersect ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementInPowersetComplementIntersect ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 contraSubsetComplement ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementTcontraSubset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionTILcontra ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionTIRcontra ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inIntersectImpInUnion ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inIntersectImpInUnion2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inIntersectImpInIntersectUnions ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 intersectInPowersetIntersectUnions ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inComplementUnionImpNotIn1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inComplementUnionImpInComplement1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionTE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionTEcontra ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan2a1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementUnionInPowersetComplement ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan2a2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan1a ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan1b ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan2a ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan2b2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan2b ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz13rule0 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz13rule1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz13rule2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz13rule3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz13rule4 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz1_1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz1_2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz1_3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz1_4 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz1_5 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 breln1all2 ) =>
% 105.60/14.49 (
% 105.60/14.49 ![
% 105.60/14.49 A:$i,R:$i]:
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 in @
% 105.60/14.49 R @
% 105.60/14.49 (
% 105.60/14.49 breln1Set
% 105.60/14.49 @
% 105.60/14.49 A ) ) =>
% 105.60/14.49 (
% 105.60/14.49 breln1 @
% 105.60/14.49 A @ R ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 105.60/14.49 thf(zf_stmt_0, negated_conjecture,
% 105.60/14.49 (~( ( setextAx ) =>
% 105.60/14.49 ( ( emptysetAx ) =>
% 105.60/14.49 ( ( setadjoinAx ) =>
% 105.60/14.49 ( ( powersetAx ) =>
% 105.60/14.49 ( ( setunionAx ) =>
% 105.60/14.49 ( ( omega0Ax ) =>
% 105.60/14.49 ( ( omegaSAx ) =>
% 105.60/14.49 ( ( omegaIndAx ) =>
% 105.60/14.49 ( ( replAx ) =>
% 105.60/14.49 ( ( foundationAx ) =>
% 105.60/14.49 ( ( wellorderingAx ) =>
% 105.60/14.49 ( ( descrp ) =>
% 105.60/14.49 ( ( dsetconstrI ) =>
% 105.60/14.49 ( ( dsetconstrEL ) =>
% 105.60/14.49 ( ( dsetconstrER ) =>
% 105.60/14.49 ( ( exuE1 ) =>
% 105.60/14.49 ( ( prop2setE ) =>
% 105.60/14.49 ( ( emptysetE ) =>
% 105.60/14.49 ( ( emptysetimpfalse ) =>
% 105.60/14.49 ( ( notinemptyset ) =>
% 105.60/14.49 ( ( exuE3e ) =>
% 105.60/14.49 ( ( setext ) =>
% 105.60/14.49 ( ( emptyI ) =>
% 105.60/14.49 ( ( noeltsimpempty ) =>
% 105.60/14.49 ( ( setbeta ) =>
% 105.60/14.49 ( ( nonemptyE1 ) =>
% 105.60/14.49 ( ( nonemptyI ) =>
% 105.60/14.49 ( ( nonemptyI1 ) =>
% 105.60/14.49 ( ( setadjoinIL ) =>
% 105.60/14.49 ( ( emptyinunitempty ) =>
% 105.60/14.49 ( ( setadjoinIR ) =>
% 105.60/14.49 ( (
% 105.60/14.49 setadjoinE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setadjoinOr ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setoftrueEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 emptyinPowerset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 emptyInPowerset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunionI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunionE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subPowSU ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exuE2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 nonemptyImpWitness ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 uniqinunit ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 notinsingleton ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 eqinunit ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 singletonsswitch ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairsetE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairsetIL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairsetIR ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 emptyE1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 vacuousDall ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 quantDeMorgan1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 quantDeMorgan2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 quantDeMorgan3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 quantDeMorgan4 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 prop2setI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 prop2set2propI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 notdexE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 notdallE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exuI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exuI3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exuI2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inCongP ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 in__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exuE3u ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exu__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 emptyset__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setadjoin__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powerset__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunion__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 omega__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 exuEu ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 descr__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dsetconstr__Cong ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 eqimpsubset2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 eqimpsubset1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetI2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 emptysetsubset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetE2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 notsubsetI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 notequalI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 notequalI2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetRefl ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetTrans ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setadjoinSub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setadjoinSub2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subset2powerset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setextsub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetemptysetimpeq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetE1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inPowerset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetsubset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 sepInPowerset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 sepSubset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionIL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairset2IR ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionIR ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionEcases ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionLsub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionRsub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectSubset5 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectEL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectLsub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectSubset2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectSubset3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectER ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 disjointsetsI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectRsub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectSubset4 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectSubset1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 bs114d ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusEL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusER ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusSubset2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusERneg ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusELneg ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusILneg ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusIRneg ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusLsub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusSubset1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 symdiffE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 symdiffI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 symdiffI2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 symdiffIneg1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 symdiffIneg2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 secondinupair ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairIL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairIR ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 kpairiskpair ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 kpairp ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 singletonsubset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 singletoninpowerset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 singletoninpowunion ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairset2E ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairsubunion ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairinpowunion ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ubforcartprodlem1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ubforcartprodlem2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ubforcartprodlem3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodpairin ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodmempair1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodmempair ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunionE2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunionsingleton1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunionsingleton2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setunionsingleton ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 singletonprop ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ex1E1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ex1I ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ex1I2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 singletonsuniq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjL1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 kfstsingleton ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 theprop ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 kfstpairEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodfstin ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjL2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjR11 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjR12 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjR1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 upairequniteq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjR2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setukpairinjR ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ksndsingleton ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ksndpairEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 kpairsurjEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodsndin ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodpairmemEL ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodpairmemER ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodmempaircEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodfstpairEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodsndpairEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 cartprodpairsurjEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dpsetconstrI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dpsetconstrSub ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setOfPairsIsBReln ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dpsetconstrERa ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dpsetconstrEL1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dpsetconstrEL2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 dpsetconstrER ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcImageSingleton ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 apProp ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 app ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 infuncsetfunc ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ap2p ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcinfuncset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 lamProp ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 lamp ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 lam2p ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 brelnall1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 brelnall2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ex1E2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcGraphProp1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcGraphProp3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcGraphProp2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcextLem ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcGraphProp4 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subbreln ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 eqbreln ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcext ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 funcext2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ap2apEq1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ap2apEq2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 beta1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 eta1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 lam2lamEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 beta2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 eta2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iffalseProp1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iffalseProp2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iftrueProp1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iftrueProp2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ifSingleton ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 ifp ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 theeq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iftrue ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iffalse ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 iftrueorfalse ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectT_lem ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionT_lem ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetT_lem ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setminusT_lem ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementT_lem ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 setextT ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 subsetTI ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetTI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 powersetTE1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementTI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementTE1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectTELcontra ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binintersectTERcontra ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 contrasubsetT ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 contrasubsetT1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 contrasubsetT2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 contrasubsetT3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 doubleComplementI1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 doubleComplementE1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 doubleComplementSub1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 doubleComplementSub2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 doubleComplementEq ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementTnotintersectT ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementImpComplementIntersect ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementSubsetComplementIntersect ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementInPowersetComplementIntersect ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 contraSubsetComplement ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementTcontraSubset ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionTILcontra ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionTIRcontra ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inIntersectImpInUnion ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inIntersectImpInUnion2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inIntersectImpInIntersectUnions ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 intersectInPowersetIntersectUnions ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inComplementUnionImpNotIn1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 inComplementUnionImpInComplement1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionTE ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 binunionTEcontra ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan2a1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 complementUnionInPowersetComplement ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan2a2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan1a ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan1b ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan2a ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan2b2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan2b ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 demorgan2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz13rule0 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz13rule1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz13rule2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz13rule3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz13rule4 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz1_1 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz1_2 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz1_3 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz1_4 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 woz1_5 ) =>
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 breln1all2 ) =>
% 105.60/14.49 (
% 105.60/14.49 ![
% 105.60/14.49 A:$i,R:$i]:
% 105.60/14.49 (
% 105.60/14.49 (
% 105.60/14.49 in @
% 105.60/14.49 R @
% 105.60/14.49 (
% 105.60/14.49 breln1Set
% 105.60/14.49 @
% 105.60/14.49 A ) ) =>
% 105.60/14.49 (
% 105.60/14.49 breln1 @
% 105.60/14.49 A @ R ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 105.60/14.49 inference('cnf.neg', [status(esa)], [breln1SetBreln1])).
% 105.60/14.49 thf(zip_derived_cl0, plain,
% 105.60/14.49 (~ (((setextAx) =>
% 105.60/14.49 (((emptysetAx) =>
% 105.60/14.49 (((setadjoinAx) =>
% 105.60/14.49 (((powersetAx) =>
% 105.60/14.49 (((setunionAx) =>
% 105.60/14.49 (((omega0Ax) =>
% 105.60/14.49 (((omegaSAx) =>
% 105.60/14.49 (((omegaIndAx) =>
% 105.60/14.49 (((replAx) =>
% 105.60/14.49 (((foundationAx) =>
% 105.60/14.49 (((wellorderingAx) =>
% 105.60/14.49 (((descrp) =>
% 105.60/14.49 (((dsetconstrI) =>
% 105.60/14.49 (((dsetconstrEL) =>
% 105.60/14.49 (((dsetconstrER) =>
% 105.60/14.49 (((exuE1) =>
% 105.60/14.49 (((prop2setE) =>
% 105.60/14.49 (((emptysetE) =>
% 105.60/14.49 (((emptysetimpfalse) =>
% 105.60/14.49 (((notinemptyset) =>
% 105.60/14.49 (((exuE3e) =>
% 105.60/14.49 (((setext) =>
% 105.60/14.49 (((emptyI) =>
% 105.60/14.49 (((noeltsimpempty) =>
% 105.60/14.49 (((setbeta) =>
% 105.60/14.49 (((nonemptyE1) =>
% 105.60/14.49 (((nonemptyI) =>
% 105.60/14.49 (((nonemptyI1) =>
% 105.60/14.49 (((setadjoinIL) =>
% 105.60/14.49 (((emptyinunitempty) =>
% 105.60/14.49 ((
% 105.60/14.49 (setadjoinIR) =>
% 105.60/14.49 ((
% 105.60/14.49 (setadjoinE) =>
% 105.60/14.49 ((
% 105.60/14.49 (setadjoinOr) =>
% 105.60/14.49 ((
% 105.60/14.49 (setoftrueEq) =>
% 105.60/14.49 ((
% 105.60/14.49 (powersetI) =>
% 105.60/14.49 ((
% 105.60/14.49 (emptyinPowerset) =>
% 105.60/14.49 ((
% 105.60/14.49 (emptyInPowerset) =>
% 105.60/14.49 ((
% 105.60/14.49 (powersetE) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunionI) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunionE) =>
% 105.60/14.49 ((
% 105.60/14.49 (subPowSU) =>
% 105.60/14.49 ((
% 105.60/14.49 (exuE2) =>
% 105.60/14.49 ((
% 105.60/14.49 (nonemptyImpWitness) =>
% 105.60/14.49 ((
% 105.60/14.49 (uniqinunit) =>
% 105.60/14.49 ((
% 105.60/14.49 (notinsingleton) =>
% 105.60/14.49 ((
% 105.60/14.49 (eqinunit) =>
% 105.60/14.49 ((
% 105.60/14.49 (singletonsswitch) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairsetE) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairsetIL) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairsetIR) =>
% 105.60/14.49 ((
% 105.60/14.49 (emptyE1) =>
% 105.60/14.49 ((
% 105.60/14.49 (vacuousDall) =>
% 105.60/14.49 ((
% 105.60/14.49 (quantDeMorgan1) =>
% 105.60/14.49 ((
% 105.60/14.49 (quantDeMorgan2) =>
% 105.60/14.49 ((
% 105.60/14.49 (quantDeMorgan3) =>
% 105.60/14.49 ((
% 105.60/14.49 (quantDeMorgan4) =>
% 105.60/14.49 ((
% 105.60/14.49 (prop2setI) =>
% 105.60/14.49 ((
% 105.60/14.49 (prop2set2propI) =>
% 105.60/14.49 ((
% 105.60/14.49 (notdexE) =>
% 105.60/14.49 ((
% 105.60/14.49 (notdallE) =>
% 105.60/14.49 ((
% 105.60/14.49 (exuI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (exuI3) =>
% 105.60/14.49 ((
% 105.60/14.49 (exuI2) =>
% 105.60/14.49 ((
% 105.60/14.49 (inCongP) =>
% 105.60/14.49 ((
% 105.60/14.49 (in__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (exuE3u) =>
% 105.60/14.49 ((
% 105.60/14.49 (exu__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (emptyset__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (setadjoin__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (powerset__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunion__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (omega__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (exuEu) =>
% 105.60/14.49 ((
% 105.60/14.49 (descr__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (dsetconstr__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (eqimpsubset2) =>
% 105.60/14.49 ((
% 105.60/14.49 (eqimpsubset1) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetI2) =>
% 105.60/14.49 ((
% 105.60/14.49 (emptysetsubset) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetE) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetE2) =>
% 105.60/14.49 ((
% 105.60/14.49 (notsubsetI) =>
% 105.60/14.49 ((
% 105.60/14.49 (notequalI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (notequalI2) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetRefl) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetTrans) =>
% 105.60/14.49 ((
% 105.60/14.49 (setadjoinSub) =>
% 105.60/14.49 ((
% 105.60/14.49 (setadjoinSub2) =>
% 105.60/14.49 ((
% 105.60/14.49 (subset2powerset) =>
% 105.60/14.49 ((
% 105.60/14.49 (setextsub) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetemptysetimpeq) =>
% 105.60/14.49 ((
% 105.60/14.49 (powersetI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (powersetE1) =>
% 105.60/14.49 ((
% 105.60/14.49 (inPowerset) =>
% 105.60/14.49 ((
% 105.60/14.49 (powersetsubset) =>
% 105.60/14.49 ((
% 105.60/14.49 (sepInPowerset) =>
% 105.60/14.49 ((
% 105.60/14.49 (sepSubset) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionIL) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairset2IR) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionIR) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionEcases) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionE) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionLsub) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionRsub) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectI) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectSubset5) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectEL) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectLsub) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectSubset2) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectSubset3) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectER) =>
% 105.60/14.49 ((
% 105.60/14.49 (disjointsetsI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectRsub) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectSubset4) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectSubset1) =>
% 105.60/14.49 ((
% 105.60/14.49 (bs114d) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusI) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusEL) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusER) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusSubset2) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusERneg) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusELneg) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusILneg) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusIRneg) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusLsub) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusSubset1) =>
% 105.60/14.49 ((
% 105.60/14.49 (symdiffE) =>
% 105.60/14.49 ((
% 105.60/14.49 (symdiffI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (symdiffI2) =>
% 105.60/14.49 ((
% 105.60/14.49 (symdiffIneg1) =>
% 105.60/14.49 ((
% 105.60/14.49 (symdiffIneg2) =>
% 105.60/14.49 ((
% 105.60/14.49 (secondinupair) =>
% 105.60/14.49 ((
% 105.60/14.49 (setukpairIL) =>
% 105.60/14.49 ((
% 105.60/14.49 (setukpairIR) =>
% 105.60/14.49 ((
% 105.60/14.49 (kpairiskpair) =>
% 105.60/14.49 ((
% 105.60/14.49 (kpairp) =>
% 105.60/14.49 ((
% 105.60/14.49 (singletonsubset) =>
% 105.60/14.49 ((
% 105.60/14.49 (singletoninpowerset) =>
% 105.60/14.49 ((
% 105.60/14.49 (singletoninpowunion) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairset2E) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairsubunion) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairinpowunion) =>
% 105.60/14.49 ((
% 105.60/14.49 (ubforcartprodlem1) =>
% 105.60/14.49 ((
% 105.60/14.49 (ubforcartprodlem2) =>
% 105.60/14.49 ((
% 105.60/14.49 (ubforcartprodlem3) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodpairin) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodmempair1) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodmempair) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunionE2) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunionsingleton1) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunionsingleton2) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunionsingleton) =>
% 105.60/14.49 ((
% 105.60/14.49 (singletonprop) =>
% 105.60/14.49 ((
% 105.60/14.49 (ex1E1) =>
% 105.60/14.49 ((
% 105.60/14.49 (ex1I) =>
% 105.60/14.49 ((
% 105.60/14.49 (ex1I2) =>
% 105.60/14.49 ((
% 105.60/14.49 (singletonsuniq) =>
% 105.60/14.49 ((
% 105.60/14.49 (setukpairinjL1) =>
% 105.60/14.49 ((
% 105.60/14.49 (kfstsingleton) =>
% 105.60/14.49 ((
% 105.60/14.49 (theprop) =>
% 105.60/14.49 ((
% 105.60/14.49 (kfstpairEq) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodfstin) =>
% 105.60/14.49 ((
% 105.60/14.49 (setukpairinjL2) =>
% 105.60/14.49 ((
% 105.60/14.49 (setukpairinjL) =>
% 105.60/14.49 ((
% 105.60/14.49 (setukpairinjR11) =>
% 105.60/14.49 ((
% 105.60/14.49 (setukpairinjR12) =>
% 105.60/14.49 ((
% 105.60/14.49 (setukpairinjR1) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairequniteq) =>
% 105.60/14.49 ((
% 105.60/14.49 (setukpairinjR2) =>
% 105.60/14.49 ((
% 105.60/14.49 (setukpairinjR) =>
% 105.60/14.49 ((
% 105.60/14.49 (ksndsingleton) =>
% 105.60/14.49 ((
% 105.60/14.49 (ksndpairEq) =>
% 105.60/14.49 ((
% 105.60/14.49 (kpairsurjEq) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodsndin) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodpairmemEL) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodpairmemER) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodmempaircEq) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodfstpairEq) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodsndpairEq) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodpairsurjEq) =>
% 105.60/14.49 ((
% 105.60/14.49 (dpsetconstrI) =>
% 105.60/14.49 ((
% 105.60/14.49 (dpsetconstrSub) =>
% 105.60/14.49 ((
% 105.60/14.49 (setOfPairsIsBReln) =>
% 105.60/14.49 ((
% 105.60/14.49 (dpsetconstrERa) =>
% 105.60/14.49 ((
% 105.60/14.49 (dpsetconstrEL1) =>
% 105.60/14.49 ((
% 105.60/14.49 (dpsetconstrEL2) =>
% 105.60/14.49 ((
% 105.60/14.49 (dpsetconstrER) =>
% 105.60/14.49 ((
% 105.60/14.49 (funcImageSingleton) =>
% 105.60/14.49 ((
% 105.60/14.49 (apProp) =>
% 105.60/14.49 ((
% 105.60/14.49 (app) =>
% 105.60/14.49 ((
% 105.60/14.49 (infuncsetfunc) =>
% 105.60/14.49 ((
% 105.60/14.49 (ap2p) =>
% 105.60/14.49 ((
% 105.60/14.49 (funcinfuncset) =>
% 105.60/14.49 ((
% 105.60/14.49 (lamProp) =>
% 105.60/14.49 ((
% 105.60/14.49 (lamp) =>
% 105.60/14.49 ((
% 105.60/14.49 (lam2p) =>
% 105.60/14.49 ((
% 105.60/14.49 (brelnall1) =>
% 105.60/14.49 ((
% 105.60/14.49 (brelnall2) =>
% 105.60/14.49 ((
% 105.60/14.49 (ex1E2) =>
% 105.60/14.49 ((
% 105.60/14.49 (funcGraphProp1) =>
% 105.60/14.49 ((
% 105.60/14.49 (funcGraphProp3) =>
% 105.60/14.49 ((
% 105.60/14.49 (funcGraphProp2) =>
% 105.60/14.49 ((
% 105.60/14.49 (funcextLem) =>
% 105.60/14.49 ((
% 105.60/14.49 (funcGraphProp4) =>
% 105.60/14.49 ((
% 105.60/14.49 (subbreln) =>
% 105.60/14.49 ((
% 105.60/14.49 (eqbreln) =>
% 105.60/14.49 ((
% 105.60/14.49 (funcext) =>
% 105.60/14.49 ((
% 105.60/14.49 (funcext2) =>
% 105.60/14.49 ((
% 105.60/14.49 (ap2apEq1) =>
% 105.60/14.49 ((
% 105.60/14.49 (ap2apEq2) =>
% 105.60/14.49 ((
% 105.60/14.49 (beta1) =>
% 105.60/14.49 ((
% 105.60/14.49 (eta1) =>
% 105.60/14.49 ((
% 105.60/14.49 (lam2lamEq) =>
% 105.60/14.49 ((
% 105.60/14.49 (beta2) =>
% 105.60/14.49 ((
% 105.60/14.49 (eta2) =>
% 105.60/14.49 ((
% 105.60/14.49 (iffalseProp1) =>
% 105.60/14.49 ((
% 105.60/14.49 (iffalseProp2) =>
% 105.60/14.49 ((
% 105.60/14.49 (iftrueProp1) =>
% 105.60/14.49 ((
% 105.60/14.49 (iftrueProp2) =>
% 105.60/14.49 ((
% 105.60/14.49 (ifSingleton) =>
% 105.60/14.49 ((
% 105.60/14.49 (ifp) =>
% 105.60/14.49 ((
% 105.60/14.49 (theeq) =>
% 105.60/14.49 ((
% 105.60/14.49 (iftrue) =>
% 105.60/14.49 ((
% 105.60/14.49 (iffalse) =>
% 105.60/14.49 ((
% 105.60/14.49 (iftrueorfalse) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectT_lem) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionT_lem) =>
% 105.60/14.49 ((
% 105.60/14.49 (powersetT_lem) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusT_lem) =>
% 105.60/14.49 ((
% 105.60/14.49 (complementT_lem) =>
% 105.60/14.49 ((
% 105.60/14.49 (setextT) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetTI) =>
% 105.60/14.49 ((
% 105.60/14.49 (powersetTI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (powersetTE1) =>
% 105.60/14.49 ((
% 105.60/14.49 (complementTI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (complementTE1) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectTELcontra) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectTERcontra) =>
% 105.60/14.49 ((
% 105.60/14.49 (contrasubsetT) =>
% 105.60/14.49 ((
% 105.60/14.49 (contrasubsetT1) =>
% 105.60/14.49 ((
% 105.60/14.49 (contrasubsetT2) =>
% 105.60/14.49 ((
% 105.60/14.49 (contrasubsetT3) =>
% 105.60/14.49 ((
% 105.60/14.49 (doubleComplementI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (doubleComplementE1) =>
% 105.60/14.49 ((
% 105.60/14.49 (doubleComplementSub1) =>
% 105.60/14.49 ((
% 105.60/14.49 (doubleComplementSub2) =>
% 105.60/14.49 ((
% 105.60/14.49 (doubleComplementEq) =>
% 105.60/14.49 ((
% 105.60/14.49 (complementTnotintersectT) =>
% 105.60/14.49 ((
% 105.60/14.49 (complementImpComplementIntersect) =>
% 105.60/14.49 ((
% 105.60/14.49 (complementSubsetComplementIntersect) =>
% 105.60/14.49 ((
% 105.60/14.49 (complementInPowersetComplementIntersect) =>
% 105.60/14.49 ((
% 105.60/14.49 (contraSubsetComplement) =>
% 105.60/14.49 ((
% 105.60/14.49 (complementTcontraSubset) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionTILcontra) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionTIRcontra) =>
% 105.60/14.49 ((
% 105.60/14.49 (inIntersectImpInUnion) =>
% 105.60/14.49 ((
% 105.60/14.49 (inIntersectImpInUnion2) =>
% 105.60/14.49 ((
% 105.60/14.49 (inIntersectImpInIntersectUnions) =>
% 105.60/14.49 ((
% 105.60/14.49 (intersectInPowersetIntersectUnions) =>
% 105.60/14.49 ((
% 105.60/14.49 (inComplementUnionImpNotIn1) =>
% 105.60/14.49 ((
% 105.60/14.49 (inComplementUnionImpInComplement1) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionTE) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionTEcontra) =>
% 105.60/14.49 ((
% 105.60/14.49 (demorgan2a1) =>
% 105.60/14.49 ((
% 105.60/14.49 (complementUnionInPowersetComplement) =>
% 105.60/14.49 ((
% 105.60/14.49 (demorgan2a2) =>
% 105.60/14.49 ((
% 105.60/14.49 (demorgan1a) =>
% 105.60/14.49 ((
% 105.60/14.49 (demorgan1b) =>
% 105.60/14.49 ((
% 105.60/14.49 (demorgan1) =>
% 105.60/14.49 ((
% 105.60/14.49 (demorgan2a) =>
% 105.60/14.49 ((
% 105.60/14.49 (demorgan2b2) =>
% 105.60/14.49 ((
% 105.60/14.49 (demorgan2b) =>
% 105.60/14.49 ((
% 105.60/14.49 (demorgan2) =>
% 105.60/14.49 ((
% 105.60/14.49 (woz13rule0) =>
% 105.60/14.49 ((
% 105.60/14.49 (woz13rule1) =>
% 105.60/14.49 ((
% 105.60/14.49 (woz13rule2) =>
% 105.60/14.49 ((
% 105.60/14.49 (woz13rule3) =>
% 105.60/14.49 ((
% 105.60/14.49 (woz13rule4) =>
% 105.60/14.49 ((
% 105.60/14.49 (woz1_1) =>
% 105.60/14.49 ((
% 105.60/14.49 (woz1_2) =>
% 105.60/14.49 ((
% 105.60/14.49 (woz1_3) =>
% 105.60/14.49 ((
% 105.60/14.49 (woz1_4) =>
% 105.60/14.49 ((
% 105.60/14.49 (woz1_5) =>
% 105.60/14.49 ((
% 105.60/14.49 (breln1all2) =>
% 105.60/14.49 ((
% 105.60/14.49 (!!) @ (
% 105.60/14.49 ^[Y0 : $i]:
% 105.60/14.49 ((
% 105.60/14.49 (!!) @ (
% 105.60/14.49 ^[Y1 : $i]:
% 105.60/14.49 ((
% 105.60/14.49 (in @
% 105.60/14.49 Y1 @
% 105.60/14.49 (
% 105.60/14.49 breln1Set @
% 105.60/14.49 Y0)) =>
% 105.60/14.49 (breln1 @
% 105.60/14.49 Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.49 inference('cnf', [status(esa)], [zf_stmt_0])).
% 105.60/14.49 thf(zip_derived_cl1, plain,
% 105.60/14.49 (~ (((setextAx) =>
% 105.60/14.49 (((emptysetAx) =>
% 105.60/14.49 (((setadjoinAx) =>
% 105.60/14.49 (((powersetAx) =>
% 105.60/14.49 (((setunionAx) =>
% 105.60/14.49 (((omega0Ax) =>
% 105.60/14.49 (((omegaSAx) =>
% 105.60/14.49 (((omegaIndAx) =>
% 105.60/14.49 (((replAx) =>
% 105.60/14.49 (((foundationAx) =>
% 105.60/14.49 (((wellorderingAx) =>
% 105.60/14.49 (((descrp) =>
% 105.60/14.49 (((dsetconstrI) =>
% 105.60/14.49 (((dsetconstrEL) =>
% 105.60/14.49 (((dsetconstrER) =>
% 105.60/14.49 (((exuE1) =>
% 105.60/14.49 (((prop2setE) =>
% 105.60/14.49 (((emptysetE) =>
% 105.60/14.49 (((emptysetimpfalse) =>
% 105.60/14.49 (((notinemptyset) =>
% 105.60/14.49 (((exuE3e) =>
% 105.60/14.49 (((setext) =>
% 105.60/14.49 (((emptyI) =>
% 105.60/14.49 (((noeltsimpempty) =>
% 105.60/14.49 (((setbeta) =>
% 105.60/14.49 (((nonemptyE1) =>
% 105.60/14.49 (((nonemptyI) =>
% 105.60/14.49 (((nonemptyI1) =>
% 105.60/14.49 (((setadjoinIL) =>
% 105.60/14.49 (((emptyinunitempty) =>
% 105.60/14.49 ((
% 105.60/14.49 (setadjoinIR) =>
% 105.60/14.49 ((
% 105.60/14.49 (setadjoinE) =>
% 105.60/14.49 ((
% 105.60/14.49 (setadjoinOr) =>
% 105.60/14.49 ((
% 105.60/14.49 (setoftrueEq) =>
% 105.60/14.49 ((
% 105.60/14.49 (powersetI) =>
% 105.60/14.49 ((
% 105.60/14.49 (emptyinPowerset) =>
% 105.60/14.49 ((
% 105.60/14.49 (emptyInPowerset) =>
% 105.60/14.49 ((
% 105.60/14.49 (powersetE) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunionI) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunionE) =>
% 105.60/14.49 ((
% 105.60/14.49 (subPowSU) =>
% 105.60/14.49 ((
% 105.60/14.49 (exuE2) =>
% 105.60/14.49 ((
% 105.60/14.49 (nonemptyImpWitness) =>
% 105.60/14.49 ((
% 105.60/14.49 (uniqinunit) =>
% 105.60/14.49 ((
% 105.60/14.49 (notinsingleton) =>
% 105.60/14.49 ((
% 105.60/14.49 (eqinunit) =>
% 105.60/14.49 ((
% 105.60/14.49 (singletonsswitch) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairsetE) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairsetIL) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairsetIR) =>
% 105.60/14.49 ((
% 105.60/14.49 (emptyE1) =>
% 105.60/14.49 ((
% 105.60/14.49 (vacuousDall) =>
% 105.60/14.49 ((
% 105.60/14.49 (quantDeMorgan1) =>
% 105.60/14.49 ((
% 105.60/14.49 (quantDeMorgan2) =>
% 105.60/14.49 ((
% 105.60/14.49 (quantDeMorgan3) =>
% 105.60/14.49 ((
% 105.60/14.49 (quantDeMorgan4) =>
% 105.60/14.49 ((
% 105.60/14.49 (prop2setI) =>
% 105.60/14.49 ((
% 105.60/14.49 (prop2set2propI) =>
% 105.60/14.49 ((
% 105.60/14.49 (notdexE) =>
% 105.60/14.49 ((
% 105.60/14.49 (notdallE) =>
% 105.60/14.49 ((
% 105.60/14.49 (exuI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (exuI3) =>
% 105.60/14.49 ((
% 105.60/14.49 (exuI2) =>
% 105.60/14.49 ((
% 105.60/14.49 (inCongP) =>
% 105.60/14.49 ((
% 105.60/14.49 (in__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (exuE3u) =>
% 105.60/14.49 ((
% 105.60/14.49 (exu__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (emptyset__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (setadjoin__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (powerset__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunion__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (omega__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (exuEu) =>
% 105.60/14.49 ((
% 105.60/14.49 (descr__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (dsetconstr__Cong) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (eqimpsubset2) =>
% 105.60/14.49 ((
% 105.60/14.49 (eqimpsubset1) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetI2) =>
% 105.60/14.49 ((
% 105.60/14.49 (emptysetsubset) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetE) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetE2) =>
% 105.60/14.49 ((
% 105.60/14.49 (notsubsetI) =>
% 105.60/14.49 ((
% 105.60/14.49 (notequalI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (notequalI2) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetRefl) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetTrans) =>
% 105.60/14.49 ((
% 105.60/14.49 (setadjoinSub) =>
% 105.60/14.49 ((
% 105.60/14.49 (setadjoinSub2) =>
% 105.60/14.49 ((
% 105.60/14.49 (subset2powerset) =>
% 105.60/14.49 ((
% 105.60/14.49 (setextsub) =>
% 105.60/14.49 ((
% 105.60/14.49 (subsetemptysetimpeq) =>
% 105.60/14.49 ((
% 105.60/14.49 (powersetI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (powersetE1) =>
% 105.60/14.49 ((
% 105.60/14.49 (inPowerset) =>
% 105.60/14.49 ((
% 105.60/14.49 (powersetsubset) =>
% 105.60/14.49 ((
% 105.60/14.49 (sepInPowerset) =>
% 105.60/14.49 ((
% 105.60/14.49 (sepSubset) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionIL) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairset2IR) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionIR) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionEcases) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionE) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionLsub) =>
% 105.60/14.49 ((
% 105.60/14.49 (binunionRsub) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectI) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectSubset5) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectEL) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectLsub) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectSubset2) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectSubset3) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectER) =>
% 105.60/14.49 ((
% 105.60/14.49 (disjointsetsI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectRsub) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectSubset4) =>
% 105.60/14.49 ((
% 105.60/14.49 (binintersectSubset1) =>
% 105.60/14.49 ((
% 105.60/14.49 (bs114d) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusI) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusEL) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusER) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusSubset2) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusERneg) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusELneg) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusILneg) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusIRneg) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusLsub) =>
% 105.60/14.49 ((
% 105.60/14.49 (setminusSubset1) =>
% 105.60/14.49 ((
% 105.60/14.49 (symdiffE) =>
% 105.60/14.49 ((
% 105.60/14.49 (symdiffI1) =>
% 105.60/14.49 ((
% 105.60/14.49 (symdiffI2) =>
% 105.60/14.49 ((
% 105.60/14.49 (symdiffIneg1) =>
% 105.60/14.49 ((
% 105.60/14.49 (symdiffIneg2) =>
% 105.60/14.49 ((
% 105.60/14.49 (secondinupair) =>
% 105.60/14.49 ((
% 105.60/14.49 (setukpairIL) =>
% 105.60/14.49 ((
% 105.60/14.49 (setukpairIR) =>
% 105.60/14.49 ((
% 105.60/14.49 (kpairiskpair) =>
% 105.60/14.49 ((
% 105.60/14.49 (kpairp) =>
% 105.60/14.49 ((
% 105.60/14.49 (singletonsubset) =>
% 105.60/14.49 ((
% 105.60/14.49 (singletoninpowerset) =>
% 105.60/14.49 ((
% 105.60/14.49 (singletoninpowunion) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairset2E) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairsubunion) =>
% 105.60/14.49 ((
% 105.60/14.49 (upairinpowunion) =>
% 105.60/14.49 ((
% 105.60/14.49 (ubforcartprodlem1) =>
% 105.60/14.49 ((
% 105.60/14.49 (ubforcartprodlem2) =>
% 105.60/14.49 ((
% 105.60/14.49 (ubforcartprodlem3) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodpairin) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodmempair1) =>
% 105.60/14.49 ((
% 105.60/14.49 (cartprodmempair) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunionE2) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunionsingleton1) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunionsingleton2) =>
% 105.60/14.49 ((
% 105.60/14.49 (setunionsingleton) =>
% 105.60/14.49 ((
% 105.60/14.49 (singletonprop) =>
% 105.60/14.49 ((
% 105.60/14.49 (ex1E1) =>
% 105.60/14.49 ((
% 105.60/14.50 (ex1I) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I2) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsuniq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (theprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstin) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR11) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR12) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR1) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairequniteq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemER) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempaircEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrI) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setOfPairsIsBReln) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrERa) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrER) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcImageSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (apProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (app) =>
% 105.60/14.50 ((
% 105.60/14.50 (infuncsetfunc) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcinfuncset) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall1) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp3) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcextLem) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp4) =>
% 105.60/14.50 ((
% 105.60/14.50 (subbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq2) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2lamEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifp) =>
% 105.60/14.50 ((
% 105.60/14.50 (theeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrue) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueorfalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextT) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTI) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTELcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTERcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT1) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT2) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT3) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTnotintersectT) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementImpComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementSubsetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementInPowersetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (contraSubsetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTcontraSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTILcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTIRcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (intersectInPowersetIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpNotIn1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpInComplement1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTEcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementUnionInPowersetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule0) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_5) =>
% 105.60/14.50 ((
% 105.60/14.50 (breln1all2) =>
% 105.60/14.50 ((
% 105.60/14.50 (!!) @ (
% 105.60/14.50 (('#B') @ (
% 105.60/14.50 !!) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#S') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 '#S') @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 =>))) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#C') @ in)) @
% 105.60/14.50 breln1Set)))))) @
% 105.60/14.50 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.50 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 105.60/14.50 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 105.60/14.50 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 105.60/14.50 define([status(thm)])).
% 105.60/14.50 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 105.60/14.50 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 105.60/14.50 thf('1', plain,
% 105.60/14.50 (( emptyinunitempty ) =
% 105.60/14.50 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 105.60/14.50 define([status(thm)])).
% 105.60/14.50 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 105.60/14.50 ((((emptyset) = (emptyset)))))).
% 105.60/14.50 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 105.60/14.50 define([status(thm)])).
% 105.60/14.50 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 105.60/14.50 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 105.60/14.50 define([status(thm)])).
% 105.60/14.50 thf(zip_derived_cl2, plain,
% 105.60/14.50 (~ (((setextAx) =>
% 105.60/14.50 (((emptysetAx) =>
% 105.60/14.50 (((setadjoinAx) =>
% 105.60/14.50 (((powersetAx) =>
% 105.60/14.50 (((setunionAx) =>
% 105.60/14.50 (((in @ emptyset @ omega) =>
% 105.60/14.50 (((omegaSAx) =>
% 105.60/14.50 (((omegaIndAx) =>
% 105.60/14.50 (((replAx) =>
% 105.60/14.50 (((foundationAx) =>
% 105.60/14.50 (((wellorderingAx) =>
% 105.60/14.50 (((descrp) =>
% 105.60/14.50 (((dsetconstrI) =>
% 105.60/14.50 (((dsetconstrEL) =>
% 105.60/14.50 (((dsetconstrER) =>
% 105.60/14.50 (((exuE1) =>
% 105.60/14.50 (((prop2setE) =>
% 105.60/14.50 (((emptysetE) =>
% 105.60/14.50 (((emptysetimpfalse) =>
% 105.60/14.50 (((notinemptyset) =>
% 105.60/14.50 (((exuE3e) =>
% 105.60/14.50 (((setext) =>
% 105.60/14.50 (((emptyI) =>
% 105.60/14.50 (((noeltsimpempty) =>
% 105.60/14.50 (((setbeta) =>
% 105.60/14.50 (((nonemptyE1) =>
% 105.60/14.50 (((nonemptyI) =>
% 105.60/14.50 (((nonemptyI1) =>
% 105.60/14.50 (((setadjoinIL) =>
% 105.60/14.50 (((in @
% 105.60/14.50 emptyset @
% 105.60/14.50 (setadjoin @
% 105.60/14.50 emptyset @
% 105.60/14.50 emptyset)) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinE) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinOr) =>
% 105.60/14.50 ((
% 105.60/14.50 (setoftrueEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyinPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subPowSU) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (nonemptyImpWitness) =>
% 105.60/14.50 ((
% 105.60/14.50 (uniqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (notinsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsswitch) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (vacuousDall) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan3) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan4) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2setI) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2set2propI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdexE) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdallE) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI3) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inCongP) =>
% 105.60/14.50 ((
% 105.60/14.50 (in__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE3u) =>
% 105.60/14.50 ((
% 105.60/14.50 (exu__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 ((
% 105.60/14.50 (emptyset) =
% 105.60/14.50 (emptyset))) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoin__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (powerset__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunion__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 ((
% 105.60/14.50 (omega) =
% 105.60/14.50 (omega))) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuEu) =>
% 105.60/14.50 ((
% 105.60/14.50 (descr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (dsetconstr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptysetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (notsubsetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetRefl) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTrans) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subset2powerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetemptysetimpeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2IR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionEcases) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectI) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset5) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset3) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectER) =>
% 105.60/14.50 ((
% 105.60/14.50 (disjointsetsI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset4) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (bs114d) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusER) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusERneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusELneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusILneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusIRneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffE) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg2) =>
% 105.60/14.50 ((
% 105.60/14.50 (secondinupair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairiskpair) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairp) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2E) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsubunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairinpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem3) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair1) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton1) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I2) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsuniq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (theprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstin) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR11) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR12) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR1) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairequniteq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemER) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempaircEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrI) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setOfPairsIsBReln) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrERa) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrER) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcImageSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (apProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (app) =>
% 105.60/14.50 ((
% 105.60/14.50 (infuncsetfunc) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcinfuncset) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall1) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp3) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcextLem) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp4) =>
% 105.60/14.50 ((
% 105.60/14.50 (subbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq2) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2lamEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifp) =>
% 105.60/14.50 ((
% 105.60/14.50 (theeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrue) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueorfalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextT) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTI) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTELcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTERcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT1) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT2) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT3) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTnotintersectT) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementImpComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementSubsetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementInPowersetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (contraSubsetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTcontraSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTILcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTIRcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (intersectInPowersetIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpNotIn1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpInComplement1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTEcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementUnionInPowersetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule0) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_5) =>
% 105.60/14.50 ((
% 105.60/14.50 (breln1all2) =>
% 105.60/14.50 ((
% 105.60/14.50 (!!) @ (
% 105.60/14.50 (('#B') @ (
% 105.60/14.50 !!) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#S') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 '#S') @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 =>))) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#C') @ in)) @
% 105.60/14.50 breln1Set)))))) @
% 105.60/14.50 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.50 inference('rw', [status(thm)], [zip_derived_cl1, '0', '1', '2', '3'])).
% 105.60/14.50 thf(zip_derived_cl3, plain,
% 105.60/14.50 (~ (((setextAx) =>
% 105.60/14.50 (((emptysetAx) =>
% 105.60/14.50 (((setadjoinAx) =>
% 105.60/14.50 (((powersetAx) =>
% 105.60/14.50 (((setunionAx) =>
% 105.60/14.50 (((in @ emptyset @ omega) =>
% 105.60/14.50 (((omegaSAx) =>
% 105.60/14.50 (((omegaIndAx) =>
% 105.60/14.50 (((replAx) =>
% 105.60/14.50 (((foundationAx) =>
% 105.60/14.50 (((wellorderingAx) =>
% 105.60/14.50 (((descrp) =>
% 105.60/14.50 (((dsetconstrI) =>
% 105.60/14.50 (((dsetconstrEL) =>
% 105.60/14.50 (((dsetconstrER) =>
% 105.60/14.50 (((exuE1) =>
% 105.60/14.50 (((prop2setE) =>
% 105.60/14.50 (((emptysetE) =>
% 105.60/14.50 (((emptysetimpfalse) =>
% 105.60/14.50 (((notinemptyset) =>
% 105.60/14.50 (((exuE3e) =>
% 105.60/14.50 (((setext) =>
% 105.60/14.50 (((emptyI) =>
% 105.60/14.50 (((noeltsimpempty) =>
% 105.60/14.50 (((setbeta) =>
% 105.60/14.50 (((nonemptyE1) =>
% 105.60/14.50 (((nonemptyI) =>
% 105.60/14.50 (((nonemptyI1) =>
% 105.60/14.50 (((setadjoinIL) =>
% 105.60/14.50 (((in @
% 105.60/14.50 emptyset @
% 105.60/14.50 (setadjoin @
% 105.60/14.50 emptyset @
% 105.60/14.50 emptyset)) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinE) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinOr) =>
% 105.60/14.50 ((
% 105.60/14.50 (setoftrueEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyinPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subPowSU) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (nonemptyImpWitness) =>
% 105.60/14.50 ((
% 105.60/14.50 (uniqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (notinsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsswitch) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (vacuousDall) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan3) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan4) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2setI) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2set2propI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdexE) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdallE) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI3) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inCongP) =>
% 105.60/14.50 ((
% 105.60/14.50 (in__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE3u) =>
% 105.60/14.50 ((
% 105.60/14.50 (exu__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoin__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (powerset__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunion__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuEu) =>
% 105.60/14.50 ((
% 105.60/14.50 (descr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (dsetconstr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptysetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (notsubsetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetRefl) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTrans) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subset2powerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetemptysetimpeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2IR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionEcases) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectI) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset5) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset3) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectER) =>
% 105.60/14.50 ((
% 105.60/14.50 (disjointsetsI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset4) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (bs114d) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusER) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusERneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusELneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusILneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusIRneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffE) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg2) =>
% 105.60/14.50 ((
% 105.60/14.50 (secondinupair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairiskpair) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairp) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2E) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsubunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairinpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem3) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair1) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton1) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I2) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsuniq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (theprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstin) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR11) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR12) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR1) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairequniteq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemER) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempaircEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrI) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setOfPairsIsBReln) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrERa) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrER) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcImageSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (apProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (app) =>
% 105.60/14.50 ((
% 105.60/14.50 (infuncsetfunc) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcinfuncset) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall1) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp3) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcextLem) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp4) =>
% 105.60/14.50 ((
% 105.60/14.50 (subbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq2) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2lamEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifp) =>
% 105.60/14.50 ((
% 105.60/14.50 (theeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrue) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueorfalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextT) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTI) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTELcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTERcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT1) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT2) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT3) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTnotintersectT) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementImpComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementSubsetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementInPowersetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (contraSubsetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTcontraSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTILcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTIRcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (intersectInPowersetIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpNotIn1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpInComplement1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTEcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementUnionInPowersetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule0) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_5) =>
% 105.60/14.50 ((
% 105.60/14.50 (breln1all2) =>
% 105.60/14.50 ((
% 105.60/14.50 (!!) @ (
% 105.60/14.50 (('#B') @ (
% 105.60/14.50 !!) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#S') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 '#S') @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 =>))) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#C') @ in)) @
% 105.60/14.50 breln1Set)))))) @
% 105.60/14.50 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.50 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl2])).
% 105.60/14.50 thf(zip_derived_cl5, plain,
% 105.60/14.50 (~ (((emptysetAx) =>
% 105.60/14.50 (((setadjoinAx) =>
% 105.60/14.50 (((powersetAx) =>
% 105.60/14.50 (((setunionAx) =>
% 105.60/14.50 (((in @ emptyset @ omega) =>
% 105.60/14.50 (((omegaSAx) =>
% 105.60/14.50 (((omegaIndAx) =>
% 105.60/14.50 (((replAx) =>
% 105.60/14.50 (((foundationAx) =>
% 105.60/14.50 (((wellorderingAx) =>
% 105.60/14.50 (((descrp) =>
% 105.60/14.50 (((dsetconstrI) =>
% 105.60/14.50 (((dsetconstrEL) =>
% 105.60/14.50 (((dsetconstrER) =>
% 105.60/14.50 (((exuE1) =>
% 105.60/14.50 (((prop2setE) =>
% 105.60/14.50 (((emptysetE) =>
% 105.60/14.50 (((emptysetimpfalse) =>
% 105.60/14.50 (((notinemptyset) =>
% 105.60/14.50 (((exuE3e) =>
% 105.60/14.50 (((setext) =>
% 105.60/14.50 (((emptyI) =>
% 105.60/14.50 (((noeltsimpempty) =>
% 105.60/14.50 (((setbeta) =>
% 105.60/14.50 (((nonemptyE1) =>
% 105.60/14.50 (((nonemptyI) =>
% 105.60/14.50 (((nonemptyI1) =>
% 105.60/14.50 (((setadjoinIL) =>
% 105.60/14.50 (((in @
% 105.60/14.50 emptyset @
% 105.60/14.50 (setadjoin @
% 105.60/14.50 emptyset @
% 105.60/14.50 emptyset)) =>
% 105.60/14.50 (((setadjoinIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinE) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinOr) =>
% 105.60/14.50 ((
% 105.60/14.50 (setoftrueEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyinPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subPowSU) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (nonemptyImpWitness) =>
% 105.60/14.50 ((
% 105.60/14.50 (uniqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (notinsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsswitch) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (vacuousDall) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan3) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan4) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2setI) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2set2propI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdexE) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdallE) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI3) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inCongP) =>
% 105.60/14.50 ((
% 105.60/14.50 (in__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE3u) =>
% 105.60/14.50 ((
% 105.60/14.50 (exu__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoin__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (powerset__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunion__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuEu) =>
% 105.60/14.50 ((
% 105.60/14.50 (descr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (dsetconstr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptysetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (notsubsetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetRefl) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTrans) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subset2powerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetemptysetimpeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2IR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionEcases) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectI) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset5) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset3) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectER) =>
% 105.60/14.50 ((
% 105.60/14.50 (disjointsetsI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset4) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (bs114d) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusER) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusERneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusELneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusILneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusIRneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffE) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg2) =>
% 105.60/14.50 ((
% 105.60/14.50 (secondinupair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairiskpair) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairp) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2E) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsubunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairinpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem3) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair1) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton1) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I2) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsuniq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (theprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstin) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR11) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR12) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR1) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairequniteq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemER) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempaircEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrI) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setOfPairsIsBReln) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrERa) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrER) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcImageSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (apProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (app) =>
% 105.60/14.50 ((
% 105.60/14.50 (infuncsetfunc) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcinfuncset) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall1) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp3) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcextLem) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp4) =>
% 105.60/14.50 ((
% 105.60/14.50 (subbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq2) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2lamEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifp) =>
% 105.60/14.50 ((
% 105.60/14.50 (theeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrue) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueorfalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextT) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTI) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTELcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTERcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT1) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT2) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT3) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTnotintersectT) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementImpComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementSubsetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementInPowersetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (contraSubsetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTcontraSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTILcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTIRcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (intersectInPowersetIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpNotIn1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpInComplement1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTEcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementUnionInPowersetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule0) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_5) =>
% 105.60/14.50 ((
% 105.60/14.50 (breln1all2) =>
% 105.60/14.50 ((
% 105.60/14.50 (!!) @ (
% 105.60/14.50 (('#B') @ (
% 105.60/14.50 !!) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#S') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 '#S') @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 =>))) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#C') @ in)) @
% 105.60/14.50 breln1Set)))))) @
% 105.60/14.50 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])).
% 105.60/14.50 thf(zip_derived_cl8, plain,
% 105.60/14.50 (~ (((setadjoinAx) =>
% 105.60/14.50 (((powersetAx) =>
% 105.60/14.50 (((setunionAx) =>
% 105.60/14.50 (((in @ emptyset @ omega) =>
% 105.60/14.50 (((omegaSAx) =>
% 105.60/14.50 (((omegaIndAx) =>
% 105.60/14.50 (((replAx) =>
% 105.60/14.50 (((foundationAx) =>
% 105.60/14.50 (((wellorderingAx) =>
% 105.60/14.50 (((descrp) =>
% 105.60/14.50 (((dsetconstrI) =>
% 105.60/14.50 (((dsetconstrEL) =>
% 105.60/14.50 (((dsetconstrER) =>
% 105.60/14.50 (((exuE1) =>
% 105.60/14.50 (((prop2setE) =>
% 105.60/14.50 (((emptysetE) =>
% 105.60/14.50 (((emptysetimpfalse) =>
% 105.60/14.50 (((notinemptyset) =>
% 105.60/14.50 (((exuE3e) =>
% 105.60/14.50 (((setext) =>
% 105.60/14.50 (((emptyI) =>
% 105.60/14.50 (((noeltsimpempty) =>
% 105.60/14.50 (((setbeta) =>
% 105.60/14.50 (((nonemptyE1) =>
% 105.60/14.50 (((nonemptyI) =>
% 105.60/14.50 (((nonemptyI1) =>
% 105.60/14.50 (((setadjoinIL) =>
% 105.60/14.50 (((in @
% 105.60/14.50 emptyset @
% 105.60/14.50 (setadjoin @
% 105.60/14.50 emptyset @
% 105.60/14.50 emptyset)) =>
% 105.60/14.50 (((setadjoinIR) =>
% 105.60/14.50 (((setadjoinE) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinOr) =>
% 105.60/14.50 ((
% 105.60/14.50 (setoftrueEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyinPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subPowSU) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (nonemptyImpWitness) =>
% 105.60/14.50 ((
% 105.60/14.50 (uniqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (notinsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsswitch) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (vacuousDall) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan3) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan4) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2setI) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2set2propI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdexE) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdallE) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI3) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inCongP) =>
% 105.60/14.50 ((
% 105.60/14.50 (in__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE3u) =>
% 105.60/14.50 ((
% 105.60/14.50 (exu__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoin__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (powerset__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunion__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuEu) =>
% 105.60/14.50 ((
% 105.60/14.50 (descr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (dsetconstr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptysetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (notsubsetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetRefl) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTrans) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subset2powerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetemptysetimpeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2IR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionEcases) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectI) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset5) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset3) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectER) =>
% 105.60/14.50 ((
% 105.60/14.50 (disjointsetsI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset4) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (bs114d) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusER) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusERneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusELneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusILneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusIRneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffE) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg2) =>
% 105.60/14.50 ((
% 105.60/14.50 (secondinupair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairiskpair) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairp) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2E) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsubunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairinpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem3) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair1) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton1) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I2) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsuniq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (theprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstin) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR11) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR12) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR1) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairequniteq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemER) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempaircEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrI) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setOfPairsIsBReln) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrERa) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrER) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcImageSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (apProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (app) =>
% 105.60/14.50 ((
% 105.60/14.50 (infuncsetfunc) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcinfuncset) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall1) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp3) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcextLem) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp4) =>
% 105.60/14.50 ((
% 105.60/14.50 (subbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq2) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2lamEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifp) =>
% 105.60/14.50 ((
% 105.60/14.50 (theeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrue) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueorfalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextT) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTI) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTELcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTERcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT1) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT2) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT3) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTnotintersectT) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementImpComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementSubsetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementInPowersetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (contraSubsetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTcontraSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTILcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTIRcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (intersectInPowersetIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpNotIn1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpInComplement1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTEcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementUnionInPowersetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule0) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_5) =>
% 105.60/14.50 ((
% 105.60/14.50 (breln1all2) =>
% 105.60/14.50 ((
% 105.60/14.50 (!!) @ (
% 105.60/14.50 (('#B') @ (
% 105.60/14.50 !!) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#S') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 '#S') @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 =>))) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#C') @ in)) @
% 105.60/14.50 breln1Set)))))) @
% 105.60/14.50 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])).
% 105.60/14.50 thf(zip_derived_cl13, plain,
% 105.60/14.50 (~ (((powersetAx) =>
% 105.60/14.50 (((setunionAx) =>
% 105.60/14.50 (((in @ emptyset @ omega) =>
% 105.60/14.50 (((omegaSAx) =>
% 105.60/14.50 (((omegaIndAx) =>
% 105.60/14.50 (((replAx) =>
% 105.60/14.50 (((foundationAx) =>
% 105.60/14.50 (((wellorderingAx) =>
% 105.60/14.50 (((descrp) =>
% 105.60/14.50 (((dsetconstrI) =>
% 105.60/14.50 (((dsetconstrEL) =>
% 105.60/14.50 (((dsetconstrER) =>
% 105.60/14.50 (((exuE1) =>
% 105.60/14.50 (((prop2setE) =>
% 105.60/14.50 (((emptysetE) =>
% 105.60/14.50 (((emptysetimpfalse) =>
% 105.60/14.50 (((notinemptyset) =>
% 105.60/14.50 (((exuE3e) =>
% 105.60/14.50 (((setext) =>
% 105.60/14.50 (((emptyI) =>
% 105.60/14.50 (((noeltsimpempty) =>
% 105.60/14.50 (((setbeta) =>
% 105.60/14.50 (((nonemptyE1) =>
% 105.60/14.50 (((nonemptyI) =>
% 105.60/14.50 (((nonemptyI1) =>
% 105.60/14.50 (((setadjoinIL) =>
% 105.60/14.50 (((in @
% 105.60/14.50 emptyset @
% 105.60/14.50 (setadjoin @
% 105.60/14.50 emptyset @
% 105.60/14.50 emptyset)) =>
% 105.60/14.50 (((setadjoinIR) =>
% 105.60/14.50 (((setadjoinE) =>
% 105.60/14.50 (((setadjoinOr) =>
% 105.60/14.50 ((
% 105.60/14.50 (setoftrueEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyinPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subPowSU) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (nonemptyImpWitness) =>
% 105.60/14.50 ((
% 105.60/14.50 (uniqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (notinsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsswitch) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (vacuousDall) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan3) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan4) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2setI) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2set2propI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdexE) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdallE) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI3) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inCongP) =>
% 105.60/14.50 ((
% 105.60/14.50 (in__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE3u) =>
% 105.60/14.50 ((
% 105.60/14.50 (exu__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoin__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (powerset__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunion__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuEu) =>
% 105.60/14.50 ((
% 105.60/14.50 (descr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (dsetconstr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptysetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (notsubsetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetRefl) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTrans) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subset2powerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetemptysetimpeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2IR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionEcases) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectI) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset5) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset3) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectER) =>
% 105.60/14.50 ((
% 105.60/14.50 (disjointsetsI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset4) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (bs114d) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusER) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusERneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusELneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusILneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusIRneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffE) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg2) =>
% 105.60/14.50 ((
% 105.60/14.50 (secondinupair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairiskpair) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairp) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2E) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsubunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairinpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem3) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair1) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton1) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I2) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsuniq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (theprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstin) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR11) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR12) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR1) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairequniteq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemER) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempaircEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrI) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setOfPairsIsBReln) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrERa) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrER) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcImageSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (apProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (app) =>
% 105.60/14.50 ((
% 105.60/14.50 (infuncsetfunc) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcinfuncset) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall1) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp3) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcextLem) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp4) =>
% 105.60/14.50 ((
% 105.60/14.50 (subbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq2) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2lamEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifp) =>
% 105.60/14.50 ((
% 105.60/14.50 (theeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrue) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueorfalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextT) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTI) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTELcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTERcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT1) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT2) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT3) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTnotintersectT) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementImpComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementSubsetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementInPowersetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (contraSubsetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTcontraSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTILcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTIRcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (intersectInPowersetIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpNotIn1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpInComplement1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTEcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementUnionInPowersetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule0) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_5) =>
% 105.60/14.50 ((
% 105.60/14.50 (breln1all2) =>
% 105.60/14.50 ((
% 105.60/14.50 (!!) @ (
% 105.60/14.50 (('#B') @ (
% 105.60/14.50 !!) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#S') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 '#S') @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 =>))) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#C') @ in)) @
% 105.60/14.50 breln1Set)))))) @
% 105.60/14.50 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])).
% 105.60/14.50 thf(zip_derived_cl19, plain,
% 105.60/14.50 (~ (((setunionAx) =>
% 105.60/14.50 (((in @ emptyset @ omega) =>
% 105.60/14.50 (((omegaSAx) =>
% 105.60/14.50 (((omegaIndAx) =>
% 105.60/14.50 (((replAx) =>
% 105.60/14.50 (((foundationAx) =>
% 105.60/14.50 (((wellorderingAx) =>
% 105.60/14.50 (((descrp) =>
% 105.60/14.50 (((dsetconstrI) =>
% 105.60/14.50 (((dsetconstrEL) =>
% 105.60/14.50 (((dsetconstrER) =>
% 105.60/14.50 (((exuE1) =>
% 105.60/14.50 (((prop2setE) =>
% 105.60/14.50 (((emptysetE) =>
% 105.60/14.50 (((emptysetimpfalse) =>
% 105.60/14.50 (((notinemptyset) =>
% 105.60/14.50 (((exuE3e) =>
% 105.60/14.50 (((setext) =>
% 105.60/14.50 (((emptyI) =>
% 105.60/14.50 (((noeltsimpempty) =>
% 105.60/14.50 (((setbeta) =>
% 105.60/14.50 (((nonemptyE1) =>
% 105.60/14.50 (((nonemptyI) =>
% 105.60/14.50 (((nonemptyI1) =>
% 105.60/14.50 (((setadjoinIL) =>
% 105.60/14.50 (((in @ emptyset @
% 105.60/14.50 (setadjoin @
% 105.60/14.50 emptyset @
% 105.60/14.50 emptyset)) =>
% 105.60/14.50 (((setadjoinIR) =>
% 105.60/14.50 (((setadjoinE) =>
% 105.60/14.50 (((setadjoinOr) =>
% 105.60/14.50 (((setoftrueEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyinPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subPowSU) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (nonemptyImpWitness) =>
% 105.60/14.50 ((
% 105.60/14.50 (uniqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (notinsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsswitch) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (vacuousDall) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan3) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan4) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2setI) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2set2propI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdexE) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdallE) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI3) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inCongP) =>
% 105.60/14.50 ((
% 105.60/14.50 (in__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE3u) =>
% 105.60/14.50 ((
% 105.60/14.50 (exu__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoin__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (powerset__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunion__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuEu) =>
% 105.60/14.50 ((
% 105.60/14.50 (descr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (dsetconstr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptysetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (notsubsetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetRefl) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTrans) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subset2powerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetemptysetimpeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2IR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionEcases) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectI) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset5) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset3) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectER) =>
% 105.60/14.50 ((
% 105.60/14.50 (disjointsetsI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset4) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (bs114d) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusER) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusERneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusELneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusILneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusIRneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffE) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg2) =>
% 105.60/14.50 ((
% 105.60/14.50 (secondinupair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairiskpair) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairp) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2E) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsubunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairinpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem3) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair1) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton1) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I2) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsuniq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (theprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstin) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR11) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR12) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR1) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairequniteq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemER) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempaircEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrI) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setOfPairsIsBReln) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrERa) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrER) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcImageSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (apProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (app) =>
% 105.60/14.50 ((
% 105.60/14.50 (infuncsetfunc) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcinfuncset) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall1) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp3) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcextLem) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp4) =>
% 105.60/14.50 ((
% 105.60/14.50 (subbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq2) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2lamEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifp) =>
% 105.60/14.50 ((
% 105.60/14.50 (theeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrue) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueorfalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextT) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTI) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTELcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTERcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT1) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT2) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT3) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTnotintersectT) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementImpComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementSubsetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementInPowersetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (contraSubsetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTcontraSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTILcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTIRcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (intersectInPowersetIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpNotIn1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpInComplement1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTEcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementUnionInPowersetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule0) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_5) =>
% 105.60/14.50 ((
% 105.60/14.50 (breln1all2) =>
% 105.60/14.50 ((
% 105.60/14.50 (!!) @ (
% 105.60/14.50 (('#B') @ (
% 105.60/14.50 !!) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#S') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 '#S') @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 =>))) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#C') @ in)) @
% 105.60/14.50 breln1Set)))))) @
% 105.60/14.50 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])).
% 105.60/14.50 thf(zip_derived_cl25, plain,
% 105.60/14.50 (~ (((in @ emptyset @ omega) =>
% 105.60/14.50 (((omegaSAx) =>
% 105.60/14.50 (((omegaIndAx) =>
% 105.60/14.50 (((replAx) =>
% 105.60/14.50 (((foundationAx) =>
% 105.60/14.50 (((wellorderingAx) =>
% 105.60/14.50 (((descrp) =>
% 105.60/14.50 (((dsetconstrI) =>
% 105.60/14.50 (((dsetconstrEL) =>
% 105.60/14.50 (((dsetconstrER) =>
% 105.60/14.50 (((exuE1) =>
% 105.60/14.50 (((prop2setE) =>
% 105.60/14.50 (((emptysetE) =>
% 105.60/14.50 (((emptysetimpfalse) =>
% 105.60/14.50 (((notinemptyset) =>
% 105.60/14.50 (((exuE3e) =>
% 105.60/14.50 (((setext) =>
% 105.60/14.50 (((emptyI) =>
% 105.60/14.50 (((noeltsimpempty) =>
% 105.60/14.50 (((setbeta) =>
% 105.60/14.50 (((nonemptyE1) =>
% 105.60/14.50 (((nonemptyI) =>
% 105.60/14.50 (((nonemptyI1) =>
% 105.60/14.50 (((setadjoinIL) =>
% 105.60/14.50 (((in @ emptyset @
% 105.60/14.50 (setadjoin @
% 105.60/14.50 emptyset @ emptyset)) =>
% 105.60/14.50 (((setadjoinIR) =>
% 105.60/14.50 (((setadjoinE) =>
% 105.60/14.50 (((setadjoinOr) =>
% 105.60/14.50 (((setoftrueEq) =>
% 105.60/14.50 (((powersetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyinPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subPowSU) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (nonemptyImpWitness) =>
% 105.60/14.50 ((
% 105.60/14.50 (uniqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (notinsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsswitch) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (vacuousDall) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan3) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan4) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2setI) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2set2propI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdexE) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdallE) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI3) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inCongP) =>
% 105.60/14.50 ((
% 105.60/14.50 (in__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE3u) =>
% 105.60/14.50 ((
% 105.60/14.50 (exu__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoin__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (powerset__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunion__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuEu) =>
% 105.60/14.50 ((
% 105.60/14.50 (descr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (dsetconstr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptysetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (notsubsetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetRefl) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTrans) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subset2powerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetemptysetimpeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2IR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionEcases) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectI) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset5) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset3) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectER) =>
% 105.60/14.50 ((
% 105.60/14.50 (disjointsetsI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset4) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (bs114d) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusER) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusERneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusELneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusILneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusIRneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffE) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg2) =>
% 105.60/14.50 ((
% 105.60/14.50 (secondinupair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairiskpair) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairp) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2E) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsubunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairinpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem3) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair1) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton1) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I2) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsuniq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (theprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstin) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR11) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR12) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR1) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairequniteq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemER) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempaircEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrI) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setOfPairsIsBReln) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrERa) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrER) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcImageSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (apProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (app) =>
% 105.60/14.50 ((
% 105.60/14.50 (infuncsetfunc) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcinfuncset) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall1) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp3) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcextLem) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp4) =>
% 105.60/14.50 ((
% 105.60/14.50 (subbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq2) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2lamEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifp) =>
% 105.60/14.50 ((
% 105.60/14.50 (theeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrue) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueorfalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextT) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTI) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTELcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTERcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT1) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT2) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT3) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTnotintersectT) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementImpComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementSubsetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementInPowersetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (contraSubsetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTcontraSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTILcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTIRcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (intersectInPowersetIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpNotIn1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpInComplement1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTEcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementUnionInPowersetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule0) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_5) =>
% 105.60/14.50 ((
% 105.60/14.50 (breln1all2) =>
% 105.60/14.50 ((
% 105.60/14.50 (!!) @ (
% 105.60/14.50 (('#B') @ (
% 105.60/14.50 !!) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#S') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 '#S') @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 =>))) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#C') @ in)) @
% 105.60/14.50 breln1Set)))))) @
% 105.60/14.50 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])).
% 105.60/14.50 thf(zip_derived_cl33, plain,
% 105.60/14.50 (~ (((omegaSAx) =>
% 105.60/14.50 (((omegaIndAx) =>
% 105.60/14.50 (((replAx) =>
% 105.60/14.50 (((foundationAx) =>
% 105.60/14.50 (((wellorderingAx) =>
% 105.60/14.50 (((descrp) =>
% 105.60/14.50 (((dsetconstrI) =>
% 105.60/14.50 (((dsetconstrEL) =>
% 105.60/14.50 (((dsetconstrER) =>
% 105.60/14.50 (((exuE1) =>
% 105.60/14.50 (((prop2setE) =>
% 105.60/14.50 (((emptysetE) =>
% 105.60/14.50 (((emptysetimpfalse) =>
% 105.60/14.50 (((notinemptyset) =>
% 105.60/14.50 (((exuE3e) =>
% 105.60/14.50 (((setext) =>
% 105.60/14.50 (((emptyI) =>
% 105.60/14.50 (((noeltsimpempty) =>
% 105.60/14.50 (((setbeta) =>
% 105.60/14.50 (((nonemptyE1) =>
% 105.60/14.50 (((nonemptyI) =>
% 105.60/14.50 (((nonemptyI1) =>
% 105.60/14.50 (((setadjoinIL) =>
% 105.60/14.50 (((in @ emptyset @
% 105.60/14.50 (setadjoin @
% 105.60/14.50 emptyset @ emptyset)) =>
% 105.60/14.50 (((setadjoinIR) =>
% 105.60/14.50 (((setadjoinE) =>
% 105.60/14.50 (((setadjoinOr) =>
% 105.60/14.50 (((setoftrueEq) =>
% 105.60/14.50 (((powersetI) =>
% 105.60/14.50 (((emptyinPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subPowSU) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (nonemptyImpWitness) =>
% 105.60/14.50 ((
% 105.60/14.50 (uniqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (notinsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsswitch) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (vacuousDall) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan3) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan4) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2setI) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2set2propI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdexE) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdallE) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI3) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inCongP) =>
% 105.60/14.50 ((
% 105.60/14.50 (in__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE3u) =>
% 105.60/14.50 ((
% 105.60/14.50 (exu__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoin__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (powerset__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunion__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuEu) =>
% 105.60/14.50 ((
% 105.60/14.50 (descr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (dsetconstr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptysetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (notsubsetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetRefl) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTrans) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subset2powerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetemptysetimpeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2IR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionEcases) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectI) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset5) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset3) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectER) =>
% 105.60/14.50 ((
% 105.60/14.50 (disjointsetsI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset4) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (bs114d) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusER) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusERneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusELneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusILneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusIRneg) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusSubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffE) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg1) =>
% 105.60/14.50 ((
% 105.60/14.50 (symdiffIneg2) =>
% 105.60/14.50 ((
% 105.60/14.50 (secondinupair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairiskpair) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairp) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletoninpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2E) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsubunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairinpowunion) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ubforcartprodlem3) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair1) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempair) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton1) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1I2) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsuniq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (theprop) =>
% 105.60/14.50 ((
% 105.60/14.50 (kfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstin) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjL) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR11) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR12) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR1) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairequniteq) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR2) =>
% 105.60/14.50 ((
% 105.60/14.50 (setukpairinjR) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ksndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (kpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndin) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemEL) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairmemER) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodmempaircEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodfstpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodsndpairEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (cartprodpairsurjEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrI) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setOfPairsIsBReln) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrERa) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL1) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrEL2) =>
% 105.60/14.50 ((
% 105.60/14.50 (dpsetconstrER) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcImageSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (apProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (app) =>
% 105.60/14.50 ((
% 105.60/14.50 (infuncsetfunc) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcinfuncset) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamProp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lamp) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2p) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall1) =>
% 105.60/14.50 ((
% 105.60/14.50 (brelnall2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ex1E2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp3) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcextLem) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcGraphProp4) =>
% 105.60/14.50 ((
% 105.60/14.50 (subbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqbreln) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext) =>
% 105.60/14.50 ((
% 105.60/14.50 (funcext2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq1) =>
% 105.60/14.50 ((
% 105.60/14.50 (ap2apEq2) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta1) =>
% 105.60/14.50 ((
% 105.60/14.50 (lam2lamEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (beta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eta2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalseProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp1) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueProp2) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifSingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (ifp) =>
% 105.60/14.50 ((
% 105.60/14.50 (theeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrue) =>
% 105.60/14.50 ((
% 105.60/14.50 (iffalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (iftrueorfalse) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setminusT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementT_lem) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextT) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTI) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTELcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectTERcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT1) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT2) =>
% 105.60/14.50 ((
% 105.60/14.50 (contrasubsetT3) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub1) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (doubleComplementEq) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTnotintersectT) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementImpComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementSubsetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementInPowersetComplementIntersect) =>
% 105.60/14.50 ((
% 105.60/14.50 (contraSubsetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementTcontraSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTILcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTIRcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInUnion2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inIntersectImpInIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (intersectInPowersetIntersectUnions) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpNotIn1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inComplementUnionImpInComplement1) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionTEcontra) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a1) =>
% 105.60/14.50 ((
% 105.60/14.50 (complementUnionInPowersetComplement) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2a) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b2) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2b) =>
% 105.60/14.50 ((
% 105.60/14.50 (demorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule0) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz13rule4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_1) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_2) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_3) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_4) =>
% 105.60/14.50 ((
% 105.60/14.50 (woz1_5) =>
% 105.60/14.50 ((
% 105.60/14.50 (breln1all2) =>
% 105.60/14.50 ((
% 105.60/14.50 (!!) @ (
% 105.60/14.50 (('#B') @ (
% 105.60/14.50 !!) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#S') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 '#S') @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 =>))) @
% 105.60/14.50 (
% 105.60/14.50 (
% 105.60/14.50 ('#B') @ (
% 105.60/14.50 (
% 105.60/14.50 ('#C') @ in)) @
% 105.60/14.50 breln1Set)))))) @
% 105.60/14.50 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 105.60/14.50 thf(zip_derived_cl40, plain,
% 105.60/14.50 (~ (((omegaIndAx) =>
% 105.60/14.50 (((replAx) =>
% 105.60/14.50 (((foundationAx) =>
% 105.60/14.50 (((wellorderingAx) =>
% 105.60/14.50 (((descrp) =>
% 105.60/14.50 (((dsetconstrI) =>
% 105.60/14.50 (((dsetconstrEL) =>
% 105.60/14.50 (((dsetconstrER) =>
% 105.60/14.50 (((exuE1) =>
% 105.60/14.50 (((prop2setE) =>
% 105.60/14.50 (((emptysetE) =>
% 105.60/14.50 (((emptysetimpfalse) =>
% 105.60/14.50 (((notinemptyset) =>
% 105.60/14.50 (((exuE3e) =>
% 105.60/14.50 (((setext) =>
% 105.60/14.50 (((emptyI) =>
% 105.60/14.50 (((noeltsimpempty) =>
% 105.60/14.50 (((setbeta) =>
% 105.60/14.50 (((nonemptyE1) =>
% 105.60/14.50 (((nonemptyI) =>
% 105.60/14.50 (((nonemptyI1) =>
% 105.60/14.50 (((setadjoinIL) =>
% 105.60/14.50 (((in @ emptyset @
% 105.60/14.50 (setadjoin @ emptyset @
% 105.60/14.50 emptyset)) =>
% 105.60/14.50 (((setadjoinIR) =>
% 105.60/14.50 (((setadjoinE) =>
% 105.60/14.50 (((setadjoinOr) =>
% 105.60/14.50 (((setoftrueEq) =>
% 105.60/14.50 (((powersetI) =>
% 105.60/14.50 (((emptyinPowerset) =>
% 105.60/14.50 (((emptyInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionI) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subPowSU) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (nonemptyImpWitness) =>
% 105.60/14.50 ((
% 105.60/14.50 (uniqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (notinsingleton) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqinunit) =>
% 105.60/14.50 ((
% 105.60/14.50 (singletonsswitch) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairsetIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptyE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (vacuousDall) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan1) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan2) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan3) =>
% 105.60/14.50 ((
% 105.60/14.50 (quantDeMorgan4) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2setI) =>
% 105.60/14.50 ((
% 105.60/14.50 (prop2set2propI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdexE) =>
% 105.60/14.50 ((
% 105.60/14.50 (notdallE) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI3) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (inCongP) =>
% 105.60/14.50 ((
% 105.60/14.50 (in__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuE3u) =>
% 105.60/14.50 ((
% 105.60/14.50 (exu__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoin__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (powerset__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (setunion__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (exuEu) =>
% 105.60/14.50 ((
% 105.60/14.50 (descr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (dsetconstr__Cong) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset2) =>
% 105.60/14.50 ((
% 105.60/14.50 (eqimpsubset1) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (emptysetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetE2) =>
% 105.60/14.50 ((
% 105.60/14.50 (notsubsetI) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (notequalI2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetRefl) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetTrans) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub) =>
% 105.60/14.50 ((
% 105.60/14.50 (setadjoinSub2) =>
% 105.60/14.50 ((
% 105.60/14.50 (subset2powerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (setextsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (subsetemptysetimpeq) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetI1) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetE1) =>
% 105.60/14.50 ((
% 105.60/14.50 (inPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (powersetsubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepInPowerset) =>
% 105.60/14.50 ((
% 105.60/14.50 (sepSubset) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIL) =>
% 105.60/14.50 ((
% 105.60/14.50 (upairset2IR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionIR) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionEcases) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionE) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionLsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binunionRsub) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectI) =>
% 105.60/14.50 ((
% 105.60/14.50 (binintersectSubset5) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset3) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectER) =>
% 105.60/14.51 ((
% 105.60/14.51 (disjointsetsI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectRsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset4) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (bs114d) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusI) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusER) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusERneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusELneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusILneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusIRneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffE) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg2) =>
% 105.60/14.51 ((
% 105.60/14.51 (secondinupair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairiskpair) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairp) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairset2E) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsubunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairinpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem3) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairin) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair1) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton1) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonprop) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1E1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1I) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1I2) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsuniq) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL1) =>
% 105.60/14.51 ((
% 105.60/14.51 (kfstsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (theprop) =>
% 105.60/14.51 ((
% 105.60/14.51 (kfstpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodfstin) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR11) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR12) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR1) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairequniteq) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR) =>
% 105.60/14.51 ((
% 105.60/14.51 (ksndsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (ksndpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairsurjEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodsndin) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairmemEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairmemER) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempaircEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodfstpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodsndpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairsurjEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrI) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrSub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setOfPairsIsBReln) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrERa) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrEL1) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrEL2) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrER) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcImageSingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (apProp) =>
% 105.60/14.51 ((
% 105.60/14.51 (app) =>
% 105.60/14.51 ((
% 105.60/14.51 (infuncsetfunc) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2p) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcinfuncset) =>
% 105.60/14.51 ((
% 105.60/14.51 (lamProp) =>
% 105.60/14.51 ((
% 105.60/14.51 (lamp) =>
% 105.60/14.51 ((
% 105.60/14.51 (lam2p) =>
% 105.60/14.51 ((
% 105.60/14.51 (brelnall1) =>
% 105.60/14.51 ((
% 105.60/14.51 (brelnall2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1E2) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp3) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcextLem) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp4) =>
% 105.60/14.51 ((
% 105.60/14.51 (subbreln) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqbreln) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcext) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcext2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2apEq1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2apEq2) =>
% 105.60/14.51 ((
% 105.60/14.51 (beta1) =>
% 105.60/14.51 ((
% 105.60/14.51 (eta1) =>
% 105.60/14.51 ((
% 105.60/14.51 (lam2lamEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (beta2) =>
% 105.60/14.51 ((
% 105.60/14.51 (eta2) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalseProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalseProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ifSingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (ifp) =>
% 105.60/14.51 ((
% 105.60/14.51 (theeq) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrue) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalse) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueorfalse) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (setextT) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetTI) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetTI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetTE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectTELcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectTERcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT1) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT2) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT3) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementSub1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementSub2) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTnotintersectT) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementImpComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementSubsetComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementInPowersetComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (contraSubsetComplement) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTcontraSubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTILcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTIRcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInUnion) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInUnion2) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInIntersectUnions) =>
% 105.60/14.51 ((
% 105.60/14.51 (intersectInPowersetIntersectUnions) =>
% 105.60/14.51 ((
% 105.60/14.51 (inComplementUnionImpNotIn1) =>
% 105.60/14.51 ((
% 105.60/14.51 (inComplementUnionImpInComplement1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTE) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTEcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementUnionInPowersetComplement) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a2) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1a) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1b) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2b2) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2b) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule0) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule1) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule3) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule4) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_1) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_3) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_4) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_5) =>
% 105.60/14.51 ((
% 105.60/14.51 (breln1all2) =>
% 105.60/14.51 ((
% 105.60/14.51 (!!) @ (
% 105.60/14.51 (('#B') @ (
% 105.60/14.51 !!) @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#S') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 '#S') @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 =>))) @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#C') @ in)) @
% 105.60/14.51 breln1Set)))))) @
% 105.60/14.51 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 105.60/14.51 thf(zip_derived_cl46, plain,
% 105.60/14.51 (~ (((replAx) =>
% 105.60/14.51 (((foundationAx) =>
% 105.60/14.51 (((wellorderingAx) =>
% 105.60/14.51 (((descrp) =>
% 105.60/14.51 (((dsetconstrI) =>
% 105.60/14.51 (((dsetconstrEL) =>
% 105.60/14.51 (((dsetconstrER) =>
% 105.60/14.51 (((exuE1) =>
% 105.60/14.51 (((prop2setE) =>
% 105.60/14.51 (((emptysetE) =>
% 105.60/14.51 (((emptysetimpfalse) =>
% 105.60/14.51 (((notinemptyset) =>
% 105.60/14.51 (((exuE3e) =>
% 105.60/14.51 (((setext) =>
% 105.60/14.51 (((emptyI) =>
% 105.60/14.51 (((noeltsimpempty) =>
% 105.60/14.51 (((setbeta) =>
% 105.60/14.51 (((nonemptyE1) =>
% 105.60/14.51 (((nonemptyI) =>
% 105.60/14.51 (((nonemptyI1) =>
% 105.60/14.51 (((setadjoinIL) =>
% 105.60/14.51 (((in @ emptyset @
% 105.60/14.51 (setadjoin @ emptyset @
% 105.60/14.51 emptyset)) =>
% 105.60/14.51 (((setadjoinIR) =>
% 105.60/14.51 (((setadjoinE) =>
% 105.60/14.51 (((setadjoinOr) =>
% 105.60/14.51 (((setoftrueEq) =>
% 105.60/14.51 (((powersetI) =>
% 105.60/14.51 (((emptyinPowerset) =>
% 105.60/14.51 (((emptyInPowerset) =>
% 105.60/14.51 (((powersetE) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionI) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionE) =>
% 105.60/14.51 ((
% 105.60/14.51 (subPowSU) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (nonemptyImpWitness) =>
% 105.60/14.51 ((
% 105.60/14.51 (uniqinunit) =>
% 105.60/14.51 ((
% 105.60/14.51 (notinsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqinunit) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsswitch) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetE) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (emptyE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (vacuousDall) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan1) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan2) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan3) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan4) =>
% 105.60/14.51 ((
% 105.60/14.51 (prop2setI) =>
% 105.60/14.51 ((
% 105.60/14.51 (prop2set2propI) =>
% 105.60/14.51 ((
% 105.60/14.51 (notdexE) =>
% 105.60/14.51 ((
% 105.60/14.51 (notdallE) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI3) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (inCongP) =>
% 105.60/14.51 ((
% 105.60/14.51 (in__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuE3u) =>
% 105.60/14.51 ((
% 105.60/14.51 (exu__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoin__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (powerset__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunion__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuEu) =>
% 105.60/14.51 ((
% 105.60/14.51 (descr__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (dsetconstr__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqimpsubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqimpsubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (emptysetsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetE) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (notsubsetI) =>
% 105.60/14.51 ((
% 105.60/14.51 (notequalI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (notequalI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetRefl) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetTrans) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoinSub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoinSub2) =>
% 105.60/14.51 ((
% 105.60/14.51 (subset2powerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (setextsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetemptysetimpeq) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (inPowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (sepInPowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (sepSubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairset2IR) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionEcases) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionE) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionRsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectI) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset5) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset3) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectER) =>
% 105.60/14.51 ((
% 105.60/14.51 (disjointsetsI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectRsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset4) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (bs114d) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusI) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusER) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusERneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusELneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusILneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusIRneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffE) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg2) =>
% 105.60/14.51 ((
% 105.60/14.51 (secondinupair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairiskpair) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairp) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairset2E) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsubunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairinpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem3) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairin) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair1) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton1) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonprop) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1E1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1I) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1I2) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsuniq) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL1) =>
% 105.60/14.51 ((
% 105.60/14.51 (kfstsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (theprop) =>
% 105.60/14.51 ((
% 105.60/14.51 (kfstpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodfstin) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR11) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR12) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR1) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairequniteq) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR) =>
% 105.60/14.51 ((
% 105.60/14.51 (ksndsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (ksndpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairsurjEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodsndin) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairmemEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairmemER) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempaircEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodfstpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodsndpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairsurjEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrI) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrSub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setOfPairsIsBReln) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrERa) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrEL1) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrEL2) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrER) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcImageSingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (apProp) =>
% 105.60/14.51 ((
% 105.60/14.51 (app) =>
% 105.60/14.51 ((
% 105.60/14.51 (infuncsetfunc) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2p) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcinfuncset) =>
% 105.60/14.51 ((
% 105.60/14.51 (lamProp) =>
% 105.60/14.51 ((
% 105.60/14.51 (lamp) =>
% 105.60/14.51 ((
% 105.60/14.51 (lam2p) =>
% 105.60/14.51 ((
% 105.60/14.51 (brelnall1) =>
% 105.60/14.51 ((
% 105.60/14.51 (brelnall2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1E2) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp3) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcextLem) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp4) =>
% 105.60/14.51 ((
% 105.60/14.51 (subbreln) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqbreln) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcext) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcext2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2apEq1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2apEq2) =>
% 105.60/14.51 ((
% 105.60/14.51 (beta1) =>
% 105.60/14.51 ((
% 105.60/14.51 (eta1) =>
% 105.60/14.51 ((
% 105.60/14.51 (lam2lamEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (beta2) =>
% 105.60/14.51 ((
% 105.60/14.51 (eta2) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalseProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalseProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ifSingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (ifp) =>
% 105.60/14.51 ((
% 105.60/14.51 (theeq) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrue) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalse) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueorfalse) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (setextT) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetTI) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetTI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetTE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectTELcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectTERcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT1) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT2) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT3) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementSub1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementSub2) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTnotintersectT) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementImpComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementSubsetComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementInPowersetComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (contraSubsetComplement) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTcontraSubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTILcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTIRcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInUnion) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInUnion2) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInIntersectUnions) =>
% 105.60/14.51 ((
% 105.60/14.51 (intersectInPowersetIntersectUnions) =>
% 105.60/14.51 ((
% 105.60/14.51 (inComplementUnionImpNotIn1) =>
% 105.60/14.51 ((
% 105.60/14.51 (inComplementUnionImpInComplement1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTE) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTEcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementUnionInPowersetComplement) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a2) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1a) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1b) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2b2) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2b) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule0) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule1) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule3) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule4) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_1) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_3) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_4) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_5) =>
% 105.60/14.51 ((
% 105.60/14.51 (breln1all2) =>
% 105.60/14.51 ((
% 105.60/14.51 (!!) @ (
% 105.60/14.51 (('#B') @ (
% 105.60/14.51 !!) @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#S') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 '#S') @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 =>))) @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#C') @ in)) @
% 105.60/14.51 breln1Set)))))) @
% 105.60/14.51 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
% 105.60/14.51 thf(zip_derived_cl52, plain,
% 105.60/14.51 (~ (((foundationAx) =>
% 105.60/14.51 (((wellorderingAx) =>
% 105.60/14.51 (((descrp) =>
% 105.60/14.51 (((dsetconstrI) =>
% 105.60/14.51 (((dsetconstrEL) =>
% 105.60/14.51 (((dsetconstrER) =>
% 105.60/14.51 (((exuE1) =>
% 105.60/14.51 (((prop2setE) =>
% 105.60/14.51 (((emptysetE) =>
% 105.60/14.51 (((emptysetimpfalse) =>
% 105.60/14.51 (((notinemptyset) =>
% 105.60/14.51 (((exuE3e) =>
% 105.60/14.51 (((setext) =>
% 105.60/14.51 (((emptyI) =>
% 105.60/14.51 (((noeltsimpempty) =>
% 105.60/14.51 (((setbeta) =>
% 105.60/14.51 (((nonemptyE1) =>
% 105.60/14.51 (((nonemptyI) =>
% 105.60/14.51 (((nonemptyI1) =>
% 105.60/14.51 (((setadjoinIL) =>
% 105.60/14.51 (((in @ emptyset @
% 105.60/14.51 (setadjoin @ emptyset @
% 105.60/14.51 emptyset)) =>
% 105.60/14.51 (((setadjoinIR) =>
% 105.60/14.51 (((setadjoinE) =>
% 105.60/14.51 (((setadjoinOr) =>
% 105.60/14.51 (((setoftrueEq) =>
% 105.60/14.51 (((powersetI) =>
% 105.60/14.51 (((emptyinPowerset) =>
% 105.60/14.51 (((emptyInPowerset) =>
% 105.60/14.51 (((powersetE) =>
% 105.60/14.51 (((setunionI) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionE) =>
% 105.60/14.51 ((
% 105.60/14.51 (subPowSU) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (nonemptyImpWitness) =>
% 105.60/14.51 ((
% 105.60/14.51 (uniqinunit) =>
% 105.60/14.51 ((
% 105.60/14.51 (notinsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqinunit) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsswitch) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetE) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (emptyE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (vacuousDall) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan1) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan2) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan3) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan4) =>
% 105.60/14.51 ((
% 105.60/14.51 (prop2setI) =>
% 105.60/14.51 ((
% 105.60/14.51 (prop2set2propI) =>
% 105.60/14.51 ((
% 105.60/14.51 (notdexE) =>
% 105.60/14.51 ((
% 105.60/14.51 (notdallE) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI3) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (inCongP) =>
% 105.60/14.51 ((
% 105.60/14.51 (in__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuE3u) =>
% 105.60/14.51 ((
% 105.60/14.51 (exu__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoin__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (powerset__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunion__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuEu) =>
% 105.60/14.51 ((
% 105.60/14.51 (descr__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (dsetconstr__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqimpsubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqimpsubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (emptysetsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetE) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (notsubsetI) =>
% 105.60/14.51 ((
% 105.60/14.51 (notequalI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (notequalI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetRefl) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetTrans) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoinSub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoinSub2) =>
% 105.60/14.51 ((
% 105.60/14.51 (subset2powerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (setextsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetemptysetimpeq) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (inPowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (sepInPowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (sepSubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairset2IR) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionEcases) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionE) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionRsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectI) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset5) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset3) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectER) =>
% 105.60/14.51 ((
% 105.60/14.51 (disjointsetsI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectRsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset4) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (bs114d) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusI) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusER) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusERneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusELneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusILneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusIRneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffE) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg2) =>
% 105.60/14.51 ((
% 105.60/14.51 (secondinupair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairiskpair) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairp) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairset2E) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsubunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairinpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem3) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairin) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair1) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton1) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonprop) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1E1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1I) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1I2) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsuniq) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL1) =>
% 105.60/14.51 ((
% 105.60/14.51 (kfstsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (theprop) =>
% 105.60/14.51 ((
% 105.60/14.51 (kfstpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodfstin) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR11) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR12) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR1) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairequniteq) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR) =>
% 105.60/14.51 ((
% 105.60/14.51 (ksndsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (ksndpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairsurjEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodsndin) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairmemEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairmemER) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempaircEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodfstpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodsndpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairsurjEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrI) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrSub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setOfPairsIsBReln) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrERa) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrEL1) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrEL2) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrER) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcImageSingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (apProp) =>
% 105.60/14.51 ((
% 105.60/14.51 (app) =>
% 105.60/14.51 ((
% 105.60/14.51 (infuncsetfunc) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2p) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcinfuncset) =>
% 105.60/14.51 ((
% 105.60/14.51 (lamProp) =>
% 105.60/14.51 ((
% 105.60/14.51 (lamp) =>
% 105.60/14.51 ((
% 105.60/14.51 (lam2p) =>
% 105.60/14.51 ((
% 105.60/14.51 (brelnall1) =>
% 105.60/14.51 ((
% 105.60/14.51 (brelnall2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1E2) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp3) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcextLem) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp4) =>
% 105.60/14.51 ((
% 105.60/14.51 (subbreln) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqbreln) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcext) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcext2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2apEq1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2apEq2) =>
% 105.60/14.51 ((
% 105.60/14.51 (beta1) =>
% 105.60/14.51 ((
% 105.60/14.51 (eta1) =>
% 105.60/14.51 ((
% 105.60/14.51 (lam2lamEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (beta2) =>
% 105.60/14.51 ((
% 105.60/14.51 (eta2) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalseProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalseProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ifSingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (ifp) =>
% 105.60/14.51 ((
% 105.60/14.51 (theeq) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrue) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalse) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueorfalse) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (setextT) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetTI) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetTI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetTE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectTELcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectTERcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT1) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT2) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT3) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementSub1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementSub2) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTnotintersectT) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementImpComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementSubsetComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementInPowersetComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (contraSubsetComplement) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTcontraSubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTILcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTIRcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInUnion) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInUnion2) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInIntersectUnions) =>
% 105.60/14.51 ((
% 105.60/14.51 (intersectInPowersetIntersectUnions) =>
% 105.60/14.51 ((
% 105.60/14.51 (inComplementUnionImpNotIn1) =>
% 105.60/14.51 ((
% 105.60/14.51 (inComplementUnionImpInComplement1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTE) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTEcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementUnionInPowersetComplement) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a2) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1a) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1b) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2b2) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2b) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule0) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule1) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule3) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule4) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_1) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_3) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_4) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_5) =>
% 105.60/14.51 ((
% 105.60/14.51 (breln1all2) =>
% 105.60/14.51 ((
% 105.60/14.51 (!!) @ (
% 105.60/14.51 (('#B') @ (
% 105.60/14.51 !!) @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#S') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 '#S') @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 =>))) @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#C') @ in)) @
% 105.60/14.51 breln1Set)))))) @
% 105.60/14.51 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 105.60/14.51 thf(zip_derived_cl58, plain,
% 105.60/14.51 (~ (((wellorderingAx) =>
% 105.60/14.51 (((descrp) =>
% 105.60/14.51 (((dsetconstrI) =>
% 105.60/14.51 (((dsetconstrEL) =>
% 105.60/14.51 (((dsetconstrER) =>
% 105.60/14.51 (((exuE1) =>
% 105.60/14.51 (((prop2setE) =>
% 105.60/14.51 (((emptysetE) =>
% 105.60/14.51 (((emptysetimpfalse) =>
% 105.60/14.51 (((notinemptyset) =>
% 105.60/14.51 (((exuE3e) =>
% 105.60/14.51 (((setext) =>
% 105.60/14.51 (((emptyI) =>
% 105.60/14.51 (((noeltsimpempty) =>
% 105.60/14.51 (((setbeta) =>
% 105.60/14.51 (((nonemptyE1) =>
% 105.60/14.51 (((nonemptyI) =>
% 105.60/14.51 (((nonemptyI1) =>
% 105.60/14.51 (((setadjoinIL) =>
% 105.60/14.51 (((in @ emptyset @
% 105.60/14.51 (setadjoin @ emptyset @
% 105.60/14.51 emptyset)) =>
% 105.60/14.51 (((setadjoinIR) =>
% 105.60/14.51 (((setadjoinE) =>
% 105.60/14.51 (((setadjoinOr) =>
% 105.60/14.51 (((setoftrueEq) =>
% 105.60/14.51 (((powersetI) =>
% 105.60/14.51 (((emptyinPowerset) =>
% 105.60/14.51 (((emptyInPowerset) =>
% 105.60/14.51 (((powersetE) =>
% 105.60/14.51 (((setunionI) =>
% 105.60/14.51 (((setunionE) =>
% 105.60/14.51 ((
% 105.60/14.51 (subPowSU) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (nonemptyImpWitness) =>
% 105.60/14.51 ((
% 105.60/14.51 (uniqinunit) =>
% 105.60/14.51 ((
% 105.60/14.51 (notinsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqinunit) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsswitch) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetE) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (emptyE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (vacuousDall) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan1) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan2) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan3) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan4) =>
% 105.60/14.51 ((
% 105.60/14.51 (prop2setI) =>
% 105.60/14.51 ((
% 105.60/14.51 (prop2set2propI) =>
% 105.60/14.51 ((
% 105.60/14.51 (notdexE) =>
% 105.60/14.51 ((
% 105.60/14.51 (notdallE) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI3) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (inCongP) =>
% 105.60/14.51 ((
% 105.60/14.51 (in__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuE3u) =>
% 105.60/14.51 ((
% 105.60/14.51 (exu__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoin__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (powerset__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunion__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuEu) =>
% 105.60/14.51 ((
% 105.60/14.51 (descr__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (dsetconstr__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqimpsubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqimpsubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (emptysetsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetE) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (notsubsetI) =>
% 105.60/14.51 ((
% 105.60/14.51 (notequalI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (notequalI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetRefl) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetTrans) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoinSub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoinSub2) =>
% 105.60/14.51 ((
% 105.60/14.51 (subset2powerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (setextsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetemptysetimpeq) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (inPowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (sepInPowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (sepSubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairset2IR) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionEcases) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionE) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionRsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectI) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset5) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset3) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectER) =>
% 105.60/14.51 ((
% 105.60/14.51 (disjointsetsI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectRsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset4) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (bs114d) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusI) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusER) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusERneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusELneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusILneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusIRneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffE) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg2) =>
% 105.60/14.51 ((
% 105.60/14.51 (secondinupair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairiskpair) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairp) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairset2E) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsubunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairinpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem3) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairin) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair1) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton1) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonprop) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1E1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1I) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1I2) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsuniq) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL1) =>
% 105.60/14.51 ((
% 105.60/14.51 (kfstsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (theprop) =>
% 105.60/14.51 ((
% 105.60/14.51 (kfstpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodfstin) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR11) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR12) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR1) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairequniteq) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR) =>
% 105.60/14.51 ((
% 105.60/14.51 (ksndsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (ksndpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairsurjEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodsndin) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairmemEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairmemER) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempaircEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodfstpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodsndpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairsurjEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrI) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrSub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setOfPairsIsBReln) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrERa) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrEL1) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrEL2) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrER) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcImageSingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (apProp) =>
% 105.60/14.51 ((
% 105.60/14.51 (app) =>
% 105.60/14.51 ((
% 105.60/14.51 (infuncsetfunc) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2p) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcinfuncset) =>
% 105.60/14.51 ((
% 105.60/14.51 (lamProp) =>
% 105.60/14.51 ((
% 105.60/14.51 (lamp) =>
% 105.60/14.51 ((
% 105.60/14.51 (lam2p) =>
% 105.60/14.51 ((
% 105.60/14.51 (brelnall1) =>
% 105.60/14.51 ((
% 105.60/14.51 (brelnall2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1E2) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp3) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcextLem) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp4) =>
% 105.60/14.51 ((
% 105.60/14.51 (subbreln) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqbreln) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcext) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcext2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2apEq1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2apEq2) =>
% 105.60/14.51 ((
% 105.60/14.51 (beta1) =>
% 105.60/14.51 ((
% 105.60/14.51 (eta1) =>
% 105.60/14.51 ((
% 105.60/14.51 (lam2lamEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (beta2) =>
% 105.60/14.51 ((
% 105.60/14.51 (eta2) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalseProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalseProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ifSingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (ifp) =>
% 105.60/14.51 ((
% 105.60/14.51 (theeq) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrue) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalse) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueorfalse) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (setextT) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetTI) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetTI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetTE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectTELcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectTERcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT1) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT2) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT3) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementSub1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementSub2) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTnotintersectT) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementImpComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementSubsetComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementInPowersetComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (contraSubsetComplement) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTcontraSubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTILcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTIRcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInUnion) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInUnion2) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInIntersectUnions) =>
% 105.60/14.51 ((
% 105.60/14.51 (intersectInPowersetIntersectUnions) =>
% 105.60/14.51 ((
% 105.60/14.51 (inComplementUnionImpNotIn1) =>
% 105.60/14.51 ((
% 105.60/14.51 (inComplementUnionImpInComplement1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTE) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTEcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementUnionInPowersetComplement) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a2) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1a) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1b) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2b2) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2b) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule0) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule1) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule3) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule4) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_1) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_3) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_4) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_5) =>
% 105.60/14.51 ((
% 105.60/14.51 (breln1all2) =>
% 105.60/14.51 ((
% 105.60/14.51 (!!) @ (
% 105.60/14.51 (('#B') @ (
% 105.60/14.51 !!) @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#S') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 '#S') @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 =>))) @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#C') @ in)) @
% 105.60/14.51 breln1Set)))))) @
% 105.60/14.51 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
% 105.60/14.51 thf(zip_derived_cl64, plain,
% 105.60/14.51 (~ (((descrp) =>
% 105.60/14.51 (((dsetconstrI) =>
% 105.60/14.51 (((dsetconstrEL) =>
% 105.60/14.51 (((dsetconstrER) =>
% 105.60/14.51 (((exuE1) =>
% 105.60/14.51 (((prop2setE) =>
% 105.60/14.51 (((emptysetE) =>
% 105.60/14.51 (((emptysetimpfalse) =>
% 105.60/14.51 (((notinemptyset) =>
% 105.60/14.51 (((exuE3e) =>
% 105.60/14.51 (((setext) =>
% 105.60/14.51 (((emptyI) =>
% 105.60/14.51 (((noeltsimpempty) =>
% 105.60/14.51 (((setbeta) =>
% 105.60/14.51 (((nonemptyE1) =>
% 105.60/14.51 (((nonemptyI) =>
% 105.60/14.51 (((nonemptyI1) =>
% 105.60/14.51 (((setadjoinIL) =>
% 105.60/14.51 (((in @ emptyset @
% 105.60/14.51 (setadjoin @ emptyset @ emptyset)) =>
% 105.60/14.51 (((setadjoinIR) =>
% 105.60/14.51 (((setadjoinE) =>
% 105.60/14.51 (((setadjoinOr) =>
% 105.60/14.51 (((setoftrueEq) =>
% 105.60/14.51 (((powersetI) =>
% 105.60/14.51 (((emptyinPowerset) =>
% 105.60/14.51 (((emptyInPowerset) =>
% 105.60/14.51 (((powersetE) =>
% 105.60/14.51 (((setunionI) =>
% 105.60/14.51 (((setunionE) =>
% 105.60/14.51 (((subPowSU) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (nonemptyImpWitness) =>
% 105.60/14.51 ((
% 105.60/14.51 (uniqinunit) =>
% 105.60/14.51 ((
% 105.60/14.51 (notinsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqinunit) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsswitch) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetE) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (emptyE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (vacuousDall) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan1) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan2) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan3) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan4) =>
% 105.60/14.51 ((
% 105.60/14.51 (prop2setI) =>
% 105.60/14.51 ((
% 105.60/14.51 (prop2set2propI) =>
% 105.60/14.51 ((
% 105.60/14.51 (notdexE) =>
% 105.60/14.51 ((
% 105.60/14.51 (notdallE) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI3) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (inCongP) =>
% 105.60/14.51 ((
% 105.60/14.51 (in__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuE3u) =>
% 105.60/14.51 ((
% 105.60/14.51 (exu__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoin__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (powerset__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunion__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuEu) =>
% 105.60/14.51 ((
% 105.60/14.51 (descr__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (dsetconstr__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqimpsubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqimpsubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (emptysetsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetE) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (notsubsetI) =>
% 105.60/14.51 ((
% 105.60/14.51 (notequalI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (notequalI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetRefl) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetTrans) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoinSub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoinSub2) =>
% 105.60/14.51 ((
% 105.60/14.51 (subset2powerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (setextsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetemptysetimpeq) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (inPowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (sepInPowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (sepSubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairset2IR) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionEcases) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionE) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionRsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectI) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset5) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset3) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectER) =>
% 105.60/14.51 ((
% 105.60/14.51 (disjointsetsI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectRsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset4) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (bs114d) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusI) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusER) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusERneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusELneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusILneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusIRneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffE) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg2) =>
% 105.60/14.51 ((
% 105.60/14.51 (secondinupair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairiskpair) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairp) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairset2E) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsubunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairinpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem3) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairin) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair1) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton1) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonprop) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1E1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1I) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1I2) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsuniq) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL1) =>
% 105.60/14.51 ((
% 105.60/14.51 (kfstsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (theprop) =>
% 105.60/14.51 ((
% 105.60/14.51 (kfstpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodfstin) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR11) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR12) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR1) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairequniteq) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR) =>
% 105.60/14.51 ((
% 105.60/14.51 (ksndsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (ksndpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairsurjEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodsndin) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairmemEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairmemER) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempaircEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodfstpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodsndpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairsurjEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrI) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrSub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setOfPairsIsBReln) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrERa) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrEL1) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrEL2) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrER) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcImageSingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (apProp) =>
% 105.60/14.51 ((
% 105.60/14.51 (app) =>
% 105.60/14.51 ((
% 105.60/14.51 (infuncsetfunc) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2p) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcinfuncset) =>
% 105.60/14.51 ((
% 105.60/14.51 (lamProp) =>
% 105.60/14.51 ((
% 105.60/14.51 (lamp) =>
% 105.60/14.51 ((
% 105.60/14.51 (lam2p) =>
% 105.60/14.51 ((
% 105.60/14.51 (brelnall1) =>
% 105.60/14.51 ((
% 105.60/14.51 (brelnall2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1E2) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp3) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcextLem) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp4) =>
% 105.60/14.51 ((
% 105.60/14.51 (subbreln) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqbreln) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcext) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcext2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2apEq1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2apEq2) =>
% 105.60/14.51 ((
% 105.60/14.51 (beta1) =>
% 105.60/14.51 ((
% 105.60/14.51 (eta1) =>
% 105.60/14.51 ((
% 105.60/14.51 (lam2lamEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (beta2) =>
% 105.60/14.51 ((
% 105.60/14.51 (eta2) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalseProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalseProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ifSingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (ifp) =>
% 105.60/14.51 ((
% 105.60/14.51 (theeq) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrue) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalse) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueorfalse) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (setextT) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetTI) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetTI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetTE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectTELcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectTERcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT1) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT2) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT3) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementSub1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementSub2) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTnotintersectT) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementImpComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementSubsetComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementInPowersetComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (contraSubsetComplement) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTcontraSubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTILcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTIRcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInUnion) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInUnion2) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInIntersectUnions) =>
% 105.60/14.51 ((
% 105.60/14.51 (intersectInPowersetIntersectUnions) =>
% 105.60/14.51 ((
% 105.60/14.51 (inComplementUnionImpNotIn1) =>
% 105.60/14.51 ((
% 105.60/14.51 (inComplementUnionImpInComplement1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTE) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTEcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementUnionInPowersetComplement) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a2) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1a) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1b) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2b2) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2b) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule0) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule1) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule3) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule4) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_1) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_3) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_4) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_5) =>
% 105.60/14.51 ((
% 105.60/14.51 (breln1all2) =>
% 105.60/14.51 ((
% 105.60/14.51 (!!) @ (
% 105.60/14.51 (('#B') @ (
% 105.60/14.51 !!) @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#S') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 '#S') @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 =>))) @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#C') @ in)) @
% 105.60/14.51 breln1Set)))))) @
% 105.60/14.51 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])).
% 105.60/14.51 thf(zip_derived_cl71, plain,
% 105.60/14.51 (~ (((dsetconstrI) =>
% 105.60/14.51 (((dsetconstrEL) =>
% 105.60/14.51 (((dsetconstrER) =>
% 105.60/14.51 (((exuE1) =>
% 105.60/14.51 (((prop2setE) =>
% 105.60/14.51 (((emptysetE) =>
% 105.60/14.51 (((emptysetimpfalse) =>
% 105.60/14.51 (((notinemptyset) =>
% 105.60/14.51 (((exuE3e) =>
% 105.60/14.51 (((setext) =>
% 105.60/14.51 (((emptyI) =>
% 105.60/14.51 (((noeltsimpempty) =>
% 105.60/14.51 (((setbeta) =>
% 105.60/14.51 (((nonemptyE1) =>
% 105.60/14.51 (((nonemptyI) =>
% 105.60/14.51 (((nonemptyI1) =>
% 105.60/14.51 (((setadjoinIL) =>
% 105.60/14.51 (((in @ emptyset @
% 105.60/14.51 (setadjoin @ emptyset @ emptyset)) =>
% 105.60/14.51 (((setadjoinIR) =>
% 105.60/14.51 (((setadjoinE) =>
% 105.60/14.51 (((setadjoinOr) =>
% 105.60/14.51 (((setoftrueEq) =>
% 105.60/14.51 (((powersetI) =>
% 105.60/14.51 (((emptyinPowerset) =>
% 105.60/14.51 (((emptyInPowerset) =>
% 105.60/14.51 (((powersetE) =>
% 105.60/14.51 (((setunionI) =>
% 105.60/14.51 (((setunionE) =>
% 105.60/14.51 (((subPowSU) =>
% 105.60/14.51 (((exuE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (nonemptyImpWitness) =>
% 105.60/14.51 ((
% 105.60/14.51 (uniqinunit) =>
% 105.60/14.51 ((
% 105.60/14.51 (notinsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqinunit) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsswitch) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetE) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (emptyE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (vacuousDall) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan1) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan2) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan3) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan4) =>
% 105.60/14.51 ((
% 105.60/14.51 (prop2setI) =>
% 105.60/14.51 ((
% 105.60/14.51 (prop2set2propI) =>
% 105.60/14.51 ((
% 105.60/14.51 (notdexE) =>
% 105.60/14.51 ((
% 105.60/14.51 (notdallE) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI3) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (inCongP) =>
% 105.60/14.51 ((
% 105.60/14.51 (in__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuE3u) =>
% 105.60/14.51 ((
% 105.60/14.51 (exu__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoin__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (powerset__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunion__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuEu) =>
% 105.60/14.51 ((
% 105.60/14.51 (descr__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (dsetconstr__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqimpsubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqimpsubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (emptysetsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetE) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (notsubsetI) =>
% 105.60/14.51 ((
% 105.60/14.51 (notequalI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (notequalI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetRefl) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetTrans) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoinSub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoinSub2) =>
% 105.60/14.51 ((
% 105.60/14.51 (subset2powerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (setextsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetemptysetimpeq) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (inPowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (sepInPowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (sepSubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairset2IR) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionEcases) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionE) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionRsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectI) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset5) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset3) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectER) =>
% 105.60/14.51 ((
% 105.60/14.51 (disjointsetsI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectRsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset4) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (bs114d) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusI) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusER) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusERneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusELneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusILneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusIRneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffE) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg2) =>
% 105.60/14.51 ((
% 105.60/14.51 (secondinupair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairiskpair) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairp) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairset2E) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsubunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairinpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem3) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairin) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair1) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton1) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonprop) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1E1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1I) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1I2) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsuniq) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL1) =>
% 105.60/14.51 ((
% 105.60/14.51 (kfstsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (theprop) =>
% 105.60/14.51 ((
% 105.60/14.51 (kfstpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodfstin) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR11) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR12) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR1) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairequniteq) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairinjR) =>
% 105.60/14.51 ((
% 105.60/14.51 (ksndsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (ksndpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairsurjEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodsndin) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairmemEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairmemER) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempaircEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodfstpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodsndpairEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairsurjEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrI) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrSub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setOfPairsIsBReln) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrERa) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrEL1) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrEL2) =>
% 105.60/14.51 ((
% 105.60/14.51 (dpsetconstrER) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcImageSingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (apProp) =>
% 105.60/14.51 ((
% 105.60/14.51 (app) =>
% 105.60/14.51 ((
% 105.60/14.51 (infuncsetfunc) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2p) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcinfuncset) =>
% 105.60/14.51 ((
% 105.60/14.51 (lamProp) =>
% 105.60/14.51 ((
% 105.60/14.51 (lamp) =>
% 105.60/14.51 ((
% 105.60/14.51 (lam2p) =>
% 105.60/14.51 ((
% 105.60/14.51 (brelnall1) =>
% 105.60/14.51 ((
% 105.60/14.51 (brelnall2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ex1E2) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp3) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcextLem) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcGraphProp4) =>
% 105.60/14.51 ((
% 105.60/14.51 (subbreln) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqbreln) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcext) =>
% 105.60/14.51 ((
% 105.60/14.51 (funcext2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2apEq1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ap2apEq2) =>
% 105.60/14.51 ((
% 105.60/14.51 (beta1) =>
% 105.60/14.51 ((
% 105.60/14.51 (eta1) =>
% 105.60/14.51 ((
% 105.60/14.51 (lam2lamEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (beta2) =>
% 105.60/14.51 ((
% 105.60/14.51 (eta2) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalseProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalseProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueProp1) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueProp2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ifSingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (ifp) =>
% 105.60/14.51 ((
% 105.60/14.51 (theeq) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrue) =>
% 105.60/14.51 ((
% 105.60/14.51 (iffalse) =>
% 105.60/14.51 ((
% 105.60/14.51 (iftrueorfalse) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementT_lem) =>
% 105.60/14.51 ((
% 105.60/14.51 (setextT) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetTI) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetTI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetTE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectTELcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectTERcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT1) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT2) =>
% 105.60/14.51 ((
% 105.60/14.51 (contrasubsetT3) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementSub1) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementSub2) =>
% 105.60/14.51 ((
% 105.60/14.51 (doubleComplementEq) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTnotintersectT) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementImpComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementSubsetComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementInPowersetComplementIntersect) =>
% 105.60/14.51 ((
% 105.60/14.51 (contraSubsetComplement) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementTcontraSubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTILcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTIRcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInUnion) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInUnion2) =>
% 105.60/14.51 ((
% 105.60/14.51 (inIntersectImpInIntersectUnions) =>
% 105.60/14.51 ((
% 105.60/14.51 (intersectInPowersetIntersectUnions) =>
% 105.60/14.51 ((
% 105.60/14.51 (inComplementUnionImpNotIn1) =>
% 105.60/14.51 ((
% 105.60/14.51 (inComplementUnionImpInComplement1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTE) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionTEcontra) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a1) =>
% 105.60/14.51 ((
% 105.60/14.51 (complementUnionInPowersetComplement) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a2) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1a) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1b) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan1) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2a) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2b2) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2b) =>
% 105.60/14.51 ((
% 105.60/14.51 (demorgan2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule0) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule1) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule3) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz13rule4) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_1) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_2) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_3) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_4) =>
% 105.60/14.51 ((
% 105.60/14.51 (woz1_5) =>
% 105.60/14.51 ((
% 105.60/14.51 (breln1all2) =>
% 105.60/14.51 ((
% 105.60/14.51 (!!) @ (
% 105.60/14.51 (('#B') @ (
% 105.60/14.51 !!) @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#S') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 '#S') @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 =>))) @
% 105.60/14.51 (
% 105.60/14.51 (
% 105.60/14.51 ('#B') @ (
% 105.60/14.51 (
% 105.60/14.51 ('#C') @ in)) @
% 105.60/14.51 breln1Set)))))) @
% 105.60/14.51 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.60/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 105.60/14.51 thf(zip_derived_cl79, plain,
% 105.60/14.51 (~ (((dsetconstrEL) =>
% 105.60/14.51 (((dsetconstrER) =>
% 105.60/14.51 (((exuE1) =>
% 105.60/14.51 (((prop2setE) =>
% 105.60/14.51 (((emptysetE) =>
% 105.60/14.51 (((emptysetimpfalse) =>
% 105.60/14.51 (((notinemptyset) =>
% 105.60/14.51 (((exuE3e) =>
% 105.60/14.51 (((setext) =>
% 105.60/14.51 (((emptyI) =>
% 105.60/14.51 (((noeltsimpempty) =>
% 105.60/14.51 (((setbeta) =>
% 105.60/14.51 (((nonemptyE1) =>
% 105.60/14.51 (((nonemptyI) =>
% 105.60/14.51 (((nonemptyI1) =>
% 105.60/14.51 (((setadjoinIL) =>
% 105.60/14.51 (((in @ emptyset @
% 105.60/14.51 (setadjoin @ emptyset @ emptyset)) =>
% 105.60/14.51 (((setadjoinIR) =>
% 105.60/14.51 (((setadjoinE) =>
% 105.60/14.51 (((setadjoinOr) =>
% 105.60/14.51 (((setoftrueEq) =>
% 105.60/14.51 (((powersetI) =>
% 105.60/14.51 (((emptyinPowerset) =>
% 105.60/14.51 (((emptyInPowerset) =>
% 105.60/14.51 (((powersetE) =>
% 105.60/14.51 (((setunionI) =>
% 105.60/14.51 (((setunionE) =>
% 105.60/14.51 (((subPowSU) =>
% 105.60/14.51 (((exuE2) =>
% 105.60/14.51 (((nonemptyImpWitness) =>
% 105.60/14.51 ((
% 105.60/14.51 (uniqinunit) =>
% 105.60/14.51 ((
% 105.60/14.51 (notinsingleton) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqinunit) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsswitch) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetE) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsetIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (emptyE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (vacuousDall) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan1) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan2) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan3) =>
% 105.60/14.51 ((
% 105.60/14.51 (quantDeMorgan4) =>
% 105.60/14.51 ((
% 105.60/14.51 (prop2setI) =>
% 105.60/14.51 ((
% 105.60/14.51 (prop2set2propI) =>
% 105.60/14.51 ((
% 105.60/14.51 (notdexE) =>
% 105.60/14.51 ((
% 105.60/14.51 (notdallE) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI3) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (inCongP) =>
% 105.60/14.51 ((
% 105.60/14.51 (in__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuE3u) =>
% 105.60/14.51 ((
% 105.60/14.51 (exu__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoin__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (powerset__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunion__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (exuEu) =>
% 105.60/14.51 ((
% 105.60/14.51 (descr__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (dsetconstr__Cong) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqimpsubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (eqimpsubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (emptysetsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetE) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (notsubsetI) =>
% 105.60/14.51 ((
% 105.60/14.51 (notequalI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (notequalI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetRefl) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetTrans) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoinSub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setadjoinSub2) =>
% 105.60/14.51 ((
% 105.60/14.51 (subset2powerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (setextsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (subsetemptysetimpeq) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetE1) =>
% 105.60/14.51 ((
% 105.60/14.51 (inPowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (powersetsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (sepInPowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (sepSubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairset2IR) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionEcases) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionE) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binunionRsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectI) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset5) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset3) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectER) =>
% 105.60/14.51 ((
% 105.60/14.51 (disjointsetsI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectRsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset4) =>
% 105.60/14.51 ((
% 105.60/14.51 (binintersectSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (bs114d) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusI) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusEL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusER) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusERneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusELneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusILneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusIRneg) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusLsub) =>
% 105.60/14.51 ((
% 105.60/14.51 (setminusSubset1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffE) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffI2) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg1) =>
% 105.60/14.51 ((
% 105.60/14.51 (symdiffIneg2) =>
% 105.60/14.51 ((
% 105.60/14.51 (secondinupair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIL) =>
% 105.60/14.51 ((
% 105.60/14.51 (setukpairIR) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairiskpair) =>
% 105.60/14.51 ((
% 105.60/14.51 (kpairp) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletonsubset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowerset) =>
% 105.60/14.51 ((
% 105.60/14.51 (singletoninpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairset2E) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairsubunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (upairinpowunion) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem1) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem2) =>
% 105.60/14.51 ((
% 105.60/14.51 (ubforcartprodlem3) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodpairin) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair1) =>
% 105.60/14.51 ((
% 105.60/14.51 (cartprodmempair) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionE2) =>
% 105.60/14.51 ((
% 105.60/14.51 (setunionsingleton1) =>
% 105.60/14.51 ((
% 105.98/14.51 (setunionsingleton2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunionsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonprop) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1E1) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1I) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1I2) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonsuniq) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjL1) =>
% 105.98/14.51 ((
% 105.98/14.51 (kfstsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (theprop) =>
% 105.98/14.51 ((
% 105.98/14.51 (kfstpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodfstin) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjL2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjL) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR11) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR12) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR1) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairequniteq) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR) =>
% 105.98/14.51 ((
% 105.98/14.51 (ksndsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (ksndpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (kpairsurjEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodsndin) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairmemEL) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairmemER) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodmempaircEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodfstpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodsndpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairsurjEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrI) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrSub) =>
% 105.98/14.51 ((
% 105.98/14.51 (setOfPairsIsBReln) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrERa) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrEL1) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrEL2) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrER) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcImageSingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (apProp) =>
% 105.98/14.51 ((
% 105.98/14.51 (app) =>
% 105.98/14.51 ((
% 105.98/14.51 (infuncsetfunc) =>
% 105.98/14.51 ((
% 105.98/14.51 (ap2p) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcinfuncset) =>
% 105.98/14.51 ((
% 105.98/14.51 (lamProp) =>
% 105.98/14.51 ((
% 105.98/14.51 (lamp) =>
% 105.98/14.51 ((
% 105.98/14.51 (lam2p) =>
% 105.98/14.51 ((
% 105.98/14.51 (brelnall1) =>
% 105.98/14.51 ((
% 105.98/14.51 (brelnall2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1E2) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp1) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp3) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp2) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcextLem) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp4) =>
% 105.98/14.51 ((
% 105.98/14.51 (subbreln) =>
% 105.98/14.51 ((
% 105.98/14.51 (eqbreln) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcext) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcext2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ap2apEq1) =>
% 105.98/14.51 ((
% 105.98/14.51 (ap2apEq2) =>
% 105.98/14.51 ((
% 105.98/14.51 (beta1) =>
% 105.98/14.51 ((
% 105.98/14.51 (eta1) =>
% 105.98/14.51 ((
% 105.98/14.51 (lam2lamEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (beta2) =>
% 105.98/14.51 ((
% 105.98/14.51 (eta2) =>
% 105.98/14.51 ((
% 105.98/14.51 (iffalseProp1) =>
% 105.98/14.51 ((
% 105.98/14.51 (iffalseProp2) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrueProp1) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrueProp2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ifSingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (ifp) =>
% 105.98/14.51 ((
% 105.98/14.51 (theeq) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrue) =>
% 105.98/14.51 ((
% 105.98/14.51 (iffalse) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrueorfalse) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (setextT) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetTI) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetTI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetTE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectTELcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectTERcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT1) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT2) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT3) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementSub1) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementSub2) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTnotintersectT) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementImpComplementIntersect) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementSubsetComplementIntersect) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementInPowersetComplementIntersect) =>
% 105.98/14.51 ((
% 105.98/14.51 (contraSubsetComplement) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTcontraSubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTILcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTIRcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (inIntersectImpInUnion) =>
% 105.98/14.51 ((
% 105.98/14.51 (inIntersectImpInUnion2) =>
% 105.98/14.51 ((
% 105.98/14.51 (inIntersectImpInIntersectUnions) =>
% 105.98/14.51 ((
% 105.98/14.51 (intersectInPowersetIntersectUnions) =>
% 105.98/14.51 ((
% 105.98/14.51 (inComplementUnionImpNotIn1) =>
% 105.98/14.51 ((
% 105.98/14.51 (inComplementUnionImpInComplement1) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTE) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTEcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2a1) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementUnionInPowersetComplement) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2a2) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan1a) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan1b) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan1) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2a) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2b2) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2b) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule0) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule1) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule2) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule3) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule4) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_1) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_2) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_3) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_4) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_5) =>
% 105.98/14.51 ((
% 105.98/14.51 (breln1all2) =>
% 105.98/14.51 ((
% 105.98/14.51 (!!) @ (
% 105.98/14.51 (('#B') @ (
% 105.98/14.51 !!) @
% 105.98/14.51 (
% 105.98/14.51 (
% 105.98/14.51 ('#S') @ (
% 105.98/14.51 (
% 105.98/14.51 ('#B') @ (
% 105.98/14.51 '#S') @
% 105.98/14.51 (
% 105.98/14.51 (
% 105.98/14.51 ('#B') @ (
% 105.98/14.51 (
% 105.98/14.51 ('#B') @ (
% 105.98/14.51 =>))) @
% 105.98/14.51 (
% 105.98/14.51 (
% 105.98/14.51 ('#B') @ (
% 105.98/14.51 (
% 105.98/14.51 ('#C') @ in)) @
% 105.98/14.51 breln1Set)))))) @
% 105.98/14.51 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])).
% 105.98/14.51 thf(zip_derived_cl89, plain,
% 105.98/14.51 (~ (((dsetconstrER) =>
% 105.98/14.51 (((exuE1) =>
% 105.98/14.51 (((prop2setE) =>
% 105.98/14.51 (((emptysetE) =>
% 105.98/14.51 (((emptysetimpfalse) =>
% 105.98/14.51 (((notinemptyset) =>
% 105.98/14.51 (((exuE3e) =>
% 105.98/14.51 (((setext) =>
% 105.98/14.51 (((emptyI) =>
% 105.98/14.51 (((noeltsimpempty) =>
% 105.98/14.51 (((setbeta) =>
% 105.98/14.51 (((nonemptyE1) =>
% 105.98/14.51 (((nonemptyI) =>
% 105.98/14.51 (((nonemptyI1) =>
% 105.98/14.51 (((setadjoinIL) =>
% 105.98/14.51 (((in @ emptyset @
% 105.98/14.51 (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.51 (((setadjoinIR) =>
% 105.98/14.51 (((setadjoinE) =>
% 105.98/14.51 (((setadjoinOr) =>
% 105.98/14.51 (((setoftrueEq) =>
% 105.98/14.51 (((powersetI) =>
% 105.98/14.51 (((emptyinPowerset) =>
% 105.98/14.51 (((emptyInPowerset) =>
% 105.98/14.51 (((powersetE) =>
% 105.98/14.51 (((setunionI) =>
% 105.98/14.51 (((setunionE) =>
% 105.98/14.51 (((subPowSU) =>
% 105.98/14.51 (((exuE2) =>
% 105.98/14.51 (((nonemptyImpWitness) =>
% 105.98/14.51 (((uniqinunit) =>
% 105.98/14.51 ((
% 105.98/14.51 (notinsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (eqinunit) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonsswitch) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairsetE) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairsetIL) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairsetIR) =>
% 105.98/14.51 ((
% 105.98/14.51 (emptyE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (vacuousDall) =>
% 105.98/14.51 ((
% 105.98/14.51 (quantDeMorgan1) =>
% 105.98/14.51 ((
% 105.98/14.51 (quantDeMorgan2) =>
% 105.98/14.51 ((
% 105.98/14.51 (quantDeMorgan3) =>
% 105.98/14.51 ((
% 105.98/14.51 (quantDeMorgan4) =>
% 105.98/14.51 ((
% 105.98/14.51 (prop2setI) =>
% 105.98/14.51 ((
% 105.98/14.51 (prop2set2propI) =>
% 105.98/14.51 ((
% 105.98/14.51 (notdexE) =>
% 105.98/14.51 ((
% 105.98/14.51 (notdallE) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuI3) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuI2) =>
% 105.98/14.51 ((
% 105.98/14.51 (inCongP) =>
% 105.98/14.51 ((
% 105.98/14.51 (in__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuE3u) =>
% 105.98/14.51 ((
% 105.98/14.51 (exu__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (setadjoin__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (powerset__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunion__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuEu) =>
% 105.98/14.51 ((
% 105.98/14.51 (descr__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (dsetconstr__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (eqimpsubset2) =>
% 105.98/14.51 ((
% 105.98/14.51 (eqimpsubset1) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetI2) =>
% 105.98/14.51 ((
% 105.98/14.51 (emptysetsubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetE) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetE2) =>
% 105.98/14.51 ((
% 105.98/14.51 (notsubsetI) =>
% 105.98/14.51 ((
% 105.98/14.51 (notequalI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (notequalI2) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetRefl) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetTrans) =>
% 105.98/14.51 ((
% 105.98/14.51 (setadjoinSub) =>
% 105.98/14.51 ((
% 105.98/14.51 (setadjoinSub2) =>
% 105.98/14.51 ((
% 105.98/14.51 (subset2powerset) =>
% 105.98/14.51 ((
% 105.98/14.51 (setextsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetemptysetimpeq) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (inPowerset) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetsubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (sepInPowerset) =>
% 105.98/14.51 ((
% 105.98/14.51 (sepSubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionIL) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairset2IR) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionIR) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionEcases) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionE) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionLsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionRsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectI) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset5) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectEL) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectLsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset2) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset3) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectER) =>
% 105.98/14.51 ((
% 105.98/14.51 (disjointsetsI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectRsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset4) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset1) =>
% 105.98/14.51 ((
% 105.98/14.51 (bs114d) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusI) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusEL) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusER) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusSubset2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusERneg) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusELneg) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusILneg) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusIRneg) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusLsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusSubset1) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffE) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffI2) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffIneg1) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffIneg2) =>
% 105.98/14.51 ((
% 105.98/14.51 (secondinupair) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairIL) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairIR) =>
% 105.98/14.51 ((
% 105.98/14.51 (kpairiskpair) =>
% 105.98/14.51 ((
% 105.98/14.51 (kpairp) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonsubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletoninpowerset) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletoninpowunion) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairset2E) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairsubunion) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairinpowunion) =>
% 105.98/14.51 ((
% 105.98/14.51 (ubforcartprodlem1) =>
% 105.98/14.51 ((
% 105.98/14.51 (ubforcartprodlem2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ubforcartprodlem3) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairin) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodmempair1) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodmempair) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunionE2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunionsingleton1) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunionsingleton2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunionsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonprop) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1E1) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1I) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1I2) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonsuniq) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjL1) =>
% 105.98/14.51 ((
% 105.98/14.51 (kfstsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (theprop) =>
% 105.98/14.51 ((
% 105.98/14.51 (kfstpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodfstin) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjL2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjL) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR11) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR12) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR1) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairequniteq) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR) =>
% 105.98/14.51 ((
% 105.98/14.51 (ksndsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (ksndpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (kpairsurjEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodsndin) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairmemEL) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairmemER) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodmempaircEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodfstpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodsndpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairsurjEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrI) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrSub) =>
% 105.98/14.51 ((
% 105.98/14.51 (setOfPairsIsBReln) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrERa) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrEL1) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrEL2) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrER) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcImageSingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (apProp) =>
% 105.98/14.51 ((
% 105.98/14.51 (app) =>
% 105.98/14.51 ((
% 105.98/14.51 (infuncsetfunc) =>
% 105.98/14.51 ((
% 105.98/14.51 (ap2p) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcinfuncset) =>
% 105.98/14.51 ((
% 105.98/14.51 (lamProp) =>
% 105.98/14.51 ((
% 105.98/14.51 (lamp) =>
% 105.98/14.51 ((
% 105.98/14.51 (lam2p) =>
% 105.98/14.51 ((
% 105.98/14.51 (brelnall1) =>
% 105.98/14.51 ((
% 105.98/14.51 (brelnall2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1E2) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp1) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp3) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp2) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcextLem) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp4) =>
% 105.98/14.51 ((
% 105.98/14.51 (subbreln) =>
% 105.98/14.51 ((
% 105.98/14.51 (eqbreln) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcext) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcext2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ap2apEq1) =>
% 105.98/14.51 ((
% 105.98/14.51 (ap2apEq2) =>
% 105.98/14.51 ((
% 105.98/14.51 (beta1) =>
% 105.98/14.51 ((
% 105.98/14.51 (eta1) =>
% 105.98/14.51 ((
% 105.98/14.51 (lam2lamEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (beta2) =>
% 105.98/14.51 ((
% 105.98/14.51 (eta2) =>
% 105.98/14.51 ((
% 105.98/14.51 (iffalseProp1) =>
% 105.98/14.51 ((
% 105.98/14.51 (iffalseProp2) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrueProp1) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrueProp2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ifSingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (ifp) =>
% 105.98/14.51 ((
% 105.98/14.51 (theeq) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrue) =>
% 105.98/14.51 ((
% 105.98/14.51 (iffalse) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrueorfalse) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (setextT) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetTI) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetTI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetTE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectTELcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectTERcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT1) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT2) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT3) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementSub1) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementSub2) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTnotintersectT) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementImpComplementIntersect) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementSubsetComplementIntersect) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementInPowersetComplementIntersect) =>
% 105.98/14.51 ((
% 105.98/14.51 (contraSubsetComplement) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTcontraSubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTILcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTIRcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (inIntersectImpInUnion) =>
% 105.98/14.51 ((
% 105.98/14.51 (inIntersectImpInUnion2) =>
% 105.98/14.51 ((
% 105.98/14.51 (inIntersectImpInIntersectUnions) =>
% 105.98/14.51 ((
% 105.98/14.51 (intersectInPowersetIntersectUnions) =>
% 105.98/14.51 ((
% 105.98/14.51 (inComplementUnionImpNotIn1) =>
% 105.98/14.51 ((
% 105.98/14.51 (inComplementUnionImpInComplement1) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTE) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTEcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2a1) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementUnionInPowersetComplement) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2a2) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan1a) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan1b) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan1) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2a) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2b2) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2b) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule0) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule1) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule2) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule3) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule4) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_1) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_2) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_3) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_4) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_5) =>
% 105.98/14.51 ((
% 105.98/14.51 (breln1all2) =>
% 105.98/14.51 ((
% 105.98/14.51 (!!) @ (
% 105.98/14.51 (('#B') @ (
% 105.98/14.51 !!) @
% 105.98/14.51 (
% 105.98/14.51 (
% 105.98/14.51 ('#S') @ (
% 105.98/14.51 (
% 105.98/14.51 ('#B') @ (
% 105.98/14.51 '#S') @
% 105.98/14.51 (
% 105.98/14.51 (
% 105.98/14.51 ('#B') @ (
% 105.98/14.51 (
% 105.98/14.51 ('#B') @ (
% 105.98/14.51 =>))) @
% 105.98/14.51 (
% 105.98/14.51 (
% 105.98/14.51 ('#B') @ (
% 105.98/14.51 (
% 105.98/14.51 ('#C') @ in)) @
% 105.98/14.51 breln1Set)))))) @
% 105.98/14.51 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 105.98/14.51 thf(zip_derived_cl105, plain,
% 105.98/14.51 (~ (((exuE1) =>
% 105.98/14.51 (((prop2setE) =>
% 105.98/14.51 (((emptysetE) =>
% 105.98/14.51 (((emptysetimpfalse) =>
% 105.98/14.51 (((notinemptyset) =>
% 105.98/14.51 (((exuE3e) =>
% 105.98/14.51 (((setext) =>
% 105.98/14.51 (((emptyI) =>
% 105.98/14.51 (((noeltsimpempty) =>
% 105.98/14.51 (((setbeta) =>
% 105.98/14.51 (((nonemptyE1) =>
% 105.98/14.51 (((nonemptyI) =>
% 105.98/14.51 (((nonemptyI1) =>
% 105.98/14.51 (((setadjoinIL) =>
% 105.98/14.51 (((in @ emptyset @
% 105.98/14.51 (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.51 (((setadjoinIR) =>
% 105.98/14.51 (((setadjoinE) =>
% 105.98/14.51 (((setadjoinOr) =>
% 105.98/14.51 (((setoftrueEq) =>
% 105.98/14.51 (((powersetI) =>
% 105.98/14.51 (((emptyinPowerset) =>
% 105.98/14.51 (((emptyInPowerset) =>
% 105.98/14.51 (((powersetE) =>
% 105.98/14.51 (((setunionI) =>
% 105.98/14.51 (((setunionE) =>
% 105.98/14.51 (((subPowSU) =>
% 105.98/14.51 (((exuE2) =>
% 105.98/14.51 (((nonemptyImpWitness) =>
% 105.98/14.51 (((uniqinunit) =>
% 105.98/14.51 (((notinsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (eqinunit) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonsswitch) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairsetE) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairsetIL) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairsetIR) =>
% 105.98/14.51 ((
% 105.98/14.51 (emptyE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (vacuousDall) =>
% 105.98/14.51 ((
% 105.98/14.51 (quantDeMorgan1) =>
% 105.98/14.51 ((
% 105.98/14.51 (quantDeMorgan2) =>
% 105.98/14.51 ((
% 105.98/14.51 (quantDeMorgan3) =>
% 105.98/14.51 ((
% 105.98/14.51 (quantDeMorgan4) =>
% 105.98/14.51 ((
% 105.98/14.51 (prop2setI) =>
% 105.98/14.51 ((
% 105.98/14.51 (prop2set2propI) =>
% 105.98/14.51 ((
% 105.98/14.51 (notdexE) =>
% 105.98/14.51 ((
% 105.98/14.51 (notdallE) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuI3) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuI2) =>
% 105.98/14.51 ((
% 105.98/14.51 (inCongP) =>
% 105.98/14.51 ((
% 105.98/14.51 (in__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuE3u) =>
% 105.98/14.51 ((
% 105.98/14.51 (exu__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (setadjoin__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (powerset__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunion__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuEu) =>
% 105.98/14.51 ((
% 105.98/14.51 (descr__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (dsetconstr__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (eqimpsubset2) =>
% 105.98/14.51 ((
% 105.98/14.51 (eqimpsubset1) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetI2) =>
% 105.98/14.51 ((
% 105.98/14.51 (emptysetsubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetE) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetE2) =>
% 105.98/14.51 ((
% 105.98/14.51 (notsubsetI) =>
% 105.98/14.51 ((
% 105.98/14.51 (notequalI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (notequalI2) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetRefl) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetTrans) =>
% 105.98/14.51 ((
% 105.98/14.51 (setadjoinSub) =>
% 105.98/14.51 ((
% 105.98/14.51 (setadjoinSub2) =>
% 105.98/14.51 ((
% 105.98/14.51 (subset2powerset) =>
% 105.98/14.51 ((
% 105.98/14.51 (setextsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetemptysetimpeq) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (inPowerset) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetsubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (sepInPowerset) =>
% 105.98/14.51 ((
% 105.98/14.51 (sepSubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionIL) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairset2IR) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionIR) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionEcases) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionE) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionLsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionRsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectI) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset5) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectEL) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectLsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset2) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset3) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectER) =>
% 105.98/14.51 ((
% 105.98/14.51 (disjointsetsI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectRsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset4) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset1) =>
% 105.98/14.51 ((
% 105.98/14.51 (bs114d) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusI) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusEL) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusER) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusSubset2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusERneg) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusELneg) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusILneg) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusIRneg) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusLsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusSubset1) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffE) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffI2) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffIneg1) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffIneg2) =>
% 105.98/14.51 ((
% 105.98/14.51 (secondinupair) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairIL) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairIR) =>
% 105.98/14.51 ((
% 105.98/14.51 (kpairiskpair) =>
% 105.98/14.51 ((
% 105.98/14.51 (kpairp) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonsubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletoninpowerset) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletoninpowunion) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairset2E) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairsubunion) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairinpowunion) =>
% 105.98/14.51 ((
% 105.98/14.51 (ubforcartprodlem1) =>
% 105.98/14.51 ((
% 105.98/14.51 (ubforcartprodlem2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ubforcartprodlem3) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairin) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodmempair1) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodmempair) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunionE2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunionsingleton1) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunionsingleton2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunionsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonprop) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1E1) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1I) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1I2) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonsuniq) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjL1) =>
% 105.98/14.51 ((
% 105.98/14.51 (kfstsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (theprop) =>
% 105.98/14.51 ((
% 105.98/14.51 (kfstpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodfstin) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjL2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjL) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR11) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR12) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR1) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairequniteq) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR) =>
% 105.98/14.51 ((
% 105.98/14.51 (ksndsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (ksndpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (kpairsurjEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodsndin) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairmemEL) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairmemER) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodmempaircEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodfstpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodsndpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairsurjEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrI) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrSub) =>
% 105.98/14.51 ((
% 105.98/14.51 (setOfPairsIsBReln) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrERa) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrEL1) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrEL2) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrER) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcImageSingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (apProp) =>
% 105.98/14.51 ((
% 105.98/14.51 (app) =>
% 105.98/14.51 ((
% 105.98/14.51 (infuncsetfunc) =>
% 105.98/14.51 ((
% 105.98/14.51 (ap2p) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcinfuncset) =>
% 105.98/14.51 ((
% 105.98/14.51 (lamProp) =>
% 105.98/14.51 ((
% 105.98/14.51 (lamp) =>
% 105.98/14.51 ((
% 105.98/14.51 (lam2p) =>
% 105.98/14.51 ((
% 105.98/14.51 (brelnall1) =>
% 105.98/14.51 ((
% 105.98/14.51 (brelnall2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1E2) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp1) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp3) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp2) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcextLem) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp4) =>
% 105.98/14.51 ((
% 105.98/14.51 (subbreln) =>
% 105.98/14.51 ((
% 105.98/14.51 (eqbreln) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcext) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcext2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ap2apEq1) =>
% 105.98/14.51 ((
% 105.98/14.51 (ap2apEq2) =>
% 105.98/14.51 ((
% 105.98/14.51 (beta1) =>
% 105.98/14.51 ((
% 105.98/14.51 (eta1) =>
% 105.98/14.51 ((
% 105.98/14.51 (lam2lamEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (beta2) =>
% 105.98/14.51 ((
% 105.98/14.51 (eta2) =>
% 105.98/14.51 ((
% 105.98/14.51 (iffalseProp1) =>
% 105.98/14.51 ((
% 105.98/14.51 (iffalseProp2) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrueProp1) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrueProp2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ifSingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (ifp) =>
% 105.98/14.51 ((
% 105.98/14.51 (theeq) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrue) =>
% 105.98/14.51 ((
% 105.98/14.51 (iffalse) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrueorfalse) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (setextT) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetTI) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetTI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetTE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectTELcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectTERcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT1) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT2) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT3) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementSub1) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementSub2) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTnotintersectT) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementImpComplementIntersect) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementSubsetComplementIntersect) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementInPowersetComplementIntersect) =>
% 105.98/14.51 ((
% 105.98/14.51 (contraSubsetComplement) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTcontraSubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTILcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTIRcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (inIntersectImpInUnion) =>
% 105.98/14.51 ((
% 105.98/14.51 (inIntersectImpInUnion2) =>
% 105.98/14.51 ((
% 105.98/14.51 (inIntersectImpInIntersectUnions) =>
% 105.98/14.51 ((
% 105.98/14.51 (intersectInPowersetIntersectUnions) =>
% 105.98/14.51 ((
% 105.98/14.51 (inComplementUnionImpNotIn1) =>
% 105.98/14.51 ((
% 105.98/14.51 (inComplementUnionImpInComplement1) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTE) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTEcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2a1) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementUnionInPowersetComplement) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2a2) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan1a) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan1b) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan1) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2a) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2b2) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2b) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule0) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule1) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule2) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule3) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule4) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_1) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_2) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_3) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_4) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz1_5) =>
% 105.98/14.51 ((
% 105.98/14.51 (breln1all2) =>
% 105.98/14.51 ((
% 105.98/14.51 (!!) @ (
% 105.98/14.51 (('#B') @ (
% 105.98/14.51 !!) @
% 105.98/14.51 (
% 105.98/14.51 (
% 105.98/14.51 ('#S') @ (
% 105.98/14.51 (
% 105.98/14.51 ('#B') @ (
% 105.98/14.51 '#S') @
% 105.98/14.51 (
% 105.98/14.51 (
% 105.98/14.51 ('#B') @ (
% 105.98/14.51 (
% 105.98/14.51 ('#B') @ (
% 105.98/14.51 =>))) @
% 105.98/14.51 (
% 105.98/14.51 (
% 105.98/14.51 ('#B') @ (
% 105.98/14.51 (
% 105.98/14.51 ('#C') @ in)) @
% 105.98/14.51 breln1Set)))))) @
% 105.98/14.51 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])).
% 105.98/14.51 thf(zip_derived_cl123, plain,
% 105.98/14.51 (~ (((prop2setE) =>
% 105.98/14.51 (((emptysetE) =>
% 105.98/14.51 (((emptysetimpfalse) =>
% 105.98/14.51 (((notinemptyset) =>
% 105.98/14.51 (((exuE3e) =>
% 105.98/14.51 (((setext) =>
% 105.98/14.51 (((emptyI) =>
% 105.98/14.51 (((noeltsimpempty) =>
% 105.98/14.51 (((setbeta) =>
% 105.98/14.51 (((nonemptyE1) =>
% 105.98/14.51 (((nonemptyI) =>
% 105.98/14.51 (((nonemptyI1) =>
% 105.98/14.51 (((setadjoinIL) =>
% 105.98/14.51 (((in @ emptyset @
% 105.98/14.51 (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.51 (((setadjoinIR) =>
% 105.98/14.51 (((setadjoinE) =>
% 105.98/14.51 (((setadjoinOr) =>
% 105.98/14.51 (((setoftrueEq) =>
% 105.98/14.51 (((powersetI) =>
% 105.98/14.51 (((emptyinPowerset) =>
% 105.98/14.51 (((emptyInPowerset) =>
% 105.98/14.51 (((powersetE) =>
% 105.98/14.51 (((setunionI) =>
% 105.98/14.51 (((setunionE) =>
% 105.98/14.51 (((subPowSU) =>
% 105.98/14.51 (((exuE2) =>
% 105.98/14.51 (((nonemptyImpWitness) =>
% 105.98/14.51 (((uniqinunit) =>
% 105.98/14.51 (((notinsingleton) =>
% 105.98/14.51 (((eqinunit) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonsswitch) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairsetE) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairsetIL) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairsetIR) =>
% 105.98/14.51 ((
% 105.98/14.51 (emptyE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (vacuousDall) =>
% 105.98/14.51 ((
% 105.98/14.51 (quantDeMorgan1) =>
% 105.98/14.51 ((
% 105.98/14.51 (quantDeMorgan2) =>
% 105.98/14.51 ((
% 105.98/14.51 (quantDeMorgan3) =>
% 105.98/14.51 ((
% 105.98/14.51 (quantDeMorgan4) =>
% 105.98/14.51 ((
% 105.98/14.51 (prop2setI) =>
% 105.98/14.51 ((
% 105.98/14.51 (prop2set2propI) =>
% 105.98/14.51 ((
% 105.98/14.51 (notdexE) =>
% 105.98/14.51 ((
% 105.98/14.51 (notdallE) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuI3) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuI2) =>
% 105.98/14.51 ((
% 105.98/14.51 (inCongP) =>
% 105.98/14.51 ((
% 105.98/14.51 (in__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuE3u) =>
% 105.98/14.51 ((
% 105.98/14.51 (exu__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (setadjoin__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (powerset__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunion__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (exuEu) =>
% 105.98/14.51 ((
% 105.98/14.51 (descr__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (dsetconstr__Cong) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (eqimpsubset2) =>
% 105.98/14.51 ((
% 105.98/14.51 (eqimpsubset1) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetI2) =>
% 105.98/14.51 ((
% 105.98/14.51 (emptysetsubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetE) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetE2) =>
% 105.98/14.51 ((
% 105.98/14.51 (notsubsetI) =>
% 105.98/14.51 ((
% 105.98/14.51 (notequalI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (notequalI2) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetRefl) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetTrans) =>
% 105.98/14.51 ((
% 105.98/14.51 (setadjoinSub) =>
% 105.98/14.51 ((
% 105.98/14.51 (setadjoinSub2) =>
% 105.98/14.51 ((
% 105.98/14.51 (subset2powerset) =>
% 105.98/14.51 ((
% 105.98/14.51 (setextsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetemptysetimpeq) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (inPowerset) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetsubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (sepInPowerset) =>
% 105.98/14.51 ((
% 105.98/14.51 (sepSubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionIL) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairset2IR) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionIR) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionEcases) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionE) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionLsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionRsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectI) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset5) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectEL) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectLsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset2) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset3) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectER) =>
% 105.98/14.51 ((
% 105.98/14.51 (disjointsetsI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectRsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset4) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectSubset1) =>
% 105.98/14.51 ((
% 105.98/14.51 (bs114d) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusI) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusEL) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusER) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusSubset2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusERneg) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusELneg) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusILneg) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusIRneg) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusLsub) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusSubset1) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffE) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffI2) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffIneg1) =>
% 105.98/14.51 ((
% 105.98/14.51 (symdiffIneg2) =>
% 105.98/14.51 ((
% 105.98/14.51 (secondinupair) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairIL) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairIR) =>
% 105.98/14.51 ((
% 105.98/14.51 (kpairiskpair) =>
% 105.98/14.51 ((
% 105.98/14.51 (kpairp) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonsubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletoninpowerset) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletoninpowunion) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairset2E) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairsubunion) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairinpowunion) =>
% 105.98/14.51 ((
% 105.98/14.51 (ubforcartprodlem1) =>
% 105.98/14.51 ((
% 105.98/14.51 (ubforcartprodlem2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ubforcartprodlem3) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairin) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodmempair1) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodmempair) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunionE2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunionsingleton1) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunionsingleton2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setunionsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonprop) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1E1) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1I) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1I2) =>
% 105.98/14.51 ((
% 105.98/14.51 (singletonsuniq) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjL1) =>
% 105.98/14.51 ((
% 105.98/14.51 (kfstsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (theprop) =>
% 105.98/14.51 ((
% 105.98/14.51 (kfstpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodfstin) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjL2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjL) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR11) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR12) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR1) =>
% 105.98/14.51 ((
% 105.98/14.51 (upairequniteq) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR2) =>
% 105.98/14.51 ((
% 105.98/14.51 (setukpairinjR) =>
% 105.98/14.51 ((
% 105.98/14.51 (ksndsingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (ksndpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (kpairsurjEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodsndin) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairmemEL) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairmemER) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodmempaircEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodfstpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodsndpairEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (cartprodpairsurjEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrI) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrSub) =>
% 105.98/14.51 ((
% 105.98/14.51 (setOfPairsIsBReln) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrERa) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrEL1) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrEL2) =>
% 105.98/14.51 ((
% 105.98/14.51 (dpsetconstrER) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcImageSingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (apProp) =>
% 105.98/14.51 ((
% 105.98/14.51 (app) =>
% 105.98/14.51 ((
% 105.98/14.51 (infuncsetfunc) =>
% 105.98/14.51 ((
% 105.98/14.51 (ap2p) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcinfuncset) =>
% 105.98/14.51 ((
% 105.98/14.51 (lamProp) =>
% 105.98/14.51 ((
% 105.98/14.51 (lamp) =>
% 105.98/14.51 ((
% 105.98/14.51 (lam2p) =>
% 105.98/14.51 ((
% 105.98/14.51 (brelnall1) =>
% 105.98/14.51 ((
% 105.98/14.51 (brelnall2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ex1E2) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp1) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp3) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp2) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcextLem) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcGraphProp4) =>
% 105.98/14.51 ((
% 105.98/14.51 (subbreln) =>
% 105.98/14.51 ((
% 105.98/14.51 (eqbreln) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcext) =>
% 105.98/14.51 ((
% 105.98/14.51 (funcext2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ap2apEq1) =>
% 105.98/14.51 ((
% 105.98/14.51 (ap2apEq2) =>
% 105.98/14.51 ((
% 105.98/14.51 (beta1) =>
% 105.98/14.51 ((
% 105.98/14.51 (eta1) =>
% 105.98/14.51 ((
% 105.98/14.51 (lam2lamEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (beta2) =>
% 105.98/14.51 ((
% 105.98/14.51 (eta2) =>
% 105.98/14.51 ((
% 105.98/14.51 (iffalseProp1) =>
% 105.98/14.51 ((
% 105.98/14.51 (iffalseProp2) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrueProp1) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrueProp2) =>
% 105.98/14.51 ((
% 105.98/14.51 (ifSingleton) =>
% 105.98/14.51 ((
% 105.98/14.51 (ifp) =>
% 105.98/14.51 ((
% 105.98/14.51 (theeq) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrue) =>
% 105.98/14.51 ((
% 105.98/14.51 (iffalse) =>
% 105.98/14.51 ((
% 105.98/14.51 (iftrueorfalse) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (setminusT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementT_lem) =>
% 105.98/14.51 ((
% 105.98/14.51 (setextT) =>
% 105.98/14.51 ((
% 105.98/14.51 (subsetTI) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetTI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (powersetTE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectTELcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (binintersectTERcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT1) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT2) =>
% 105.98/14.51 ((
% 105.98/14.51 (contrasubsetT3) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementI1) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementE1) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementSub1) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementSub2) =>
% 105.98/14.51 ((
% 105.98/14.51 (doubleComplementEq) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTnotintersectT) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementImpComplementIntersect) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementSubsetComplementIntersect) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementInPowersetComplementIntersect) =>
% 105.98/14.51 ((
% 105.98/14.51 (contraSubsetComplement) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementTcontraSubset) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTILcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTIRcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (inIntersectImpInUnion) =>
% 105.98/14.51 ((
% 105.98/14.51 (inIntersectImpInUnion2) =>
% 105.98/14.51 ((
% 105.98/14.51 (inIntersectImpInIntersectUnions) =>
% 105.98/14.51 ((
% 105.98/14.51 (intersectInPowersetIntersectUnions) =>
% 105.98/14.51 ((
% 105.98/14.51 (inComplementUnionImpNotIn1) =>
% 105.98/14.51 ((
% 105.98/14.51 (inComplementUnionImpInComplement1) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTE) =>
% 105.98/14.51 ((
% 105.98/14.51 (binunionTEcontra) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2a1) =>
% 105.98/14.51 ((
% 105.98/14.51 (complementUnionInPowersetComplement) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2a2) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan1a) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan1b) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan1) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2a) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2b2) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2b) =>
% 105.98/14.51 ((
% 105.98/14.51 (demorgan2) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule0) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule1) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule2) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule3) =>
% 105.98/14.51 ((
% 105.98/14.51 (woz13rule4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_5) =>
% 105.98/14.52 ((
% 105.98/14.52 (breln1all2) =>
% 105.98/14.52 ((
% 105.98/14.52 (!!) @ (
% 105.98/14.52 (('#B') @ (
% 105.98/14.52 !!) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#S') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 '#S') @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 =>))) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#C') @ in)) @
% 105.98/14.52 breln1Set)))))) @
% 105.98/14.52 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])).
% 105.98/14.52 thf(zip_derived_cl142, plain,
% 105.98/14.52 (~ (((emptysetE) =>
% 105.98/14.52 (((emptysetimpfalse) =>
% 105.98/14.52 (((notinemptyset) =>
% 105.98/14.52 (((exuE3e) =>
% 105.98/14.52 (((setext) =>
% 105.98/14.52 (((emptyI) =>
% 105.98/14.52 (((noeltsimpempty) =>
% 105.98/14.52 (((setbeta) =>
% 105.98/14.52 (((nonemptyE1) =>
% 105.98/14.52 (((nonemptyI) =>
% 105.98/14.52 (((nonemptyI1) =>
% 105.98/14.52 (((setadjoinIL) =>
% 105.98/14.52 (((in @ emptyset @
% 105.98/14.52 (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.52 (((setadjoinIR) =>
% 105.98/14.52 (((setadjoinE) =>
% 105.98/14.52 (((setadjoinOr) =>
% 105.98/14.52 (((setoftrueEq) =>
% 105.98/14.52 (((powersetI) =>
% 105.98/14.52 (((emptyinPowerset) =>
% 105.98/14.52 (((emptyInPowerset) =>
% 105.98/14.52 (((powersetE) =>
% 105.98/14.52 (((setunionI) =>
% 105.98/14.52 (((setunionE) =>
% 105.98/14.52 (((subPowSU) =>
% 105.98/14.52 (((exuE2) =>
% 105.98/14.52 (((nonemptyImpWitness) =>
% 105.98/14.52 (((uniqinunit) =>
% 105.98/14.52 (((notinsingleton) =>
% 105.98/14.52 (((eqinunit) =>
% 105.98/14.52 (((singletonsswitch) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsetE) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsetIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsetIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptyE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (vacuousDall) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan3) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan4) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2setI) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2set2propI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdexE) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdallE) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI3) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inCongP) =>
% 105.98/14.52 ((
% 105.98/14.52 (in__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuE3u) =>
% 105.98/14.52 ((
% 105.98/14.52 (exu__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoin__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (powerset__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunion__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuEu) =>
% 105.98/14.52 ((
% 105.98/14.52 (descr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (dsetconstr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptysetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (notsubsetI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetRefl) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTrans) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subset2powerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetemptysetimpeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepInPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2IR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionEcases) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectI) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset5) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset3) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectER) =>
% 105.98/14.52 ((
% 105.98/14.52 (disjointsetsI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset4) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (bs114d) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusI) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusER) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusERneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusELneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusILneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusIRneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffE) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg2) =>
% 105.98/14.52 ((
% 105.98/14.52 (secondinupair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairiskpair) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairp) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2E) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsubunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairinpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem3) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair1) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton1) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I2) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsuniq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (theprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstin) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR11) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR12) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR1) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairequniteq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemER) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempaircEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrI) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setOfPairsIsBReln) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrERa) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrER) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcImageSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (apProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (app) =>
% 105.98/14.52 ((
% 105.98/14.52 (infuncsetfunc) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcinfuncset) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall1) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp3) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcextLem) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp4) =>
% 105.98/14.52 ((
% 105.98/14.52 (subbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq2) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2lamEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifp) =>
% 105.98/14.52 ((
% 105.98/14.52 (theeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrue) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueorfalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextT) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTI) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTELcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTERcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT1) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT2) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT3) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTnotintersectT) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementImpComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementSubsetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementInPowersetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (contraSubsetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTcontraSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTILcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTIRcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (intersectInPowersetIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpNotIn1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpInComplement1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTEcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementUnionInPowersetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule0) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_5) =>
% 105.98/14.52 ((
% 105.98/14.52 (breln1all2) =>
% 105.98/14.52 ((
% 105.98/14.52 (!!) @ (
% 105.98/14.52 (('#B') @ (
% 105.98/14.52 !!) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#S') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 '#S') @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 =>))) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#C') @ in)) @
% 105.98/14.52 breln1Set)))))) @
% 105.98/14.52 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 105.98/14.52 thf(zip_derived_cl158, plain,
% 105.98/14.52 (~ (((emptysetimpfalse) =>
% 105.98/14.52 (((notinemptyset) =>
% 105.98/14.52 (((exuE3e) =>
% 105.98/14.52 (((setext) =>
% 105.98/14.52 (((emptyI) =>
% 105.98/14.52 (((noeltsimpempty) =>
% 105.98/14.52 (((setbeta) =>
% 105.98/14.52 (((nonemptyE1) =>
% 105.98/14.52 (((nonemptyI) =>
% 105.98/14.52 (((nonemptyI1) =>
% 105.98/14.52 (((setadjoinIL) =>
% 105.98/14.52 (((in @ emptyset @
% 105.98/14.52 (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.52 (((setadjoinIR) =>
% 105.98/14.52 (((setadjoinE) =>
% 105.98/14.52 (((setadjoinOr) =>
% 105.98/14.52 (((setoftrueEq) =>
% 105.98/14.52 (((powersetI) =>
% 105.98/14.52 (((emptyinPowerset) =>
% 105.98/14.52 (((emptyInPowerset) =>
% 105.98/14.52 (((powersetE) =>
% 105.98/14.52 (((setunionI) =>
% 105.98/14.52 (((setunionE) =>
% 105.98/14.52 (((subPowSU) =>
% 105.98/14.52 (((exuE2) =>
% 105.98/14.52 (((nonemptyImpWitness) =>
% 105.98/14.52 (((uniqinunit) =>
% 105.98/14.52 (((notinsingleton) =>
% 105.98/14.52 (((eqinunit) =>
% 105.98/14.52 (((singletonsswitch) =>
% 105.98/14.52 (((upairsetE) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsetIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsetIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptyE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (vacuousDall) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan3) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan4) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2setI) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2set2propI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdexE) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdallE) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI3) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inCongP) =>
% 105.98/14.52 ((
% 105.98/14.52 (in__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuE3u) =>
% 105.98/14.52 ((
% 105.98/14.52 (exu__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoin__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (powerset__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunion__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuEu) =>
% 105.98/14.52 ((
% 105.98/14.52 (descr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (dsetconstr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptysetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (notsubsetI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetRefl) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTrans) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subset2powerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetemptysetimpeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepInPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2IR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionEcases) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectI) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset5) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset3) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectER) =>
% 105.98/14.52 ((
% 105.98/14.52 (disjointsetsI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset4) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (bs114d) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusI) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusER) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusERneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusELneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusILneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusIRneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffE) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg2) =>
% 105.98/14.52 ((
% 105.98/14.52 (secondinupair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairiskpair) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairp) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2E) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsubunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairinpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem3) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair1) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton1) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I2) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsuniq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (theprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstin) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR11) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR12) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR1) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairequniteq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemER) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempaircEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrI) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setOfPairsIsBReln) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrERa) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrER) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcImageSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (apProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (app) =>
% 105.98/14.52 ((
% 105.98/14.52 (infuncsetfunc) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcinfuncset) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall1) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp3) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcextLem) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp4) =>
% 105.98/14.52 ((
% 105.98/14.52 (subbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq2) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2lamEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifp) =>
% 105.98/14.52 ((
% 105.98/14.52 (theeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrue) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueorfalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextT) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTI) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTELcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTERcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT1) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT2) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT3) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTnotintersectT) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementImpComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementSubsetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementInPowersetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (contraSubsetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTcontraSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTILcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTIRcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (intersectInPowersetIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpNotIn1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpInComplement1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTEcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementUnionInPowersetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule0) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_5) =>
% 105.98/14.52 ((
% 105.98/14.52 (breln1all2) =>
% 105.98/14.52 ((
% 105.98/14.52 (!!) @ (
% 105.98/14.52 (('#B') @ (
% 105.98/14.52 !!) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#S') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 '#S') @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 =>))) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#C') @ in)) @
% 105.98/14.52 breln1Set)))))) @
% 105.98/14.52 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])).
% 105.98/14.52 thf(zip_derived_cl174, plain,
% 105.98/14.52 (~ (((notinemptyset) =>
% 105.98/14.52 (((exuE3e) =>
% 105.98/14.52 (((setext) =>
% 105.98/14.52 (((emptyI) =>
% 105.98/14.52 (((noeltsimpempty) =>
% 105.98/14.52 (((setbeta) =>
% 105.98/14.52 (((nonemptyE1) =>
% 105.98/14.52 (((nonemptyI) =>
% 105.98/14.52 (((nonemptyI1) =>
% 105.98/14.52 (((setadjoinIL) =>
% 105.98/14.52 (((in @ emptyset @
% 105.98/14.52 (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.52 (((setadjoinIR) =>
% 105.98/14.52 (((setadjoinE) =>
% 105.98/14.52 (((setadjoinOr) =>
% 105.98/14.52 (((setoftrueEq) =>
% 105.98/14.52 (((powersetI) =>
% 105.98/14.52 (((emptyinPowerset) =>
% 105.98/14.52 (((emptyInPowerset) =>
% 105.98/14.52 (((powersetE) =>
% 105.98/14.52 (((setunionI) =>
% 105.98/14.52 (((setunionE) =>
% 105.98/14.52 (((subPowSU) =>
% 105.98/14.52 (((exuE2) =>
% 105.98/14.52 (((nonemptyImpWitness) =>
% 105.98/14.52 (((uniqinunit) =>
% 105.98/14.52 (((notinsingleton) =>
% 105.98/14.52 (((eqinunit) =>
% 105.98/14.52 (((singletonsswitch) =>
% 105.98/14.52 (((upairsetE) =>
% 105.98/14.52 (((upairsetIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsetIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptyE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (vacuousDall) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan3) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan4) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2setI) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2set2propI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdexE) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdallE) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI3) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inCongP) =>
% 105.98/14.52 ((
% 105.98/14.52 (in__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuE3u) =>
% 105.98/14.52 ((
% 105.98/14.52 (exu__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoin__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (powerset__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunion__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuEu) =>
% 105.98/14.52 ((
% 105.98/14.52 (descr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (dsetconstr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptysetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (notsubsetI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetRefl) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTrans) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subset2powerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetemptysetimpeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepInPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2IR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionEcases) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectI) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset5) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset3) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectER) =>
% 105.98/14.52 ((
% 105.98/14.52 (disjointsetsI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset4) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (bs114d) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusI) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusER) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusERneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusELneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusILneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusIRneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffE) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg2) =>
% 105.98/14.52 ((
% 105.98/14.52 (secondinupair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairiskpair) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairp) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2E) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsubunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairinpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem3) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair1) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton1) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I2) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsuniq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (theprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstin) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR11) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR12) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR1) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairequniteq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemER) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempaircEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrI) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setOfPairsIsBReln) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrERa) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrER) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcImageSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (apProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (app) =>
% 105.98/14.52 ((
% 105.98/14.52 (infuncsetfunc) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcinfuncset) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall1) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp3) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcextLem) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp4) =>
% 105.98/14.52 ((
% 105.98/14.52 (subbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq2) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2lamEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifp) =>
% 105.98/14.52 ((
% 105.98/14.52 (theeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrue) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueorfalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextT) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTI) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTELcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTERcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT1) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT2) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT3) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTnotintersectT) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementImpComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementSubsetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementInPowersetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (contraSubsetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTcontraSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTILcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTIRcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (intersectInPowersetIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpNotIn1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpInComplement1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTEcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementUnionInPowersetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule0) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_5) =>
% 105.98/14.52 ((
% 105.98/14.52 (breln1all2) =>
% 105.98/14.52 ((
% 105.98/14.52 (!!) @ (
% 105.98/14.52 (('#B') @ (
% 105.98/14.52 !!) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#S') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 '#S') @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 =>))) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#C') @ in)) @
% 105.98/14.52 breln1Set)))))) @
% 105.98/14.52 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 105.98/14.52 thf(zip_derived_cl189, plain,
% 105.98/14.52 (~ (((exuE3e) =>
% 105.98/14.52 (((setext) =>
% 105.98/14.52 (((emptyI) =>
% 105.98/14.52 (((noeltsimpempty) =>
% 105.98/14.52 (((setbeta) =>
% 105.98/14.52 (((nonemptyE1) =>
% 105.98/14.52 (((nonemptyI) =>
% 105.98/14.52 (((nonemptyI1) =>
% 105.98/14.52 (((setadjoinIL) =>
% 105.98/14.52 (((in @ emptyset @
% 105.98/14.52 (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.52 (((setadjoinIR) =>
% 105.98/14.52 (((setadjoinE) =>
% 105.98/14.52 (((setadjoinOr) =>
% 105.98/14.52 (((setoftrueEq) =>
% 105.98/14.52 (((powersetI) =>
% 105.98/14.52 (((emptyinPowerset) =>
% 105.98/14.52 (((emptyInPowerset) =>
% 105.98/14.52 (((powersetE) =>
% 105.98/14.52 (((setunionI) =>
% 105.98/14.52 (((setunionE) =>
% 105.98/14.52 (((subPowSU) =>
% 105.98/14.52 (((exuE2) =>
% 105.98/14.52 (((nonemptyImpWitness) =>
% 105.98/14.52 (((uniqinunit) =>
% 105.98/14.52 (((notinsingleton) =>
% 105.98/14.52 (((eqinunit) =>
% 105.98/14.52 (((singletonsswitch) =>
% 105.98/14.52 (((upairsetE) =>
% 105.98/14.52 (((upairsetIL) =>
% 105.98/14.52 (((upairsetIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptyE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (vacuousDall) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan3) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan4) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2setI) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2set2propI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdexE) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdallE) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI3) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inCongP) =>
% 105.98/14.52 ((
% 105.98/14.52 (in__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuE3u) =>
% 105.98/14.52 ((
% 105.98/14.52 (exu__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoin__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (powerset__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunion__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuEu) =>
% 105.98/14.52 ((
% 105.98/14.52 (descr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (dsetconstr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptysetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (notsubsetI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetRefl) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTrans) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subset2powerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetemptysetimpeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepInPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2IR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionEcases) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectI) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset5) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset3) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectER) =>
% 105.98/14.52 ((
% 105.98/14.52 (disjointsetsI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset4) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (bs114d) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusI) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusER) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusERneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusELneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusILneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusIRneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffE) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg2) =>
% 105.98/14.52 ((
% 105.98/14.52 (secondinupair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairiskpair) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairp) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2E) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsubunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairinpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem3) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair1) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton1) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I2) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsuniq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (theprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstin) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR11) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR12) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR1) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairequniteq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemER) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempaircEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrI) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setOfPairsIsBReln) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrERa) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrER) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcImageSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (apProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (app) =>
% 105.98/14.52 ((
% 105.98/14.52 (infuncsetfunc) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcinfuncset) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall1) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp3) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcextLem) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp4) =>
% 105.98/14.52 ((
% 105.98/14.52 (subbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq2) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2lamEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifp) =>
% 105.98/14.52 ((
% 105.98/14.52 (theeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrue) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueorfalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextT) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTI) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTELcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTERcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT1) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT2) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT3) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTnotintersectT) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementImpComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementSubsetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementInPowersetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (contraSubsetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTcontraSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTILcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTIRcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (intersectInPowersetIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpNotIn1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpInComplement1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTEcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementUnionInPowersetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule0) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_5) =>
% 105.98/14.52 ((
% 105.98/14.52 (breln1all2) =>
% 105.98/14.52 ((
% 105.98/14.52 (!!) @ (
% 105.98/14.52 (('#B') @ (
% 105.98/14.52 !!) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#S') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 '#S') @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 =>))) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#C') @ in)) @
% 105.98/14.52 breln1Set)))))) @
% 105.98/14.52 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl174])).
% 105.98/14.52 thf(zip_derived_cl206, plain,
% 105.98/14.52 (~ (((setext) =>
% 105.98/14.52 (((emptyI) =>
% 105.98/14.52 (((noeltsimpempty) =>
% 105.98/14.52 (((setbeta) =>
% 105.98/14.52 (((nonemptyE1) =>
% 105.98/14.52 (((nonemptyI) =>
% 105.98/14.52 (((nonemptyI1) =>
% 105.98/14.52 (((setadjoinIL) =>
% 105.98/14.52 (((in @ emptyset @
% 105.98/14.52 (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.52 (((setadjoinIR) =>
% 105.98/14.52 (((setadjoinE) =>
% 105.98/14.52 (((setadjoinOr) =>
% 105.98/14.52 (((setoftrueEq) =>
% 105.98/14.52 (((powersetI) =>
% 105.98/14.52 (((emptyinPowerset) =>
% 105.98/14.52 (((emptyInPowerset) =>
% 105.98/14.52 (((powersetE) =>
% 105.98/14.52 (((setunionI) =>
% 105.98/14.52 (((setunionE) =>
% 105.98/14.52 (((subPowSU) =>
% 105.98/14.52 (((exuE2) =>
% 105.98/14.52 (((nonemptyImpWitness) =>
% 105.98/14.52 (((uniqinunit) =>
% 105.98/14.52 (((notinsingleton) =>
% 105.98/14.52 (((eqinunit) =>
% 105.98/14.52 (((singletonsswitch) =>
% 105.98/14.52 (((upairsetE) =>
% 105.98/14.52 (((upairsetIL) =>
% 105.98/14.52 (((upairsetIR) =>
% 105.98/14.52 (((emptyE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (vacuousDall) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan3) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan4) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2setI) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2set2propI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdexE) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdallE) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI3) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inCongP) =>
% 105.98/14.52 ((
% 105.98/14.52 (in__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuE3u) =>
% 105.98/14.52 ((
% 105.98/14.52 (exu__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoin__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (powerset__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunion__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuEu) =>
% 105.98/14.52 ((
% 105.98/14.52 (descr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (dsetconstr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptysetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (notsubsetI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetRefl) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTrans) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subset2powerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetemptysetimpeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepInPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2IR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionEcases) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectI) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset5) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset3) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectER) =>
% 105.98/14.52 ((
% 105.98/14.52 (disjointsetsI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset4) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (bs114d) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusI) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusER) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusERneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusELneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusILneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusIRneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffE) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg2) =>
% 105.98/14.52 ((
% 105.98/14.52 (secondinupair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairiskpair) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairp) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2E) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsubunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairinpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem3) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair1) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton1) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I2) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsuniq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (theprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstin) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR11) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR12) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR1) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairequniteq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemER) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempaircEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrI) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setOfPairsIsBReln) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrERa) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrER) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcImageSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (apProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (app) =>
% 105.98/14.52 ((
% 105.98/14.52 (infuncsetfunc) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcinfuncset) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall1) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp3) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcextLem) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp4) =>
% 105.98/14.52 ((
% 105.98/14.52 (subbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq2) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2lamEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifp) =>
% 105.98/14.52 ((
% 105.98/14.52 (theeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrue) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueorfalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextT) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTI) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTELcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTERcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT1) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT2) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT3) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTnotintersectT) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementImpComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementSubsetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementInPowersetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (contraSubsetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTcontraSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTILcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTIRcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (intersectInPowersetIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpNotIn1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpInComplement1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTEcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementUnionInPowersetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule0) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_5) =>
% 105.98/14.52 ((
% 105.98/14.52 (breln1all2) =>
% 105.98/14.52 ((
% 105.98/14.52 (!!) @ (
% 105.98/14.52 (('#B') @ (
% 105.98/14.52 !!) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#S') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 '#S') @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 =>))) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#C') @ in)) @
% 105.98/14.52 breln1Set)))))) @
% 105.98/14.52 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
% 105.98/14.52 thf(zip_derived_cl222, plain,
% 105.98/14.52 (~ (((emptyI) =>
% 105.98/14.52 (((noeltsimpempty) =>
% 105.98/14.52 (((setbeta) =>
% 105.98/14.52 (((nonemptyE1) =>
% 105.98/14.52 (((nonemptyI) =>
% 105.98/14.52 (((nonemptyI1) =>
% 105.98/14.52 (((setadjoinIL) =>
% 105.98/14.52 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.52 (((setadjoinIR) =>
% 105.98/14.52 (((setadjoinE) =>
% 105.98/14.52 (((setadjoinOr) =>
% 105.98/14.52 (((setoftrueEq) =>
% 105.98/14.52 (((powersetI) =>
% 105.98/14.52 (((emptyinPowerset) =>
% 105.98/14.52 (((emptyInPowerset) =>
% 105.98/14.52 (((powersetE) =>
% 105.98/14.52 (((setunionI) =>
% 105.98/14.52 (((setunionE) =>
% 105.98/14.52 (((subPowSU) =>
% 105.98/14.52 (((exuE2) =>
% 105.98/14.52 (((nonemptyImpWitness) =>
% 105.98/14.52 (((uniqinunit) =>
% 105.98/14.52 (((notinsingleton) =>
% 105.98/14.52 (((eqinunit) =>
% 105.98/14.52 (((singletonsswitch) =>
% 105.98/14.52 (((upairsetE) =>
% 105.98/14.52 (((upairsetIL) =>
% 105.98/14.52 (((upairsetIR) =>
% 105.98/14.52 (((emptyE1) =>
% 105.98/14.52 (((vacuousDall) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan3) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan4) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2setI) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2set2propI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdexE) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdallE) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI3) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inCongP) =>
% 105.98/14.52 ((
% 105.98/14.52 (in__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuE3u) =>
% 105.98/14.52 ((
% 105.98/14.52 (exu__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoin__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (powerset__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunion__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuEu) =>
% 105.98/14.52 ((
% 105.98/14.52 (descr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (dsetconstr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptysetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (notsubsetI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetRefl) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTrans) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subset2powerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetemptysetimpeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepInPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2IR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionEcases) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectI) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset5) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset3) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectER) =>
% 105.98/14.52 ((
% 105.98/14.52 (disjointsetsI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset4) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (bs114d) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusI) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusER) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusERneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusELneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusILneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusIRneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffE) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg2) =>
% 105.98/14.52 ((
% 105.98/14.52 (secondinupair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairiskpair) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairp) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2E) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsubunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairinpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem3) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair1) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton1) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I2) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsuniq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (theprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstin) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR11) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR12) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR1) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairequniteq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemER) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempaircEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrI) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setOfPairsIsBReln) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrERa) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrER) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcImageSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (apProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (app) =>
% 105.98/14.52 ((
% 105.98/14.52 (infuncsetfunc) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcinfuncset) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall1) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp3) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcextLem) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp4) =>
% 105.98/14.52 ((
% 105.98/14.52 (subbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq2) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2lamEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifp) =>
% 105.98/14.52 ((
% 105.98/14.52 (theeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrue) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueorfalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextT) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTI) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTELcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTERcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT1) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT2) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT3) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTnotintersectT) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementImpComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementSubsetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementInPowersetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (contraSubsetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTcontraSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTILcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTIRcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (intersectInPowersetIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpNotIn1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpInComplement1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTEcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementUnionInPowersetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule0) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_5) =>
% 105.98/14.52 ((
% 105.98/14.52 (breln1all2) =>
% 105.98/14.52 ((
% 105.98/14.52 (!!) @ (
% 105.98/14.52 (('#B') @ (
% 105.98/14.52 !!) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#S') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 '#S') @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 =>))) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#C') @ in)) @
% 105.98/14.52 breln1Set)))))) @
% 105.98/14.52 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 105.98/14.52 thf(zip_derived_cl236, plain,
% 105.98/14.52 (~ (((noeltsimpempty) =>
% 105.98/14.52 (((setbeta) =>
% 105.98/14.52 (((nonemptyE1) =>
% 105.98/14.52 (((nonemptyI) =>
% 105.98/14.52 (((nonemptyI1) =>
% 105.98/14.52 (((setadjoinIL) =>
% 105.98/14.52 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.52 (((setadjoinIR) =>
% 105.98/14.52 (((setadjoinE) =>
% 105.98/14.52 (((setadjoinOr) =>
% 105.98/14.52 (((setoftrueEq) =>
% 105.98/14.52 (((powersetI) =>
% 105.98/14.52 (((emptyinPowerset) =>
% 105.98/14.52 (((emptyInPowerset) =>
% 105.98/14.52 (((powersetE) =>
% 105.98/14.52 (((setunionI) =>
% 105.98/14.52 (((setunionE) =>
% 105.98/14.52 (((subPowSU) =>
% 105.98/14.52 (((exuE2) =>
% 105.98/14.52 (((nonemptyImpWitness) =>
% 105.98/14.52 (((uniqinunit) =>
% 105.98/14.52 (((notinsingleton) =>
% 105.98/14.52 (((eqinunit) =>
% 105.98/14.52 (((singletonsswitch) =>
% 105.98/14.52 (((upairsetE) =>
% 105.98/14.52 (((upairsetIL) =>
% 105.98/14.52 (((upairsetIR) =>
% 105.98/14.52 (((emptyE1) =>
% 105.98/14.52 (((vacuousDall) =>
% 105.98/14.52 (((quantDeMorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan3) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan4) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2setI) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2set2propI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdexE) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdallE) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI3) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inCongP) =>
% 105.98/14.52 ((
% 105.98/14.52 (in__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuE3u) =>
% 105.98/14.52 ((
% 105.98/14.52 (exu__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoin__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (powerset__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunion__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuEu) =>
% 105.98/14.52 ((
% 105.98/14.52 (descr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (dsetconstr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptysetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (notsubsetI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetRefl) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTrans) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subset2powerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetemptysetimpeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepInPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2IR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionEcases) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectI) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset5) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset3) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectER) =>
% 105.98/14.52 ((
% 105.98/14.52 (disjointsetsI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset4) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (bs114d) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusI) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusER) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusERneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusELneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusILneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusIRneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffE) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg2) =>
% 105.98/14.52 ((
% 105.98/14.52 (secondinupair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairiskpair) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairp) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2E) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsubunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairinpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem3) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair1) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton1) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I2) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsuniq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (theprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstin) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR11) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR12) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR1) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairequniteq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemER) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempaircEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrI) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setOfPairsIsBReln) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrERa) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrER) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcImageSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (apProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (app) =>
% 105.98/14.52 ((
% 105.98/14.52 (infuncsetfunc) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcinfuncset) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall1) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp3) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcextLem) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp4) =>
% 105.98/14.52 ((
% 105.98/14.52 (subbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq2) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2lamEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifp) =>
% 105.98/14.52 ((
% 105.98/14.52 (theeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrue) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueorfalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextT) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTI) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTELcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTERcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT1) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT2) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT3) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTnotintersectT) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementImpComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementSubsetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementInPowersetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (contraSubsetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTcontraSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTILcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTIRcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (intersectInPowersetIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpNotIn1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpInComplement1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTEcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementUnionInPowersetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule0) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_5) =>
% 105.98/14.52 ((
% 105.98/14.52 (breln1all2) =>
% 105.98/14.52 ((
% 105.98/14.52 (!!) @ (
% 105.98/14.52 (('#B') @ (
% 105.98/14.52 !!) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#S') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 '#S') @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 =>))) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#C') @ in)) @
% 105.98/14.52 breln1Set)))))) @
% 105.98/14.52 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
% 105.98/14.52 thf(zip_derived_cl251, plain,
% 105.98/14.52 (~ (((setbeta) =>
% 105.98/14.52 (((nonemptyE1) =>
% 105.98/14.52 (((nonemptyI) =>
% 105.98/14.52 (((nonemptyI1) =>
% 105.98/14.52 (((setadjoinIL) =>
% 105.98/14.52 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.52 (((setadjoinIR) =>
% 105.98/14.52 (((setadjoinE) =>
% 105.98/14.52 (((setadjoinOr) =>
% 105.98/14.52 (((setoftrueEq) =>
% 105.98/14.52 (((powersetI) =>
% 105.98/14.52 (((emptyinPowerset) =>
% 105.98/14.52 (((emptyInPowerset) =>
% 105.98/14.52 (((powersetE) =>
% 105.98/14.52 (((setunionI) =>
% 105.98/14.52 (((setunionE) =>
% 105.98/14.52 (((subPowSU) =>
% 105.98/14.52 (((exuE2) =>
% 105.98/14.52 (((nonemptyImpWitness) =>
% 105.98/14.52 (((uniqinunit) =>
% 105.98/14.52 (((notinsingleton) =>
% 105.98/14.52 (((eqinunit) =>
% 105.98/14.52 (((singletonsswitch) =>
% 105.98/14.52 (((upairsetE) =>
% 105.98/14.52 (((upairsetIL) =>
% 105.98/14.52 (((upairsetIR) =>
% 105.98/14.52 (((emptyE1) =>
% 105.98/14.52 (((vacuousDall) =>
% 105.98/14.52 (((quantDeMorgan1) =>
% 105.98/14.52 (((quantDeMorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan3) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan4) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2setI) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2set2propI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdexE) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdallE) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI3) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inCongP) =>
% 105.98/14.52 ((
% 105.98/14.52 (in__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuE3u) =>
% 105.98/14.52 ((
% 105.98/14.52 (exu__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoin__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (powerset__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunion__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuEu) =>
% 105.98/14.52 ((
% 105.98/14.52 (descr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (dsetconstr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptysetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (notsubsetI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetRefl) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTrans) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subset2powerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetemptysetimpeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepInPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2IR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionEcases) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectI) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset5) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset3) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectER) =>
% 105.98/14.52 ((
% 105.98/14.52 (disjointsetsI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset4) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (bs114d) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusI) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusER) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusERneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusELneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusILneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusIRneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffE) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg2) =>
% 105.98/14.52 ((
% 105.98/14.52 (secondinupair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairiskpair) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairp) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2E) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsubunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairinpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem3) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair1) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton1) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I2) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsuniq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (theprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstin) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR11) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR12) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR1) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairequniteq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemER) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempaircEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrI) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setOfPairsIsBReln) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrERa) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrER) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcImageSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (apProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (app) =>
% 105.98/14.52 ((
% 105.98/14.52 (infuncsetfunc) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcinfuncset) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall1) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp3) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcextLem) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp4) =>
% 105.98/14.52 ((
% 105.98/14.52 (subbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq2) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2lamEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifp) =>
% 105.98/14.52 ((
% 105.98/14.52 (theeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrue) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueorfalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextT) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTI) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTELcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTERcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT1) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT2) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT3) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTnotintersectT) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementImpComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementSubsetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementInPowersetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (contraSubsetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTcontraSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTILcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTIRcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (intersectInPowersetIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpNotIn1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpInComplement1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTEcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementUnionInPowersetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule0) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_5) =>
% 105.98/14.52 ((
% 105.98/14.52 (breln1all2) =>
% 105.98/14.52 ((
% 105.98/14.52 (!!) @ (
% 105.98/14.52 (('#B') @ (
% 105.98/14.52 !!) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#S') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 '#S') @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 =>))) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#C') @ in)) @
% 105.98/14.52 breln1Set)))))) @
% 105.98/14.52 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])).
% 105.98/14.52 thf(zip_derived_cl264, plain,
% 105.98/14.52 (~ (((nonemptyE1) =>
% 105.98/14.52 (((nonemptyI) =>
% 105.98/14.52 (((nonemptyI1) =>
% 105.98/14.52 (((setadjoinIL) =>
% 105.98/14.52 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.52 (((setadjoinIR) =>
% 105.98/14.52 (((setadjoinE) =>
% 105.98/14.52 (((setadjoinOr) =>
% 105.98/14.52 (((setoftrueEq) =>
% 105.98/14.52 (((powersetI) =>
% 105.98/14.52 (((emptyinPowerset) =>
% 105.98/14.52 (((emptyInPowerset) =>
% 105.98/14.52 (((powersetE) =>
% 105.98/14.52 (((setunionI) =>
% 105.98/14.52 (((setunionE) =>
% 105.98/14.52 (((subPowSU) =>
% 105.98/14.52 (((exuE2) =>
% 105.98/14.52 (((nonemptyImpWitness) =>
% 105.98/14.52 (((uniqinunit) =>
% 105.98/14.52 (((notinsingleton) =>
% 105.98/14.52 (((eqinunit) =>
% 105.98/14.52 (((singletonsswitch) =>
% 105.98/14.52 (((upairsetE) =>
% 105.98/14.52 (((upairsetIL) =>
% 105.98/14.52 (((upairsetIR) =>
% 105.98/14.52 (((emptyE1) =>
% 105.98/14.52 (((vacuousDall) =>
% 105.98/14.52 (((quantDeMorgan1) =>
% 105.98/14.52 (((quantDeMorgan2) =>
% 105.98/14.52 (((quantDeMorgan3) =>
% 105.98/14.52 ((
% 105.98/14.52 (quantDeMorgan4) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2setI) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2set2propI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdexE) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdallE) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI3) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inCongP) =>
% 105.98/14.52 ((
% 105.98/14.52 (in__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuE3u) =>
% 105.98/14.52 ((
% 105.98/14.52 (exu__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoin__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (powerset__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunion__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuEu) =>
% 105.98/14.52 ((
% 105.98/14.52 (descr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (dsetconstr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptysetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (notsubsetI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetRefl) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTrans) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subset2powerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetemptysetimpeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepInPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2IR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionEcases) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectI) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset5) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset3) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectER) =>
% 105.98/14.52 ((
% 105.98/14.52 (disjointsetsI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset4) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (bs114d) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusI) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusER) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusERneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusELneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusILneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusIRneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffE) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg2) =>
% 105.98/14.52 ((
% 105.98/14.52 (secondinupair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairiskpair) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairp) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2E) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsubunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairinpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem3) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair1) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton1) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I2) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsuniq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (theprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstin) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR11) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR12) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR1) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairequniteq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemER) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempaircEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrI) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setOfPairsIsBReln) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrERa) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrER) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcImageSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (apProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (app) =>
% 105.98/14.52 ((
% 105.98/14.52 (infuncsetfunc) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcinfuncset) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall1) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp3) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcextLem) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp4) =>
% 105.98/14.52 ((
% 105.98/14.52 (subbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq2) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta1) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2lamEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (beta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eta2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalseProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ifp) =>
% 105.98/14.52 ((
% 105.98/14.52 (theeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrue) =>
% 105.98/14.52 ((
% 105.98/14.52 (iffalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (iftrueorfalse) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementT_lem) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextT) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTI) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTELcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectTERcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT1) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT2) =>
% 105.98/14.52 ((
% 105.98/14.52 (contrasubsetT3) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub1) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (doubleComplementEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTnotintersectT) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementImpComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementSubsetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementInPowersetComplementIntersect) =>
% 105.98/14.52 ((
% 105.98/14.52 (contraSubsetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementTcontraSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTILcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTIRcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInUnion2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inIntersectImpInIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (intersectInPowersetIntersectUnions) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpNotIn1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inComplementUnionImpInComplement1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionTEcontra) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a1) =>
% 105.98/14.52 ((
% 105.98/14.52 (complementUnionInPowersetComplement) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan1) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2a) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b2) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2b) =>
% 105.98/14.52 ((
% 105.98/14.52 (demorgan2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule0) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz13rule4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_1) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_2) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_3) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_4) =>
% 105.98/14.52 ((
% 105.98/14.52 (woz1_5) =>
% 105.98/14.52 ((
% 105.98/14.52 (breln1all2) =>
% 105.98/14.52 ((
% 105.98/14.52 (!!) @ (
% 105.98/14.52 (('#B') @ (
% 105.98/14.52 !!) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#S') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 '#S') @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 =>))) @
% 105.98/14.52 (
% 105.98/14.52 (
% 105.98/14.52 ('#B') @ (
% 105.98/14.52 (
% 105.98/14.52 ('#C') @ in)) @
% 105.98/14.52 breln1Set)))))) @
% 105.98/14.52 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl251])).
% 105.98/14.52 thf(zip_derived_cl280, plain,
% 105.98/14.52 (~ (((nonemptyI) =>
% 105.98/14.52 (((nonemptyI1) =>
% 105.98/14.52 (((setadjoinIL) =>
% 105.98/14.52 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.52 (((setadjoinIR) =>
% 105.98/14.52 (((setadjoinE) =>
% 105.98/14.52 (((setadjoinOr) =>
% 105.98/14.52 (((setoftrueEq) =>
% 105.98/14.52 (((powersetI) =>
% 105.98/14.52 (((emptyinPowerset) =>
% 105.98/14.52 (((emptyInPowerset) =>
% 105.98/14.52 (((powersetE) =>
% 105.98/14.52 (((setunionI) =>
% 105.98/14.52 (((setunionE) =>
% 105.98/14.52 (((subPowSU) =>
% 105.98/14.52 (((exuE2) =>
% 105.98/14.52 (((nonemptyImpWitness) =>
% 105.98/14.52 (((uniqinunit) =>
% 105.98/14.52 (((notinsingleton) =>
% 105.98/14.52 (((eqinunit) =>
% 105.98/14.52 (((singletonsswitch) =>
% 105.98/14.52 (((upairsetE) =>
% 105.98/14.52 (((upairsetIL) =>
% 105.98/14.52 (((upairsetIR) =>
% 105.98/14.52 (((emptyE1) =>
% 105.98/14.52 (((vacuousDall) =>
% 105.98/14.52 (((quantDeMorgan1) =>
% 105.98/14.52 (((quantDeMorgan2) =>
% 105.98/14.52 (((quantDeMorgan3) =>
% 105.98/14.52 (((quantDeMorgan4) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2setI) =>
% 105.98/14.52 ((
% 105.98/14.52 (prop2set2propI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdexE) =>
% 105.98/14.52 ((
% 105.98/14.52 (notdallE) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI3) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (inCongP) =>
% 105.98/14.52 ((
% 105.98/14.52 (in__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuE3u) =>
% 105.98/14.52 ((
% 105.98/14.52 (exu__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoin__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (powerset__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunion__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (exuEu) =>
% 105.98/14.52 ((
% 105.98/14.52 (descr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (dsetconstr__Cong) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqimpsubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (emptysetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (notsubsetI) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (notequalI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetRefl) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetTrans) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setadjoinSub2) =>
% 105.98/14.52 ((
% 105.98/14.52 (subset2powerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (setextsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (subsetemptysetimpeq) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetE1) =>
% 105.98/14.52 ((
% 105.98/14.52 (inPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (powersetsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepInPowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (sepSubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2IR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionEcases) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionE) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binunionRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectI) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset5) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset3) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectER) =>
% 105.98/14.52 ((
% 105.98/14.52 (disjointsetsI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectRsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset4) =>
% 105.98/14.52 ((
% 105.98/14.52 (binintersectSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (bs114d) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusI) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusER) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusERneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusELneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusILneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusIRneg) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusLsub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setminusSubset1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffE) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffI2) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg1) =>
% 105.98/14.52 ((
% 105.98/14.52 (symdiffIneg2) =>
% 105.98/14.52 ((
% 105.98/14.52 (secondinupair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairIR) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairiskpair) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairp) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsubset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowerset) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletoninpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairset2E) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairsubunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairinpowunion) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ubforcartprodlem3) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair1) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempair) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionE2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton1) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setunionsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1I2) =>
% 105.98/14.52 ((
% 105.98/14.52 (singletonsuniq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (theprop) =>
% 105.98/14.52 ((
% 105.98/14.52 (kfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstin) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjL) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR11) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR12) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR1) =>
% 105.98/14.52 ((
% 105.98/14.52 (upairequniteq) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR2) =>
% 105.98/14.52 ((
% 105.98/14.52 (setukpairinjR) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndsingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (ksndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (kpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndin) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemEL) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairmemER) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodmempaircEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodfstpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodsndpairEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (cartprodpairsurjEq) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrI) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrSub) =>
% 105.98/14.52 ((
% 105.98/14.52 (setOfPairsIsBReln) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrERa) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL1) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrEL2) =>
% 105.98/14.52 ((
% 105.98/14.52 (dpsetconstrER) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcImageSingleton) =>
% 105.98/14.52 ((
% 105.98/14.52 (apProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (app) =>
% 105.98/14.52 ((
% 105.98/14.52 (infuncsetfunc) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcinfuncset) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamProp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lamp) =>
% 105.98/14.52 ((
% 105.98/14.52 (lam2p) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall1) =>
% 105.98/14.52 ((
% 105.98/14.52 (brelnall2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ex1E2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp1) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp3) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp2) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcextLem) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcGraphProp4) =>
% 105.98/14.52 ((
% 105.98/14.52 (subbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (eqbreln) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext) =>
% 105.98/14.52 ((
% 105.98/14.52 (funcext2) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq1) =>
% 105.98/14.52 ((
% 105.98/14.52 (ap2apEq2) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2lamEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifp) =>
% 105.98/14.53 ((
% 105.98/14.53 (theeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrue) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueorfalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextT) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTI) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTELcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTERcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT1) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT2) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT3) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTnotintersectT) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementImpComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementSubsetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementInPowersetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (contraSubsetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTcontraSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTILcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTIRcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (intersectInPowersetIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpNotIn1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpInComplement1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTEcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementUnionInPowersetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule0) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_5) =>
% 105.98/14.53 ((
% 105.98/14.53 (breln1all2) =>
% 105.98/14.53 ((
% 105.98/14.53 (!!) @ (
% 105.98/14.53 (('#B') @ (
% 105.98/14.53 !!) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#S') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 '#S') @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 =>))) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#C') @ in)) @
% 105.98/14.53 breln1Set)))))) @
% 105.98/14.53 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl264])).
% 105.98/14.53 thf(zip_derived_cl293, plain,
% 105.98/14.53 (~ (((nonemptyI1) =>
% 105.98/14.53 (((setadjoinIL) =>
% 105.98/14.53 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.53 (((setadjoinIR) =>
% 105.98/14.53 (((setadjoinE) =>
% 105.98/14.53 (((setadjoinOr) =>
% 105.98/14.53 (((setoftrueEq) =>
% 105.98/14.53 (((powersetI) =>
% 105.98/14.53 (((emptyinPowerset) =>
% 105.98/14.53 (((emptyInPowerset) =>
% 105.98/14.53 (((powersetE) =>
% 105.98/14.53 (((setunionI) =>
% 105.98/14.53 (((setunionE) =>
% 105.98/14.53 (((subPowSU) =>
% 105.98/14.53 (((exuE2) =>
% 105.98/14.53 (((nonemptyImpWitness) =>
% 105.98/14.53 (((uniqinunit) =>
% 105.98/14.53 (((notinsingleton) =>
% 105.98/14.53 (((eqinunit) =>
% 105.98/14.53 (((singletonsswitch) =>
% 105.98/14.53 (((upairsetE) =>
% 105.98/14.53 (((upairsetIL) =>
% 105.98/14.53 (((upairsetIR) =>
% 105.98/14.53 (((emptyE1) =>
% 105.98/14.53 (((vacuousDall) =>
% 105.98/14.53 (((quantDeMorgan1) =>
% 105.98/14.53 (((quantDeMorgan2) =>
% 105.98/14.53 (((quantDeMorgan3) =>
% 105.98/14.53 (((quantDeMorgan4) =>
% 105.98/14.53 (((prop2setI) =>
% 105.98/14.53 ((
% 105.98/14.53 (prop2set2propI) =>
% 105.98/14.53 ((
% 105.98/14.53 (notdexE) =>
% 105.98/14.53 ((
% 105.98/14.53 (notdallE) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI3) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inCongP) =>
% 105.98/14.53 ((
% 105.98/14.53 (in__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuE3u) =>
% 105.98/14.53 ((
% 105.98/14.53 (exu__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoin__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (powerset__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunion__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuEu) =>
% 105.98/14.53 ((
% 105.98/14.53 (descr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (dsetconstr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (emptysetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (notsubsetI) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetRefl) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTrans) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subset2powerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetemptysetimpeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepInPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2IR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionEcases) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectI) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset5) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset3) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectER) =>
% 105.98/14.53 ((
% 105.98/14.53 (disjointsetsI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset4) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (bs114d) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusI) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusER) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusERneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusELneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusILneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusIRneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffE) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg2) =>
% 105.98/14.53 ((
% 105.98/14.53 (secondinupair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairiskpair) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairp) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2E) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairsubunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairinpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem3) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair1) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton1) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I2) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsuniq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (theprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstin) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR11) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR12) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR1) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairequniteq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemER) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempaircEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrI) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setOfPairsIsBReln) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrERa) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrER) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcImageSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (apProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (app) =>
% 105.98/14.53 ((
% 105.98/14.53 (infuncsetfunc) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcinfuncset) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall1) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp3) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcextLem) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp4) =>
% 105.98/14.53 ((
% 105.98/14.53 (subbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq2) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2lamEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifp) =>
% 105.98/14.53 ((
% 105.98/14.53 (theeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrue) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueorfalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextT) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTI) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTELcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTERcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT1) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT2) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT3) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTnotintersectT) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementImpComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementSubsetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementInPowersetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (contraSubsetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTcontraSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTILcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTIRcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (intersectInPowersetIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpNotIn1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpInComplement1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTEcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementUnionInPowersetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule0) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_5) =>
% 105.98/14.53 ((
% 105.98/14.53 (breln1all2) =>
% 105.98/14.53 ((
% 105.98/14.53 (!!) @ (
% 105.98/14.53 (('#B') @ (
% 105.98/14.53 !!) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#S') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 '#S') @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 =>))) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#C') @ in)) @
% 105.98/14.53 breln1Set)))))) @
% 105.98/14.53 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
% 105.98/14.53 thf(zip_derived_cl307, plain,
% 105.98/14.53 (~ (((setadjoinIL) =>
% 105.98/14.53 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.53 (((setadjoinIR) =>
% 105.98/14.53 (((setadjoinE) =>
% 105.98/14.53 (((setadjoinOr) =>
% 105.98/14.53 (((setoftrueEq) =>
% 105.98/14.53 (((powersetI) =>
% 105.98/14.53 (((emptyinPowerset) =>
% 105.98/14.53 (((emptyInPowerset) =>
% 105.98/14.53 (((powersetE) =>
% 105.98/14.53 (((setunionI) =>
% 105.98/14.53 (((setunionE) =>
% 105.98/14.53 (((subPowSU) =>
% 105.98/14.53 (((exuE2) =>
% 105.98/14.53 (((nonemptyImpWitness) =>
% 105.98/14.53 (((uniqinunit) =>
% 105.98/14.53 (((notinsingleton) =>
% 105.98/14.53 (((eqinunit) =>
% 105.98/14.53 (((singletonsswitch) =>
% 105.98/14.53 (((upairsetE) =>
% 105.98/14.53 (((upairsetIL) =>
% 105.98/14.53 (((upairsetIR) =>
% 105.98/14.53 (((emptyE1) =>
% 105.98/14.53 (((vacuousDall) =>
% 105.98/14.53 (((quantDeMorgan1) =>
% 105.98/14.53 (((quantDeMorgan2) =>
% 105.98/14.53 (((quantDeMorgan3) =>
% 105.98/14.53 (((quantDeMorgan4) =>
% 105.98/14.53 (((prop2setI) =>
% 105.98/14.53 (((prop2set2propI) =>
% 105.98/14.53 ((
% 105.98/14.53 (notdexE) =>
% 105.98/14.53 ((
% 105.98/14.53 (notdallE) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI3) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inCongP) =>
% 105.98/14.53 ((
% 105.98/14.53 (in__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuE3u) =>
% 105.98/14.53 ((
% 105.98/14.53 (exu__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoin__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (powerset__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunion__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuEu) =>
% 105.98/14.53 ((
% 105.98/14.53 (descr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (dsetconstr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (emptysetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (notsubsetI) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetRefl) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTrans) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subset2powerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetemptysetimpeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepInPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2IR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionEcases) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectI) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset5) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset3) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectER) =>
% 105.98/14.53 ((
% 105.98/14.53 (disjointsetsI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset4) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (bs114d) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusI) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusER) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusERneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusELneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusILneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusIRneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffE) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg2) =>
% 105.98/14.53 ((
% 105.98/14.53 (secondinupair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairiskpair) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairp) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2E) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairsubunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairinpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem3) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair1) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton1) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I2) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsuniq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (theprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstin) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR11) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR12) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR1) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairequniteq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemER) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempaircEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrI) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setOfPairsIsBReln) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrERa) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrER) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcImageSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (apProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (app) =>
% 105.98/14.53 ((
% 105.98/14.53 (infuncsetfunc) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcinfuncset) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall1) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp3) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcextLem) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp4) =>
% 105.98/14.53 ((
% 105.98/14.53 (subbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq2) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2lamEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifp) =>
% 105.98/14.53 ((
% 105.98/14.53 (theeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrue) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueorfalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextT) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTI) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTELcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTERcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT1) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT2) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT3) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTnotintersectT) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementImpComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementSubsetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementInPowersetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (contraSubsetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTcontraSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTILcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTIRcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (intersectInPowersetIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpNotIn1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpInComplement1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTEcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementUnionInPowersetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule0) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_5) =>
% 105.98/14.53 ((
% 105.98/14.53 (breln1all2) =>
% 105.98/14.53 ((
% 105.98/14.53 (!!) @ (
% 105.98/14.53 (('#B') @ (
% 105.98/14.53 !!) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#S') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 '#S') @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 =>))) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#C') @ in)) @
% 105.98/14.53 breln1Set)))))) @
% 105.98/14.53 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])).
% 105.98/14.53 thf(zip_derived_cl322, plain,
% 105.98/14.53 (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 105.98/14.53 (((setadjoinIR) =>
% 105.98/14.53 (((setadjoinE) =>
% 105.98/14.53 (((setadjoinOr) =>
% 105.98/14.53 (((setoftrueEq) =>
% 105.98/14.53 (((powersetI) =>
% 105.98/14.53 (((emptyinPowerset) =>
% 105.98/14.53 (((emptyInPowerset) =>
% 105.98/14.53 (((powersetE) =>
% 105.98/14.53 (((setunionI) =>
% 105.98/14.53 (((setunionE) =>
% 105.98/14.53 (((subPowSU) =>
% 105.98/14.53 (((exuE2) =>
% 105.98/14.53 (((nonemptyImpWitness) =>
% 105.98/14.53 (((uniqinunit) =>
% 105.98/14.53 (((notinsingleton) =>
% 105.98/14.53 (((eqinunit) =>
% 105.98/14.53 (((singletonsswitch) =>
% 105.98/14.53 (((upairsetE) =>
% 105.98/14.53 (((upairsetIL) =>
% 105.98/14.53 (((upairsetIR) =>
% 105.98/14.53 (((emptyE1) =>
% 105.98/14.53 (((vacuousDall) =>
% 105.98/14.53 (((quantDeMorgan1) =>
% 105.98/14.53 (((quantDeMorgan2) =>
% 105.98/14.53 (((quantDeMorgan3) =>
% 105.98/14.53 (((quantDeMorgan4) =>
% 105.98/14.53 (((prop2setI) =>
% 105.98/14.53 (((prop2set2propI) =>
% 105.98/14.53 (((notdexE) =>
% 105.98/14.53 ((
% 105.98/14.53 (notdallE) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI3) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inCongP) =>
% 105.98/14.53 ((
% 105.98/14.53 (in__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuE3u) =>
% 105.98/14.53 ((
% 105.98/14.53 (exu__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoin__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (powerset__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunion__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuEu) =>
% 105.98/14.53 ((
% 105.98/14.53 (descr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (dsetconstr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (emptysetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (notsubsetI) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetRefl) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTrans) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subset2powerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetemptysetimpeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepInPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2IR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionEcases) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectI) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset5) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset3) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectER) =>
% 105.98/14.53 ((
% 105.98/14.53 (disjointsetsI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset4) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (bs114d) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusI) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusER) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusERneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusELneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusILneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusIRneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffE) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg2) =>
% 105.98/14.53 ((
% 105.98/14.53 (secondinupair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairiskpair) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairp) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2E) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairsubunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairinpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem3) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair1) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton1) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I2) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsuniq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (theprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstin) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR11) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR12) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR1) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairequniteq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemER) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempaircEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrI) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setOfPairsIsBReln) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrERa) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrER) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcImageSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (apProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (app) =>
% 105.98/14.53 ((
% 105.98/14.53 (infuncsetfunc) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcinfuncset) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall1) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp3) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcextLem) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp4) =>
% 105.98/14.53 ((
% 105.98/14.53 (subbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq2) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2lamEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifp) =>
% 105.98/14.53 ((
% 105.98/14.53 (theeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrue) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueorfalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextT) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTI) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTELcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTERcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT1) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT2) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT3) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTnotintersectT) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementImpComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementSubsetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementInPowersetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (contraSubsetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTcontraSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTILcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTIRcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (intersectInPowersetIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpNotIn1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpInComplement1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTEcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementUnionInPowersetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule0) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_5) =>
% 105.98/14.53 ((
% 105.98/14.53 (breln1all2) =>
% 105.98/14.53 ((
% 105.98/14.53 (!!) @ (
% 105.98/14.53 (('#B') @ (
% 105.98/14.53 !!) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#S') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 '#S') @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 =>))) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#C') @ in)) @
% 105.98/14.53 breln1Set)))))) @
% 105.98/14.53 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])).
% 105.98/14.53 thf(zip_derived_cl337, plain,
% 105.98/14.53 (~ (((setadjoinIR) =>
% 105.98/14.53 (((setadjoinE) =>
% 105.98/14.53 (((setadjoinOr) =>
% 105.98/14.53 (((setoftrueEq) =>
% 105.98/14.53 (((powersetI) =>
% 105.98/14.53 (((emptyinPowerset) =>
% 105.98/14.53 (((emptyInPowerset) =>
% 105.98/14.53 (((powersetE) =>
% 105.98/14.53 (((setunionI) =>
% 105.98/14.53 (((setunionE) =>
% 105.98/14.53 (((subPowSU) =>
% 105.98/14.53 (((exuE2) =>
% 105.98/14.53 (((nonemptyImpWitness) =>
% 105.98/14.53 (((uniqinunit) =>
% 105.98/14.53 (((notinsingleton) =>
% 105.98/14.53 (((eqinunit) =>
% 105.98/14.53 (((singletonsswitch) =>
% 105.98/14.53 (((upairsetE) =>
% 105.98/14.53 (((upairsetIL) =>
% 105.98/14.53 (((upairsetIR) =>
% 105.98/14.53 (((emptyE1) =>
% 105.98/14.53 (((vacuousDall) =>
% 105.98/14.53 (((quantDeMorgan1) =>
% 105.98/14.53 (((quantDeMorgan2) =>
% 105.98/14.53 (((quantDeMorgan3) =>
% 105.98/14.53 (((quantDeMorgan4) =>
% 105.98/14.53 (((prop2setI) =>
% 105.98/14.53 (((prop2set2propI) =>
% 105.98/14.53 (((notdexE) =>
% 105.98/14.53 (((notdallE) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI3) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inCongP) =>
% 105.98/14.53 ((
% 105.98/14.53 (in__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuE3u) =>
% 105.98/14.53 ((
% 105.98/14.53 (exu__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoin__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (powerset__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunion__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuEu) =>
% 105.98/14.53 ((
% 105.98/14.53 (descr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (dsetconstr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (emptysetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (notsubsetI) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetRefl) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTrans) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subset2powerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetemptysetimpeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepInPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2IR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionEcases) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectI) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset5) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset3) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectER) =>
% 105.98/14.53 ((
% 105.98/14.53 (disjointsetsI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset4) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (bs114d) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusI) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusER) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusERneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusELneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusILneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusIRneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffE) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg2) =>
% 105.98/14.53 ((
% 105.98/14.53 (secondinupair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairiskpair) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairp) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2E) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairsubunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairinpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem3) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair1) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton1) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I2) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsuniq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (theprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstin) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR11) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR12) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR1) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairequniteq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemER) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempaircEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrI) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setOfPairsIsBReln) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrERa) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrER) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcImageSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (apProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (app) =>
% 105.98/14.53 ((
% 105.98/14.53 (infuncsetfunc) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcinfuncset) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall1) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp3) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcextLem) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp4) =>
% 105.98/14.53 ((
% 105.98/14.53 (subbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq2) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2lamEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifp) =>
% 105.98/14.53 ((
% 105.98/14.53 (theeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrue) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueorfalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextT) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTI) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTELcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTERcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT1) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT2) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT3) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTnotintersectT) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementImpComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementSubsetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementInPowersetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (contraSubsetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTcontraSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTILcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTIRcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (intersectInPowersetIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpNotIn1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpInComplement1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTEcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementUnionInPowersetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule0) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_5) =>
% 105.98/14.53 ((
% 105.98/14.53 (breln1all2) =>
% 105.98/14.53 ((
% 105.98/14.53 (!!) @ (
% 105.98/14.53 (('#B') @ (
% 105.98/14.53 !!) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#S') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 '#S') @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 =>))) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#C') @ in)) @
% 105.98/14.53 breln1Set)))))) @
% 105.98/14.53 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl322])).
% 105.98/14.53 thf(zip_derived_cl349, plain,
% 105.98/14.53 (~ (((setadjoinE) =>
% 105.98/14.53 (((setadjoinOr) =>
% 105.98/14.53 (((setoftrueEq) =>
% 105.98/14.53 (((powersetI) =>
% 105.98/14.53 (((emptyinPowerset) =>
% 105.98/14.53 (((emptyInPowerset) =>
% 105.98/14.53 (((powersetE) =>
% 105.98/14.53 (((setunionI) =>
% 105.98/14.53 (((setunionE) =>
% 105.98/14.53 (((subPowSU) =>
% 105.98/14.53 (((exuE2) =>
% 105.98/14.53 (((nonemptyImpWitness) =>
% 105.98/14.53 (((uniqinunit) =>
% 105.98/14.53 (((notinsingleton) =>
% 105.98/14.53 (((eqinunit) =>
% 105.98/14.53 (((singletonsswitch) =>
% 105.98/14.53 (((upairsetE) =>
% 105.98/14.53 (((upairsetIL) =>
% 105.98/14.53 (((upairsetIR) =>
% 105.98/14.53 (((emptyE1) =>
% 105.98/14.53 (((vacuousDall) =>
% 105.98/14.53 (((quantDeMorgan1) =>
% 105.98/14.53 (((quantDeMorgan2) =>
% 105.98/14.53 (((quantDeMorgan3) =>
% 105.98/14.53 (((quantDeMorgan4) =>
% 105.98/14.53 (((prop2setI) =>
% 105.98/14.53 (((prop2set2propI) =>
% 105.98/14.53 (((notdexE) =>
% 105.98/14.53 (((notdallE) =>
% 105.98/14.53 (((exuI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI3) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inCongP) =>
% 105.98/14.53 ((
% 105.98/14.53 (in__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuE3u) =>
% 105.98/14.53 ((
% 105.98/14.53 (exu__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoin__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (powerset__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunion__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuEu) =>
% 105.98/14.53 ((
% 105.98/14.53 (descr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (dsetconstr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (emptysetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (notsubsetI) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetRefl) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTrans) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subset2powerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetemptysetimpeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepInPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2IR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionEcases) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectI) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset5) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset3) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectER) =>
% 105.98/14.53 ((
% 105.98/14.53 (disjointsetsI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset4) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (bs114d) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusI) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusER) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusERneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusELneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusILneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusIRneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffE) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg2) =>
% 105.98/14.53 ((
% 105.98/14.53 (secondinupair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairiskpair) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairp) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2E) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairsubunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairinpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem3) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair1) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton1) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I2) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsuniq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (theprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstin) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR11) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR12) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR1) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairequniteq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemER) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempaircEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrI) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setOfPairsIsBReln) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrERa) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrER) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcImageSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (apProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (app) =>
% 105.98/14.53 ((
% 105.98/14.53 (infuncsetfunc) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcinfuncset) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall1) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp3) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcextLem) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp4) =>
% 105.98/14.53 ((
% 105.98/14.53 (subbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq2) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2lamEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifp) =>
% 105.98/14.53 ((
% 105.98/14.53 (theeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrue) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueorfalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextT) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTI) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTELcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTERcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT1) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT2) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT3) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTnotintersectT) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementImpComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementSubsetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementInPowersetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (contraSubsetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTcontraSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTILcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTIRcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (intersectInPowersetIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpNotIn1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpInComplement1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTEcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementUnionInPowersetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule0) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_5) =>
% 105.98/14.53 ((
% 105.98/14.53 (breln1all2) =>
% 105.98/14.53 ((
% 105.98/14.53 (!!) @ (
% 105.98/14.53 (('#B') @ (
% 105.98/14.53 !!) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#S') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 '#S') @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 =>))) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#C') @ in)) @
% 105.98/14.53 breln1Set)))))) @
% 105.98/14.53 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
% 105.98/14.53 thf(zip_derived_cl355, plain,
% 105.98/14.53 (~ (((setadjoinOr) =>
% 105.98/14.53 (((setoftrueEq) =>
% 105.98/14.53 (((powersetI) =>
% 105.98/14.53 (((emptyinPowerset) =>
% 105.98/14.53 (((emptyInPowerset) =>
% 105.98/14.53 (((powersetE) =>
% 105.98/14.53 (((setunionI) =>
% 105.98/14.53 (((setunionE) =>
% 105.98/14.53 (((subPowSU) =>
% 105.98/14.53 (((exuE2) =>
% 105.98/14.53 (((nonemptyImpWitness) =>
% 105.98/14.53 (((uniqinunit) =>
% 105.98/14.53 (((notinsingleton) =>
% 105.98/14.53 (((eqinunit) =>
% 105.98/14.53 (((singletonsswitch) =>
% 105.98/14.53 (((upairsetE) =>
% 105.98/14.53 (((upairsetIL) =>
% 105.98/14.53 (((upairsetIR) =>
% 105.98/14.53 (((emptyE1) =>
% 105.98/14.53 (((vacuousDall) =>
% 105.98/14.53 (((quantDeMorgan1) =>
% 105.98/14.53 (((quantDeMorgan2) =>
% 105.98/14.53 (((quantDeMorgan3) =>
% 105.98/14.53 (((quantDeMorgan4) =>
% 105.98/14.53 (((prop2setI) =>
% 105.98/14.53 (((prop2set2propI) =>
% 105.98/14.53 (((notdexE) =>
% 105.98/14.53 (((notdallE) =>
% 105.98/14.53 (((exuI1) =>
% 105.98/14.53 (((exuI3) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inCongP) =>
% 105.98/14.53 ((
% 105.98/14.53 (in__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuE3u) =>
% 105.98/14.53 ((
% 105.98/14.53 (exu__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoin__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (powerset__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunion__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuEu) =>
% 105.98/14.53 ((
% 105.98/14.53 (descr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (dsetconstr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (emptysetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (notsubsetI) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetRefl) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTrans) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subset2powerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetemptysetimpeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepInPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2IR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionEcases) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectI) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset5) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset3) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectER) =>
% 105.98/14.53 ((
% 105.98/14.53 (disjointsetsI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset4) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (bs114d) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusI) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusER) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusERneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusELneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusILneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusIRneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffE) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg2) =>
% 105.98/14.53 ((
% 105.98/14.53 (secondinupair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairiskpair) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairp) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2E) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairsubunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairinpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem3) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair1) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton1) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I2) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsuniq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (theprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstin) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR11) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR12) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR1) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairequniteq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemER) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempaircEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrI) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setOfPairsIsBReln) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrERa) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrER) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcImageSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (apProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (app) =>
% 105.98/14.53 ((
% 105.98/14.53 (infuncsetfunc) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcinfuncset) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall1) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp3) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcextLem) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp4) =>
% 105.98/14.53 ((
% 105.98/14.53 (subbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq2) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2lamEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifp) =>
% 105.98/14.53 ((
% 105.98/14.53 (theeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrue) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueorfalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextT) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTI) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTELcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTERcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT1) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT2) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT3) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTnotintersectT) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementImpComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementSubsetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementInPowersetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (contraSubsetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTcontraSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTILcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTIRcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (intersectInPowersetIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpNotIn1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpInComplement1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTEcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementUnionInPowersetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule0) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_5) =>
% 105.98/14.53 ((
% 105.98/14.53 (breln1all2) =>
% 105.98/14.53 ((
% 105.98/14.53 (!!) @ (
% 105.98/14.53 (('#B') @ (
% 105.98/14.53 !!) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#S') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 '#S') @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 =>))) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#C') @ in)) @
% 105.98/14.53 breln1Set)))))) @
% 105.98/14.53 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl349])).
% 105.98/14.53 thf(zip_derived_cl362, plain,
% 105.98/14.53 (~ (((setoftrueEq) =>
% 105.98/14.53 (((powersetI) =>
% 105.98/14.53 (((emptyinPowerset) =>
% 105.98/14.53 (((emptyInPowerset) =>
% 105.98/14.53 (((powersetE) =>
% 105.98/14.53 (((setunionI) =>
% 105.98/14.53 (((setunionE) =>
% 105.98/14.53 (((subPowSU) =>
% 105.98/14.53 (((exuE2) =>
% 105.98/14.53 (((nonemptyImpWitness) =>
% 105.98/14.53 (((uniqinunit) =>
% 105.98/14.53 (((notinsingleton) =>
% 105.98/14.53 (((eqinunit) =>
% 105.98/14.53 (((singletonsswitch) =>
% 105.98/14.53 (((upairsetE) =>
% 105.98/14.53 (((upairsetIL) =>
% 105.98/14.53 (((upairsetIR) =>
% 105.98/14.53 (((emptyE1) =>
% 105.98/14.53 (((vacuousDall) =>
% 105.98/14.53 (((quantDeMorgan1) =>
% 105.98/14.53 (((quantDeMorgan2) =>
% 105.98/14.53 (((quantDeMorgan3) =>
% 105.98/14.53 (((quantDeMorgan4) =>
% 105.98/14.53 (((prop2setI) =>
% 105.98/14.53 (((prop2set2propI) =>
% 105.98/14.53 (((notdexE) =>
% 105.98/14.53 (((notdallE) =>
% 105.98/14.53 (((exuI1) =>
% 105.98/14.53 (((exuI3) =>
% 105.98/14.53 (((exuI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inCongP) =>
% 105.98/14.53 ((
% 105.98/14.53 (in__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuE3u) =>
% 105.98/14.53 ((
% 105.98/14.53 (exu__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoin__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (powerset__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunion__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuEu) =>
% 105.98/14.53 ((
% 105.98/14.53 (descr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (dsetconstr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (emptysetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (notsubsetI) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetRefl) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTrans) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subset2powerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetemptysetimpeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepInPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2IR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionEcases) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectI) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset5) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset3) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectER) =>
% 105.98/14.53 ((
% 105.98/14.53 (disjointsetsI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset4) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (bs114d) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusI) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusER) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusERneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusELneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusILneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusIRneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffE) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg2) =>
% 105.98/14.53 ((
% 105.98/14.53 (secondinupair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairiskpair) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairp) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2E) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairsubunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairinpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem3) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair1) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton1) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I2) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsuniq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (theprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstin) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR11) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR12) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR1) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairequniteq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemER) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempaircEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrI) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setOfPairsIsBReln) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrERa) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrER) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcImageSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (apProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (app) =>
% 105.98/14.53 ((
% 105.98/14.53 (infuncsetfunc) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcinfuncset) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall1) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp3) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcextLem) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp4) =>
% 105.98/14.53 ((
% 105.98/14.53 (subbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq2) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2lamEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifp) =>
% 105.98/14.53 ((
% 105.98/14.53 (theeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrue) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueorfalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextT) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTI) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTELcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTERcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT1) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT2) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT3) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTnotintersectT) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementImpComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementSubsetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementInPowersetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (contraSubsetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTcontraSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTILcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTIRcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (intersectInPowersetIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpNotIn1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpInComplement1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTEcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementUnionInPowersetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule0) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_5) =>
% 105.98/14.53 ((
% 105.98/14.53 (breln1all2) =>
% 105.98/14.53 ((
% 105.98/14.53 (!!) @ (
% 105.98/14.53 (('#B') @ (
% 105.98/14.53 !!) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#S') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 '#S') @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 =>))) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#C') @ in)) @
% 105.98/14.53 breln1Set)))))) @
% 105.98/14.53 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl355])).
% 105.98/14.53 thf(zip_derived_cl369, plain,
% 105.98/14.53 (~ (((powersetI) =>
% 105.98/14.53 (((emptyinPowerset) =>
% 105.98/14.53 (((emptyInPowerset) =>
% 105.98/14.53 (((powersetE) =>
% 105.98/14.53 (((setunionI) =>
% 105.98/14.53 (((setunionE) =>
% 105.98/14.53 (((subPowSU) =>
% 105.98/14.53 (((exuE2) =>
% 105.98/14.53 (((nonemptyImpWitness) =>
% 105.98/14.53 (((uniqinunit) =>
% 105.98/14.53 (((notinsingleton) =>
% 105.98/14.53 (((eqinunit) =>
% 105.98/14.53 (((singletonsswitch) =>
% 105.98/14.53 (((upairsetE) =>
% 105.98/14.53 (((upairsetIL) =>
% 105.98/14.53 (((upairsetIR) =>
% 105.98/14.53 (((emptyE1) =>
% 105.98/14.53 (((vacuousDall) =>
% 105.98/14.53 (((quantDeMorgan1) =>
% 105.98/14.53 (((quantDeMorgan2) =>
% 105.98/14.53 (((quantDeMorgan3) =>
% 105.98/14.53 (((quantDeMorgan4) =>
% 105.98/14.53 (((prop2setI) =>
% 105.98/14.53 (((prop2set2propI) =>
% 105.98/14.53 (((notdexE) =>
% 105.98/14.53 (((notdallE) =>
% 105.98/14.53 (((exuI1) =>
% 105.98/14.53 (((exuI3) =>
% 105.98/14.53 (((exuI2) =>
% 105.98/14.53 (((inCongP) =>
% 105.98/14.53 ((
% 105.98/14.53 (in__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuE3u) =>
% 105.98/14.53 ((
% 105.98/14.53 (exu__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoin__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (powerset__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunion__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuEu) =>
% 105.98/14.53 ((
% 105.98/14.53 (descr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (dsetconstr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (emptysetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (notsubsetI) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetRefl) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTrans) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subset2powerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetemptysetimpeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepInPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2IR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionEcases) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectI) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset5) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset3) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectER) =>
% 105.98/14.53 ((
% 105.98/14.53 (disjointsetsI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset4) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (bs114d) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusI) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusER) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusERneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusELneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusILneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusIRneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffE) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg2) =>
% 105.98/14.53 ((
% 105.98/14.53 (secondinupair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairiskpair) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairp) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2E) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairsubunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairinpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem3) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair1) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton1) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I2) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsuniq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (theprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstin) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR11) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR12) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR1) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairequniteq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemER) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempaircEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrI) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setOfPairsIsBReln) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrERa) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrER) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcImageSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (apProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (app) =>
% 105.98/14.53 ((
% 105.98/14.53 (infuncsetfunc) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcinfuncset) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall1) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp3) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcextLem) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp4) =>
% 105.98/14.53 ((
% 105.98/14.53 (subbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq2) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2lamEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifp) =>
% 105.98/14.53 ((
% 105.98/14.53 (theeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrue) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueorfalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextT) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTI) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTELcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTERcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT1) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT2) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT3) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTnotintersectT) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementImpComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementSubsetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementInPowersetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (contraSubsetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTcontraSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTILcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTIRcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (intersectInPowersetIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpNotIn1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpInComplement1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTEcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementUnionInPowersetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule0) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_5) =>
% 105.98/14.53 ((
% 105.98/14.53 (breln1all2) =>
% 105.98/14.53 ((
% 105.98/14.53 (!!) @ (
% 105.98/14.53 (('#B') @ (
% 105.98/14.53 !!) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#S') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 '#S') @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 =>))) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#C') @ in)) @
% 105.98/14.53 breln1Set)))))) @
% 105.98/14.53 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])).
% 105.98/14.53 thf(zip_derived_cl376, plain,
% 105.98/14.53 (~ (((emptyinPowerset) =>
% 105.98/14.53 (((emptyInPowerset) =>
% 105.98/14.53 (((powersetE) =>
% 105.98/14.53 (((setunionI) =>
% 105.98/14.53 (((setunionE) =>
% 105.98/14.53 (((subPowSU) =>
% 105.98/14.53 (((exuE2) =>
% 105.98/14.53 (((nonemptyImpWitness) =>
% 105.98/14.53 (((uniqinunit) =>
% 105.98/14.53 (((notinsingleton) =>
% 105.98/14.53 (((eqinunit) =>
% 105.98/14.53 (((singletonsswitch) =>
% 105.98/14.53 (((upairsetE) =>
% 105.98/14.53 (((upairsetIL) =>
% 105.98/14.53 (((upairsetIR) =>
% 105.98/14.53 (((emptyE1) =>
% 105.98/14.53 (((vacuousDall) =>
% 105.98/14.53 (((quantDeMorgan1) =>
% 105.98/14.53 (((quantDeMorgan2) =>
% 105.98/14.53 (((quantDeMorgan3) =>
% 105.98/14.53 (((quantDeMorgan4) =>
% 105.98/14.53 (((prop2setI) =>
% 105.98/14.53 (((prop2set2propI) =>
% 105.98/14.53 (((notdexE) =>
% 105.98/14.53 (((notdallE) =>
% 105.98/14.53 (((exuI1) =>
% 105.98/14.53 (((exuI3) =>
% 105.98/14.53 (((exuI2) =>
% 105.98/14.53 (((inCongP) =>
% 105.98/14.53 (((in__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuE3u) =>
% 105.98/14.53 ((
% 105.98/14.53 (exu__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoin__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (powerset__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunion__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuEu) =>
% 105.98/14.53 ((
% 105.98/14.53 (descr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (dsetconstr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (emptysetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (notsubsetI) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetRefl) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTrans) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subset2powerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetemptysetimpeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepInPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2IR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionEcases) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectI) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset5) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset3) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectER) =>
% 105.98/14.53 ((
% 105.98/14.53 (disjointsetsI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset4) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (bs114d) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusI) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusER) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusERneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusELneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusILneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusIRneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffE) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg2) =>
% 105.98/14.53 ((
% 105.98/14.53 (secondinupair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairiskpair) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairp) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2E) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairsubunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairinpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem3) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair1) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton1) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I2) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsuniq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (theprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (kfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstin) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR11) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR12) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR1) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairequniteq) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairinjR) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ksndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairmemER) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempaircEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodfstpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodsndpairEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairsurjEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrI) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setOfPairsIsBReln) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrERa) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL1) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrEL2) =>
% 105.98/14.53 ((
% 105.98/14.53 (dpsetconstrER) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcImageSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (apProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (app) =>
% 105.98/14.53 ((
% 105.98/14.53 (infuncsetfunc) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcinfuncset) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamProp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lamp) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2p) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall1) =>
% 105.98/14.53 ((
% 105.98/14.53 (brelnall2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp3) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcextLem) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcGraphProp4) =>
% 105.98/14.53 ((
% 105.98/14.53 (subbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqbreln) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext) =>
% 105.98/14.53 ((
% 105.98/14.53 (funcext2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ap2apEq2) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta1) =>
% 105.98/14.53 ((
% 105.98/14.53 (lam2lamEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (beta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eta2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalseProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp1) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueProp2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifSingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (ifp) =>
% 105.98/14.53 ((
% 105.98/14.53 (theeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrue) =>
% 105.98/14.53 ((
% 105.98/14.53 (iffalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (iftrueorfalse) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementT_lem) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextT) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTI) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTELcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectTERcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT1) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT2) =>
% 105.98/14.53 ((
% 105.98/14.53 (contrasubsetT3) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub1) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (doubleComplementEq) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTnotintersectT) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementImpComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementSubsetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementInPowersetComplementIntersect) =>
% 105.98/14.53 ((
% 105.98/14.53 (contraSubsetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementTcontraSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTILcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTIRcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInUnion2) =>
% 105.98/14.53 ((
% 105.98/14.53 (inIntersectImpInIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (intersectInPowersetIntersectUnions) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpNotIn1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inComplementUnionImpInComplement1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionTEcontra) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a1) =>
% 105.98/14.53 ((
% 105.98/14.53 (complementUnionInPowersetComplement) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan1) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2a) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b2) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2b) =>
% 105.98/14.53 ((
% 105.98/14.53 (demorgan2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule0) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz13rule4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_1) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_2) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_3) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_4) =>
% 105.98/14.53 ((
% 105.98/14.53 (woz1_5) =>
% 105.98/14.53 ((
% 105.98/14.53 (breln1all2) =>
% 105.98/14.53 ((
% 105.98/14.53 (!!) @ (
% 105.98/14.53 (('#B') @ (
% 105.98/14.53 !!) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#S') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 '#S') @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 =>))) @
% 105.98/14.53 (
% 105.98/14.53 (
% 105.98/14.53 ('#B') @ (
% 105.98/14.53 (
% 105.98/14.53 ('#C') @ in)) @
% 105.98/14.53 breln1Set)))))) @
% 105.98/14.53 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl369])).
% 105.98/14.53 thf(zip_derived_cl384, plain,
% 105.98/14.53 (~ (((emptyInPowerset) =>
% 105.98/14.53 (((powersetE) =>
% 105.98/14.53 (((setunionI) =>
% 105.98/14.53 (((setunionE) =>
% 105.98/14.53 (((subPowSU) =>
% 105.98/14.53 (((exuE2) =>
% 105.98/14.53 (((nonemptyImpWitness) =>
% 105.98/14.53 (((uniqinunit) =>
% 105.98/14.53 (((notinsingleton) =>
% 105.98/14.53 (((eqinunit) =>
% 105.98/14.53 (((singletonsswitch) =>
% 105.98/14.53 (((upairsetE) =>
% 105.98/14.53 (((upairsetIL) =>
% 105.98/14.53 (((upairsetIR) =>
% 105.98/14.53 (((emptyE1) =>
% 105.98/14.53 (((vacuousDall) =>
% 105.98/14.53 (((quantDeMorgan1) =>
% 105.98/14.53 (((quantDeMorgan2) =>
% 105.98/14.53 (((quantDeMorgan3) =>
% 105.98/14.53 (((quantDeMorgan4) =>
% 105.98/14.53 (((prop2setI) =>
% 105.98/14.53 (((prop2set2propI) =>
% 105.98/14.53 (((notdexE) =>
% 105.98/14.53 (((notdallE) =>
% 105.98/14.53 (((exuI1) =>
% 105.98/14.53 (((exuI3) =>
% 105.98/14.53 (((exuI2) =>
% 105.98/14.53 (((inCongP) =>
% 105.98/14.53 (((in__Cong) =>
% 105.98/14.53 (((exuE3u) =>
% 105.98/14.53 ((
% 105.98/14.53 (exu__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoin__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (powerset__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunion__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (exuEu) =>
% 105.98/14.53 ((
% 105.98/14.53 (descr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (dsetconstr__Cong) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (eqimpsubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (emptysetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (notsubsetI) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (notequalI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetRefl) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetTrans) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setadjoinSub2) =>
% 105.98/14.53 ((
% 105.98/14.53 (subset2powerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (setextsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (subsetemptysetimpeq) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetE1) =>
% 105.98/14.53 ((
% 105.98/14.53 (inPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (powersetsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepInPowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (sepSubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2IR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionEcases) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionE) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binunionRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectI) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset5) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset3) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectER) =>
% 105.98/14.53 ((
% 105.98/14.53 (disjointsetsI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectRsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset4) =>
% 105.98/14.53 ((
% 105.98/14.53 (binintersectSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (bs114d) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusI) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusEL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusER) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusERneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusELneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusILneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusIRneg) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusLsub) =>
% 105.98/14.53 ((
% 105.98/14.53 (setminusSubset1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffE) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffI2) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg1) =>
% 105.98/14.53 ((
% 105.98/14.53 (symdiffIneg2) =>
% 105.98/14.53 ((
% 105.98/14.53 (secondinupair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIL) =>
% 105.98/14.53 ((
% 105.98/14.53 (setukpairIR) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairiskpair) =>
% 105.98/14.53 ((
% 105.98/14.53 (kpairp) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsubset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowerset) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletoninpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairset2E) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairsubunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (upairinpowunion) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem2) =>
% 105.98/14.53 ((
% 105.98/14.53 (ubforcartprodlem3) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodpairin) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair1) =>
% 105.98/14.53 ((
% 105.98/14.53 (cartprodmempair) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionE2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton1) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton2) =>
% 105.98/14.53 ((
% 105.98/14.53 (setunionsingleton) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonprop) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1E1) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I) =>
% 105.98/14.53 ((
% 105.98/14.53 (ex1I2) =>
% 105.98/14.53 ((
% 105.98/14.53 (singletonsuniq) =>
% 105.98/14.53 ((
% 105.98/14.54 (setukpairinjL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (theprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstin) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR11) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR12) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR1) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairequniteq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemER) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempaircEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrI) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setOfPairsIsBReln) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrERa) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrER) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcImageSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (apProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (app) =>
% 105.98/14.54 ((
% 105.98/14.54 (infuncsetfunc) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcinfuncset) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall1) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp3) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcextLem) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp4) =>
% 105.98/14.54 ((
% 105.98/14.54 (subbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq2) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2lamEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifp) =>
% 105.98/14.54 ((
% 105.98/14.54 (theeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrue) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueorfalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextT) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTI) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTELcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTERcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT1) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT2) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT3) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTnotintersectT) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementImpComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementSubsetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementInPowersetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (contraSubsetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTcontraSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTILcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTIRcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion2) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (intersectInPowersetIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpNotIn1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpInComplement1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTEcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementUnionInPowersetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule0) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_5) =>
% 105.98/14.54 ((
% 105.98/14.54 (breln1all2) =>
% 105.98/14.54 ((
% 105.98/14.54 (!!) @ (
% 105.98/14.54 (('#B') @ (
% 105.98/14.54 !!) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#S') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 '#S') @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 =>))) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#C') @ in)) @
% 105.98/14.54 breln1Set)))))) @
% 105.98/14.54 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl376])).
% 105.98/14.54 thf(zip_derived_cl392, plain,
% 105.98/14.54 (~ (((powersetE) =>
% 105.98/14.54 (((setunionI) =>
% 105.98/14.54 (((setunionE) =>
% 105.98/14.54 (((subPowSU) =>
% 105.98/14.54 (((exuE2) =>
% 105.98/14.54 (((nonemptyImpWitness) =>
% 105.98/14.54 (((uniqinunit) =>
% 105.98/14.54 (((notinsingleton) =>
% 105.98/14.54 (((eqinunit) =>
% 105.98/14.54 (((singletonsswitch) =>
% 105.98/14.54 (((upairsetE) =>
% 105.98/14.54 (((upairsetIL) =>
% 105.98/14.54 (((upairsetIR) =>
% 105.98/14.54 (((emptyE1) =>
% 105.98/14.54 (((vacuousDall) =>
% 105.98/14.54 (((quantDeMorgan1) =>
% 105.98/14.54 (((quantDeMorgan2) =>
% 105.98/14.54 (((quantDeMorgan3) =>
% 105.98/14.54 (((quantDeMorgan4) =>
% 105.98/14.54 (((prop2setI) =>
% 105.98/14.54 (((prop2set2propI) =>
% 105.98/14.54 (((notdexE) =>
% 105.98/14.54 (((notdallE) =>
% 105.98/14.54 (((exuI1) =>
% 105.98/14.54 (((exuI3) =>
% 105.98/14.54 (((exuI2) =>
% 105.98/14.54 (((inCongP) =>
% 105.98/14.54 (((in__Cong) =>
% 105.98/14.54 (((exuE3u) =>
% 105.98/14.54 (((exu__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoin__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (powerset__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunion__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (exuEu) =>
% 105.98/14.54 ((
% 105.98/14.54 (descr__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (dsetconstr__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (emptysetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (notsubsetI) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetRefl) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTrans) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subset2powerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetemptysetimpeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepInPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2IR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionEcases) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectI) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset5) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset3) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectER) =>
% 105.98/14.54 ((
% 105.98/14.54 (disjointsetsI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset4) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (bs114d) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusI) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusER) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusERneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusELneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusILneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusIRneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffE) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg2) =>
% 105.98/14.54 ((
% 105.98/14.54 (secondinupair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairiskpair) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairp) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2E) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairsubunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairinpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem3) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair1) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton1) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I2) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsuniq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (theprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstin) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR11) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR12) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR1) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairequniteq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemER) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempaircEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrI) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setOfPairsIsBReln) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrERa) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrER) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcImageSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (apProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (app) =>
% 105.98/14.54 ((
% 105.98/14.54 (infuncsetfunc) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcinfuncset) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall1) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp3) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcextLem) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp4) =>
% 105.98/14.54 ((
% 105.98/14.54 (subbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq2) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2lamEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifp) =>
% 105.98/14.54 ((
% 105.98/14.54 (theeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrue) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueorfalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextT) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTI) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTELcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTERcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT1) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT2) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT3) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTnotintersectT) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementImpComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementSubsetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementInPowersetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (contraSubsetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTcontraSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTILcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTIRcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion2) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (intersectInPowersetIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpNotIn1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpInComplement1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTEcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementUnionInPowersetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule0) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_5) =>
% 105.98/14.54 ((
% 105.98/14.54 (breln1all2) =>
% 105.98/14.54 ((
% 105.98/14.54 (!!) @ (
% 105.98/14.54 (('#B') @ (
% 105.98/14.54 !!) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#S') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 '#S') @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 =>))) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#C') @ in)) @
% 105.98/14.54 breln1Set)))))) @
% 105.98/14.54 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])).
% 105.98/14.54 thf(zip_derived_cl400, plain,
% 105.98/14.54 (~ (((setunionI) =>
% 105.98/14.54 (((setunionE) =>
% 105.98/14.54 (((subPowSU) =>
% 105.98/14.54 (((exuE2) =>
% 105.98/14.54 (((nonemptyImpWitness) =>
% 105.98/14.54 (((uniqinunit) =>
% 105.98/14.54 (((notinsingleton) =>
% 105.98/14.54 (((eqinunit) =>
% 105.98/14.54 (((singletonsswitch) =>
% 105.98/14.54 (((upairsetE) =>
% 105.98/14.54 (((upairsetIL) =>
% 105.98/14.54 (((upairsetIR) =>
% 105.98/14.54 (((emptyE1) =>
% 105.98/14.54 (((vacuousDall) =>
% 105.98/14.54 (((quantDeMorgan1) =>
% 105.98/14.54 (((quantDeMorgan2) =>
% 105.98/14.54 (((quantDeMorgan3) =>
% 105.98/14.54 (((quantDeMorgan4) =>
% 105.98/14.54 (((prop2setI) =>
% 105.98/14.54 (((prop2set2propI) =>
% 105.98/14.54 (((notdexE) =>
% 105.98/14.54 (((notdallE) =>
% 105.98/14.54 (((exuI1) =>
% 105.98/14.54 (((exuI3) =>
% 105.98/14.54 (((exuI2) =>
% 105.98/14.54 (((inCongP) =>
% 105.98/14.54 (((in__Cong) =>
% 105.98/14.54 (((exuE3u) =>
% 105.98/14.54 (((exu__Cong) =>
% 105.98/14.54 (((setadjoin__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (powerset__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunion__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (exuEu) =>
% 105.98/14.54 ((
% 105.98/14.54 (descr__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (dsetconstr__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (emptysetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (notsubsetI) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetRefl) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTrans) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subset2powerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetemptysetimpeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepInPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2IR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionEcases) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectI) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset5) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset3) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectER) =>
% 105.98/14.54 ((
% 105.98/14.54 (disjointsetsI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset4) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (bs114d) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusI) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusER) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusERneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusELneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusILneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusIRneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffE) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg2) =>
% 105.98/14.54 ((
% 105.98/14.54 (secondinupair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairiskpair) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairp) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2E) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairsubunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairinpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem3) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair1) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton1) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I2) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsuniq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (theprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstin) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR11) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR12) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR1) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairequniteq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemER) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempaircEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrI) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setOfPairsIsBReln) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrERa) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrER) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcImageSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (apProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (app) =>
% 105.98/14.54 ((
% 105.98/14.54 (infuncsetfunc) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcinfuncset) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall1) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp3) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcextLem) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp4) =>
% 105.98/14.54 ((
% 105.98/14.54 (subbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq2) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2lamEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifp) =>
% 105.98/14.54 ((
% 105.98/14.54 (theeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrue) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueorfalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextT) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTI) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTELcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTERcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT1) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT2) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT3) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTnotintersectT) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementImpComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementSubsetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementInPowersetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (contraSubsetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTcontraSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTILcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTIRcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion2) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (intersectInPowersetIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpNotIn1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpInComplement1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTEcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementUnionInPowersetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule0) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_5) =>
% 105.98/14.54 ((
% 105.98/14.54 (breln1all2) =>
% 105.98/14.54 ((
% 105.98/14.54 (!!) @ (
% 105.98/14.54 (('#B') @ (
% 105.98/14.54 !!) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#S') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 '#S') @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 =>))) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#C') @ in)) @
% 105.98/14.54 breln1Set)))))) @
% 105.98/14.54 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])).
% 105.98/14.54 thf(zip_derived_cl408, plain,
% 105.98/14.54 (~ (((setunionE) =>
% 105.98/14.54 (((subPowSU) =>
% 105.98/14.54 (((exuE2) =>
% 105.98/14.54 (((nonemptyImpWitness) =>
% 105.98/14.54 (((uniqinunit) =>
% 105.98/14.54 (((notinsingleton) =>
% 105.98/14.54 (((eqinunit) =>
% 105.98/14.54 (((singletonsswitch) =>
% 105.98/14.54 (((upairsetE) =>
% 105.98/14.54 (((upairsetIL) =>
% 105.98/14.54 (((upairsetIR) =>
% 105.98/14.54 (((emptyE1) =>
% 105.98/14.54 (((vacuousDall) =>
% 105.98/14.54 (((quantDeMorgan1) =>
% 105.98/14.54 (((quantDeMorgan2) =>
% 105.98/14.54 (((quantDeMorgan3) =>
% 105.98/14.54 (((quantDeMorgan4) =>
% 105.98/14.54 (((prop2setI) =>
% 105.98/14.54 (((prop2set2propI) =>
% 105.98/14.54 (((notdexE) =>
% 105.98/14.54 (((notdallE) =>
% 105.98/14.54 (((exuI1) =>
% 105.98/14.54 (((exuI3) =>
% 105.98/14.54 (((exuI2) =>
% 105.98/14.54 (((inCongP) =>
% 105.98/14.54 (((in__Cong) =>
% 105.98/14.54 (((exuE3u) =>
% 105.98/14.54 (((exu__Cong) =>
% 105.98/14.54 (((setadjoin__Cong) =>
% 105.98/14.54 (((powerset__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunion__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (exuEu) =>
% 105.98/14.54 ((
% 105.98/14.54 (descr__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (dsetconstr__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (emptysetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (notsubsetI) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetRefl) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTrans) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subset2powerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetemptysetimpeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepInPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2IR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionEcases) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectI) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset5) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset3) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectER) =>
% 105.98/14.54 ((
% 105.98/14.54 (disjointsetsI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset4) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (bs114d) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusI) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusER) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusERneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusELneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusILneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusIRneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffE) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg2) =>
% 105.98/14.54 ((
% 105.98/14.54 (secondinupair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairiskpair) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairp) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2E) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairsubunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairinpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem3) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair1) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton1) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I2) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsuniq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (theprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstin) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR11) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR12) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR1) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairequniteq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemER) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempaircEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrI) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setOfPairsIsBReln) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrERa) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrER) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcImageSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (apProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (app) =>
% 105.98/14.54 ((
% 105.98/14.54 (infuncsetfunc) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcinfuncset) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall1) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp3) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcextLem) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp4) =>
% 105.98/14.54 ((
% 105.98/14.54 (subbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq2) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2lamEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifp) =>
% 105.98/14.54 ((
% 105.98/14.54 (theeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrue) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueorfalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextT) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTI) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTELcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTERcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT1) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT2) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT3) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTnotintersectT) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementImpComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementSubsetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementInPowersetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (contraSubsetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTcontraSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTILcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTIRcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion2) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (intersectInPowersetIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpNotIn1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpInComplement1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTEcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementUnionInPowersetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule0) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_5) =>
% 105.98/14.54 ((
% 105.98/14.54 (breln1all2) =>
% 105.98/14.54 ((
% 105.98/14.54 (!!) @ (
% 105.98/14.54 (('#B') @ (
% 105.98/14.54 !!) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#S') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 '#S') @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 =>))) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#C') @ in)) @
% 105.98/14.54 breln1Set)))))) @
% 105.98/14.54 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
% 105.98/14.54 thf(zip_derived_cl417, plain,
% 105.98/14.54 (~ (((subPowSU) =>
% 105.98/14.54 (((exuE2) =>
% 105.98/14.54 (((nonemptyImpWitness) =>
% 105.98/14.54 (((uniqinunit) =>
% 105.98/14.54 (((notinsingleton) =>
% 105.98/14.54 (((eqinunit) =>
% 105.98/14.54 (((singletonsswitch) =>
% 105.98/14.54 (((upairsetE) =>
% 105.98/14.54 (((upairsetIL) =>
% 105.98/14.54 (((upairsetIR) =>
% 105.98/14.54 (((emptyE1) =>
% 105.98/14.54 (((vacuousDall) =>
% 105.98/14.54 (((quantDeMorgan1) =>
% 105.98/14.54 (((quantDeMorgan2) =>
% 105.98/14.54 (((quantDeMorgan3) =>
% 105.98/14.54 (((quantDeMorgan4) =>
% 105.98/14.54 (((prop2setI) =>
% 105.98/14.54 (((prop2set2propI) =>
% 105.98/14.54 (((notdexE) =>
% 105.98/14.54 (((notdallE) =>
% 105.98/14.54 (((exuI1) =>
% 105.98/14.54 (((exuI3) =>
% 105.98/14.54 (((exuI2) =>
% 105.98/14.54 (((inCongP) =>
% 105.98/14.54 (((in__Cong) =>
% 105.98/14.54 (((exuE3u) =>
% 105.98/14.54 (((exu__Cong) =>
% 105.98/14.54 (((setadjoin__Cong) =>
% 105.98/14.54 (((powerset__Cong) =>
% 105.98/14.54 (((setunion__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (exuEu) =>
% 105.98/14.54 ((
% 105.98/14.54 (descr__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (dsetconstr__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (emptysetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (notsubsetI) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetRefl) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTrans) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subset2powerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetemptysetimpeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepInPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2IR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionEcases) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectI) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset5) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset3) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectER) =>
% 105.98/14.54 ((
% 105.98/14.54 (disjointsetsI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset4) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (bs114d) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusI) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusER) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusERneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusELneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusILneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusIRneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffE) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg2) =>
% 105.98/14.54 ((
% 105.98/14.54 (secondinupair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairiskpair) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairp) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2E) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairsubunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairinpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem3) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair1) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton1) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I2) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsuniq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (theprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstin) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR11) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR12) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR1) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairequniteq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemER) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempaircEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrI) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setOfPairsIsBReln) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrERa) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrER) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcImageSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (apProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (app) =>
% 105.98/14.54 ((
% 105.98/14.54 (infuncsetfunc) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcinfuncset) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall1) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp3) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcextLem) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp4) =>
% 105.98/14.54 ((
% 105.98/14.54 (subbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq2) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2lamEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifp) =>
% 105.98/14.54 ((
% 105.98/14.54 (theeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrue) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueorfalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextT) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTI) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTELcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTERcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT1) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT2) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT3) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTnotintersectT) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementImpComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementSubsetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementInPowersetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (contraSubsetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTcontraSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTILcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTIRcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion2) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (intersectInPowersetIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpNotIn1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpInComplement1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTEcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementUnionInPowersetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule0) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_5) =>
% 105.98/14.54 ((
% 105.98/14.54 (breln1all2) =>
% 105.98/14.54 ((
% 105.98/14.54 (!!) @ (
% 105.98/14.54 (('#B') @ (
% 105.98/14.54 !!) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#S') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 '#S') @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 =>))) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#C') @ in)) @
% 105.98/14.54 breln1Set)))))) @
% 105.98/14.54 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])).
% 105.98/14.54 thf(zip_derived_cl428, plain,
% 105.98/14.54 (~ (((exuE2) =>
% 105.98/14.54 (((nonemptyImpWitness) =>
% 105.98/14.54 (((uniqinunit) =>
% 105.98/14.54 (((notinsingleton) =>
% 105.98/14.54 (((eqinunit) =>
% 105.98/14.54 (((singletonsswitch) =>
% 105.98/14.54 (((upairsetE) =>
% 105.98/14.54 (((upairsetIL) =>
% 105.98/14.54 (((upairsetIR) =>
% 105.98/14.54 (((emptyE1) =>
% 105.98/14.54 (((vacuousDall) =>
% 105.98/14.54 (((quantDeMorgan1) =>
% 105.98/14.54 (((quantDeMorgan2) =>
% 105.98/14.54 (((quantDeMorgan3) =>
% 105.98/14.54 (((quantDeMorgan4) =>
% 105.98/14.54 (((prop2setI) =>
% 105.98/14.54 (((prop2set2propI) =>
% 105.98/14.54 (((notdexE) =>
% 105.98/14.54 (((notdallE) =>
% 105.98/14.54 (((exuI1) =>
% 105.98/14.54 (((exuI3) =>
% 105.98/14.54 (((exuI2) =>
% 105.98/14.54 (((inCongP) =>
% 105.98/14.54 (((in__Cong) =>
% 105.98/14.54 (((exuE3u) =>
% 105.98/14.54 (((exu__Cong) =>
% 105.98/14.54 (((setadjoin__Cong) =>
% 105.98/14.54 (((powerset__Cong) =>
% 105.98/14.54 (((setunion__Cong) =>
% 105.98/14.54 (((exuEu) =>
% 105.98/14.54 ((
% 105.98/14.54 (descr__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (dsetconstr__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (emptysetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (notsubsetI) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetRefl) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTrans) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subset2powerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetemptysetimpeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepInPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2IR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionEcases) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectI) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset5) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset3) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectER) =>
% 105.98/14.54 ((
% 105.98/14.54 (disjointsetsI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset4) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (bs114d) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusI) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusER) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusERneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusELneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusILneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusIRneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffE) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg2) =>
% 105.98/14.54 ((
% 105.98/14.54 (secondinupair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairiskpair) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairp) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2E) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairsubunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairinpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem3) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair1) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton1) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I2) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsuniq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (theprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstin) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR11) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR12) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR1) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairequniteq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemER) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempaircEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrI) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setOfPairsIsBReln) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrERa) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrER) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcImageSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (apProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (app) =>
% 105.98/14.54 ((
% 105.98/14.54 (infuncsetfunc) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcinfuncset) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall1) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp3) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcextLem) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp4) =>
% 105.98/14.54 ((
% 105.98/14.54 (subbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq2) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2lamEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifp) =>
% 105.98/14.54 ((
% 105.98/14.54 (theeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrue) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueorfalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextT) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTI) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTELcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTERcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT1) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT2) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT3) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTnotintersectT) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementImpComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementSubsetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementInPowersetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (contraSubsetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTcontraSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTILcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTIRcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion2) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (intersectInPowersetIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpNotIn1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpInComplement1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTEcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementUnionInPowersetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule0) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_5) =>
% 105.98/14.54 ((
% 105.98/14.54 (breln1all2) =>
% 105.98/14.54 ((
% 105.98/14.54 (!!) @ (
% 105.98/14.54 (('#B') @ (
% 105.98/14.54 !!) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#S') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 '#S') @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 =>))) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#C') @ in)) @
% 105.98/14.54 breln1Set)))))) @
% 105.98/14.54 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])).
% 105.98/14.54 thf(zip_derived_cl439, plain,
% 105.98/14.54 (~ (((nonemptyImpWitness) =>
% 105.98/14.54 (((uniqinunit) =>
% 105.98/14.54 (((notinsingleton) =>
% 105.98/14.54 (((eqinunit) =>
% 105.98/14.54 (((singletonsswitch) =>
% 105.98/14.54 (((upairsetE) =>
% 105.98/14.54 (((upairsetIL) =>
% 105.98/14.54 (((upairsetIR) =>
% 105.98/14.54 (((emptyE1) =>
% 105.98/14.54 (((vacuousDall) =>
% 105.98/14.54 (((quantDeMorgan1) =>
% 105.98/14.54 (((quantDeMorgan2) =>
% 105.98/14.54 (((quantDeMorgan3) =>
% 105.98/14.54 (((quantDeMorgan4) =>
% 105.98/14.54 (((prop2setI) =>
% 105.98/14.54 (((prop2set2propI) =>
% 105.98/14.54 (((notdexE) =>
% 105.98/14.54 (((notdallE) =>
% 105.98/14.54 (((exuI1) =>
% 105.98/14.54 (((exuI3) =>
% 105.98/14.54 (((exuI2) =>
% 105.98/14.54 (((inCongP) =>
% 105.98/14.54 (((in__Cong) =>
% 105.98/14.54 (((exuE3u) =>
% 105.98/14.54 (((exu__Cong) =>
% 105.98/14.54 (((setadjoin__Cong) =>
% 105.98/14.54 (((powerset__Cong) =>
% 105.98/14.54 (((setunion__Cong) =>
% 105.98/14.54 (((exuEu) =>
% 105.98/14.54 (((descr__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (dsetconstr__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (emptysetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (notsubsetI) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetRefl) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTrans) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subset2powerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetemptysetimpeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepInPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2IR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionEcases) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectI) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset5) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset3) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectER) =>
% 105.98/14.54 ((
% 105.98/14.54 (disjointsetsI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset4) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (bs114d) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusI) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusER) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusERneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusELneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusILneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusIRneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffE) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg2) =>
% 105.98/14.54 ((
% 105.98/14.54 (secondinupair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairiskpair) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairp) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2E) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairsubunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairinpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem3) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair1) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton1) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I2) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsuniq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (theprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstin) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR11) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR12) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR1) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairequniteq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemER) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempaircEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrI) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setOfPairsIsBReln) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrERa) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrER) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcImageSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (apProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (app) =>
% 105.98/14.54 ((
% 105.98/14.54 (infuncsetfunc) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcinfuncset) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall1) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp3) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcextLem) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp4) =>
% 105.98/14.54 ((
% 105.98/14.54 (subbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq2) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2lamEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifp) =>
% 105.98/14.54 ((
% 105.98/14.54 (theeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrue) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueorfalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextT) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTI) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTELcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTERcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT1) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT2) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT3) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTnotintersectT) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementImpComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementSubsetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementInPowersetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (contraSubsetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTcontraSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTILcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTIRcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion2) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (intersectInPowersetIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpNotIn1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpInComplement1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTEcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementUnionInPowersetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule0) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_5) =>
% 105.98/14.54 ((
% 105.98/14.54 (breln1all2) =>
% 105.98/14.54 ((
% 105.98/14.54 (!!) @ (
% 105.98/14.54 (('#B') @ (
% 105.98/14.54 !!) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#S') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 '#S') @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 =>))) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#C') @ in)) @
% 105.98/14.54 breln1Set)))))) @
% 105.98/14.54 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
% 105.98/14.54 thf(zip_derived_cl449, plain,
% 105.98/14.54 (~ (((uniqinunit) =>
% 105.98/14.54 (((notinsingleton) =>
% 105.98/14.54 (((eqinunit) =>
% 105.98/14.54 (((singletonsswitch) =>
% 105.98/14.54 (((upairsetE) =>
% 105.98/14.54 (((upairsetIL) =>
% 105.98/14.54 (((upairsetIR) =>
% 105.98/14.54 (((emptyE1) =>
% 105.98/14.54 (((vacuousDall) =>
% 105.98/14.54 (((quantDeMorgan1) =>
% 105.98/14.54 (((quantDeMorgan2) =>
% 105.98/14.54 (((quantDeMorgan3) =>
% 105.98/14.54 (((quantDeMorgan4) =>
% 105.98/14.54 (((prop2setI) =>
% 105.98/14.54 (((prop2set2propI) =>
% 105.98/14.54 (((notdexE) =>
% 105.98/14.54 (((notdallE) =>
% 105.98/14.54 (((exuI1) =>
% 105.98/14.54 (((exuI3) =>
% 105.98/14.54 (((exuI2) =>
% 105.98/14.54 (((inCongP) =>
% 105.98/14.54 (((in__Cong) =>
% 105.98/14.54 (((exuE3u) =>
% 105.98/14.54 (((exu__Cong) =>
% 105.98/14.54 (((setadjoin__Cong) =>
% 105.98/14.54 (((powerset__Cong) =>
% 105.98/14.54 (((setunion__Cong) =>
% 105.98/14.54 (((exuEu) =>
% 105.98/14.54 (((descr__Cong) =>
% 105.98/14.54 (((dsetconstr__Cong) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (emptysetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (notsubsetI) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetRefl) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTrans) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subset2powerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetemptysetimpeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepInPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2IR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionEcases) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectI) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset5) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset3) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectER) =>
% 105.98/14.54 ((
% 105.98/14.54 (disjointsetsI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset4) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (bs114d) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusI) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusER) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusERneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusELneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusILneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusIRneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffE) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg2) =>
% 105.98/14.54 ((
% 105.98/14.54 (secondinupair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairiskpair) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairp) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2E) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairsubunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairinpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem3) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair1) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton1) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I2) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsuniq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (theprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstin) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR11) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR12) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR1) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairequniteq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemER) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempaircEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrI) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setOfPairsIsBReln) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrERa) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrER) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcImageSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (apProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (app) =>
% 105.98/14.54 ((
% 105.98/14.54 (infuncsetfunc) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcinfuncset) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall1) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp3) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcextLem) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp4) =>
% 105.98/14.54 ((
% 105.98/14.54 (subbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq2) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2lamEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifp) =>
% 105.98/14.54 ((
% 105.98/14.54 (theeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrue) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueorfalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextT) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTI) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTELcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTERcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT1) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT2) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT3) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTnotintersectT) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementImpComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementSubsetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementInPowersetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (contraSubsetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTcontraSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTILcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTIRcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion2) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (intersectInPowersetIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpNotIn1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpInComplement1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTEcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementUnionInPowersetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule0) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_5) =>
% 105.98/14.54 ((
% 105.98/14.54 (breln1all2) =>
% 105.98/14.54 ((
% 105.98/14.54 (!!) @ (
% 105.98/14.54 (('#B') @ (
% 105.98/14.54 !!) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#S') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 '#S') @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 =>))) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#C') @ in)) @
% 105.98/14.54 breln1Set)))))) @
% 105.98/14.54 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
% 105.98/14.54 thf(zip_derived_cl458, plain,
% 105.98/14.54 (~ (((notinsingleton) =>
% 105.98/14.54 (((eqinunit) =>
% 105.98/14.54 (((singletonsswitch) =>
% 105.98/14.54 (((upairsetE) =>
% 105.98/14.54 (((upairsetIL) =>
% 105.98/14.54 (((upairsetIR) =>
% 105.98/14.54 (((emptyE1) =>
% 105.98/14.54 (((vacuousDall) =>
% 105.98/14.54 (((quantDeMorgan1) =>
% 105.98/14.54 (((quantDeMorgan2) =>
% 105.98/14.54 (((quantDeMorgan3) =>
% 105.98/14.54 (((quantDeMorgan4) =>
% 105.98/14.54 (((prop2setI) =>
% 105.98/14.54 (((prop2set2propI) =>
% 105.98/14.54 (((notdexE) =>
% 105.98/14.54 (((notdallE) =>
% 105.98/14.54 (((exuI1) =>
% 105.98/14.54 (((exuI3) =>
% 105.98/14.54 (((exuI2) =>
% 105.98/14.54 (((inCongP) =>
% 105.98/14.54 (((in__Cong) =>
% 105.98/14.54 (((exuE3u) =>
% 105.98/14.54 (((exu__Cong) =>
% 105.98/14.54 (((setadjoin__Cong) =>
% 105.98/14.54 (((powerset__Cong) =>
% 105.98/14.54 (((setunion__Cong) =>
% 105.98/14.54 (((exuEu) =>
% 105.98/14.54 (((descr__Cong) =>
% 105.98/14.54 (((dsetconstr__Cong) =>
% 105.98/14.54 (((subsetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (emptysetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (notsubsetI) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetRefl) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTrans) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subset2powerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetemptysetimpeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepInPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2IR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionEcases) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectI) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset5) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset3) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectER) =>
% 105.98/14.54 ((
% 105.98/14.54 (disjointsetsI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset4) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (bs114d) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusI) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusER) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusERneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusELneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusILneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusIRneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffE) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg2) =>
% 105.98/14.54 ((
% 105.98/14.54 (secondinupair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairiskpair) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairp) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2E) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairsubunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairinpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem3) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair1) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton1) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I2) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsuniq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (theprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstin) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR11) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR12) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR1) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairequniteq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemER) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempaircEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrI) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setOfPairsIsBReln) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrERa) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrER) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcImageSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (apProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (app) =>
% 105.98/14.54 ((
% 105.98/14.54 (infuncsetfunc) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcinfuncset) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall1) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp3) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcextLem) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp4) =>
% 105.98/14.54 ((
% 105.98/14.54 (subbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq2) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2lamEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifp) =>
% 105.98/14.54 ((
% 105.98/14.54 (theeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrue) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueorfalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextT) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTI) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTELcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTERcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT1) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT2) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT3) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTnotintersectT) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementImpComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementSubsetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementInPowersetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (contraSubsetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTcontraSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTILcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTIRcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion2) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (intersectInPowersetIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpNotIn1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpInComplement1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTEcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementUnionInPowersetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule0) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_5) =>
% 105.98/14.54 ((
% 105.98/14.54 (breln1all2) =>
% 105.98/14.54 ((
% 105.98/14.54 (!!) @ (
% 105.98/14.54 (('#B') @ (
% 105.98/14.54 !!) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#S') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 '#S') @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 =>))) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#C') @ in)) @
% 105.98/14.54 breln1Set)))))) @
% 105.98/14.54 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
% 105.98/14.54 thf(zip_derived_cl467, plain,
% 105.98/14.54 (~ (((eqinunit) =>
% 105.98/14.54 (((singletonsswitch) =>
% 105.98/14.54 (((upairsetE) =>
% 105.98/14.54 (((upairsetIL) =>
% 105.98/14.54 (((upairsetIR) =>
% 105.98/14.54 (((emptyE1) =>
% 105.98/14.54 (((vacuousDall) =>
% 105.98/14.54 (((quantDeMorgan1) =>
% 105.98/14.54 (((quantDeMorgan2) =>
% 105.98/14.54 (((quantDeMorgan3) =>
% 105.98/14.54 (((quantDeMorgan4) =>
% 105.98/14.54 (((prop2setI) =>
% 105.98/14.54 (((prop2set2propI) =>
% 105.98/14.54 (((notdexE) =>
% 105.98/14.54 (((notdallE) =>
% 105.98/14.54 (((exuI1) =>
% 105.98/14.54 (((exuI3) =>
% 105.98/14.54 (((exuI2) =>
% 105.98/14.54 (((inCongP) =>
% 105.98/14.54 (((in__Cong) =>
% 105.98/14.54 (((exuE3u) =>
% 105.98/14.54 (((exu__Cong) =>
% 105.98/14.54 (((setadjoin__Cong) =>
% 105.98/14.54 (((powerset__Cong) =>
% 105.98/14.54 (((setunion__Cong) =>
% 105.98/14.54 (((exuEu) =>
% 105.98/14.54 (((descr__Cong) =>
% 105.98/14.54 (((dsetconstr__Cong) =>
% 105.98/14.54 (((subsetI1) =>
% 105.98/14.54 (((eqimpsubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqimpsubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (emptysetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (notsubsetI) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetRefl) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTrans) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subset2powerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetemptysetimpeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepInPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2IR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionEcases) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectI) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset5) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset3) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectER) =>
% 105.98/14.54 ((
% 105.98/14.54 (disjointsetsI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset4) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (bs114d) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusI) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusER) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusERneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusELneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusILneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusIRneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffE) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg2) =>
% 105.98/14.54 ((
% 105.98/14.54 (secondinupair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairiskpair) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairp) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2E) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairsubunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairinpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem3) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair1) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton1) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I2) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsuniq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (theprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstin) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR11) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR12) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR1) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairequniteq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemER) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempaircEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrI) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setOfPairsIsBReln) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrERa) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrER) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcImageSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (apProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (app) =>
% 105.98/14.54 ((
% 105.98/14.54 (infuncsetfunc) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcinfuncset) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall1) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp3) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcextLem) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp4) =>
% 105.98/14.54 ((
% 105.98/14.54 (subbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq2) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2lamEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifp) =>
% 105.98/14.54 ((
% 105.98/14.54 (theeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrue) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueorfalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextT) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTI) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTELcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTERcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT1) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT2) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT3) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTnotintersectT) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementImpComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementSubsetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementInPowersetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (contraSubsetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTcontraSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTILcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTIRcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion2) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (intersectInPowersetIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpNotIn1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpInComplement1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTEcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementUnionInPowersetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule0) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_5) =>
% 105.98/14.54 ((
% 105.98/14.54 (breln1all2) =>
% 105.98/14.54 ((
% 105.98/14.54 (!!) @ (
% 105.98/14.54 (('#B') @ (
% 105.98/14.54 !!) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#S') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 '#S') @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 =>))) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#C') @ in)) @
% 105.98/14.54 breln1Set)))))) @
% 105.98/14.54 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl458])).
% 105.98/14.54 thf(zip_derived_cl475, plain,
% 105.98/14.54 (~ (((singletonsswitch) =>
% 105.98/14.54 (((upairsetE) =>
% 105.98/14.54 (((upairsetIL) =>
% 105.98/14.54 (((upairsetIR) =>
% 105.98/14.54 (((emptyE1) =>
% 105.98/14.54 (((vacuousDall) =>
% 105.98/14.54 (((quantDeMorgan1) =>
% 105.98/14.54 (((quantDeMorgan2) =>
% 105.98/14.54 (((quantDeMorgan3) =>
% 105.98/14.54 (((quantDeMorgan4) =>
% 105.98/14.54 (((prop2setI) =>
% 105.98/14.54 (((prop2set2propI) =>
% 105.98/14.54 (((notdexE) =>
% 105.98/14.54 (((notdallE) =>
% 105.98/14.54 (((exuI1) =>
% 105.98/14.54 (((exuI3) =>
% 105.98/14.54 (((exuI2) =>
% 105.98/14.54 (((inCongP) =>
% 105.98/14.54 (((in__Cong) =>
% 105.98/14.54 (((exuE3u) =>
% 105.98/14.54 (((exu__Cong) =>
% 105.98/14.54 (((setadjoin__Cong) =>
% 105.98/14.54 (((powerset__Cong) =>
% 105.98/14.54 (((setunion__Cong) =>
% 105.98/14.54 (((exuEu) =>
% 105.98/14.54 (((descr__Cong) =>
% 105.98/14.54 (((dsetconstr__Cong) =>
% 105.98/14.54 (((subsetI1) =>
% 105.98/14.54 (((eqimpsubset2) =>
% 105.98/14.54 (((eqimpsubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (emptysetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (notsubsetI) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (notequalI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetRefl) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTrans) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setadjoinSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (subset2powerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetemptysetimpeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepInPowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (sepSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2IR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionEcases) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectI) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset5) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset3) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectER) =>
% 105.98/14.54 ((
% 105.98/14.54 (disjointsetsI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectRsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset4) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (bs114d) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusI) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusER) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusERneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusELneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusILneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusIRneg) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusLsub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusSubset1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffE) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffI2) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg1) =>
% 105.98/14.54 ((
% 105.98/14.54 (symdiffIneg2) =>
% 105.98/14.54 ((
% 105.98/14.54 (secondinupair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairIR) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairiskpair) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairp) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowerset) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletoninpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairset2E) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairsubunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairinpowunion) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ubforcartprodlem3) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair1) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempair) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionE2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton1) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setunionsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1I2) =>
% 105.98/14.54 ((
% 105.98/14.54 (singletonsuniq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (theprop) =>
% 105.98/14.54 ((
% 105.98/14.54 (kfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstin) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjL) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR11) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR12) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR1) =>
% 105.98/14.54 ((
% 105.98/14.54 (upairequniteq) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR2) =>
% 105.98/14.54 ((
% 105.98/14.54 (setukpairinjR) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndsingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ksndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (kpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndin) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemEL) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairmemER) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodmempaircEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodfstpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodsndpairEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (cartprodpairsurjEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrI) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrSub) =>
% 105.98/14.54 ((
% 105.98/14.54 (setOfPairsIsBReln) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrERa) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL1) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrEL2) =>
% 105.98/14.54 ((
% 105.98/14.54 (dpsetconstrER) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcImageSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (apProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (app) =>
% 105.98/14.54 ((
% 105.98/14.54 (infuncsetfunc) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcinfuncset) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamProp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lamp) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2p) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall1) =>
% 105.98/14.54 ((
% 105.98/14.54 (brelnall2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ex1E2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp3) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcextLem) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcGraphProp4) =>
% 105.98/14.54 ((
% 105.98/14.54 (subbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (eqbreln) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext) =>
% 105.98/14.54 ((
% 105.98/14.54 (funcext2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq1) =>
% 105.98/14.54 ((
% 105.98/14.54 (ap2apEq2) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta1) =>
% 105.98/14.54 ((
% 105.98/14.54 (lam2lamEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (beta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (eta2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalseProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp1) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueProp2) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifSingleton) =>
% 105.98/14.54 ((
% 105.98/14.54 (ifp) =>
% 105.98/14.54 ((
% 105.98/14.54 (theeq) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrue) =>
% 105.98/14.54 ((
% 105.98/14.54 (iffalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (iftrueorfalse) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setminusT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementT_lem) =>
% 105.98/14.54 ((
% 105.98/14.54 (setextT) =>
% 105.98/14.54 ((
% 105.98/14.54 (subsetTI) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (powersetTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTELcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binintersectTERcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT1) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT2) =>
% 105.98/14.54 ((
% 105.98/14.54 (contrasubsetT3) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementI1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementE1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub1) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementSub2) =>
% 105.98/14.54 ((
% 105.98/14.54 (doubleComplementEq) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTnotintersectT) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementImpComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementSubsetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementInPowersetComplementIntersect) =>
% 105.98/14.54 ((
% 105.98/14.54 (contraSubsetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementTcontraSubset) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTILcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTIRcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInUnion2) =>
% 105.98/14.54 ((
% 105.98/14.54 (inIntersectImpInIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (intersectInPowersetIntersectUnions) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpNotIn1) =>
% 105.98/14.54 ((
% 105.98/14.54 (inComplementUnionImpInComplement1) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTE) =>
% 105.98/14.54 ((
% 105.98/14.54 (binunionTEcontra) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a1) =>
% 105.98/14.54 ((
% 105.98/14.54 (complementUnionInPowersetComplement) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan1) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2a) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b2) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2b) =>
% 105.98/14.54 ((
% 105.98/14.54 (demorgan2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule0) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz13rule4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_1) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_2) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_3) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_4) =>
% 105.98/14.54 ((
% 105.98/14.54 (woz1_5) =>
% 105.98/14.54 ((
% 105.98/14.54 (breln1all2) =>
% 105.98/14.54 ((
% 105.98/14.54 (!!) @ (
% 105.98/14.54 (('#B') @ (
% 105.98/14.54 !!) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#S') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 '#S') @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 =>))) @
% 105.98/14.54 (
% 105.98/14.54 (
% 105.98/14.54 ('#B') @ (
% 105.98/14.54 (
% 105.98/14.54 ('#C') @ in)) @
% 105.98/14.54 breln1Set)))))) @
% 105.98/14.54 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])).
% 105.98/14.54 thf(zip_derived_cl485, plain,
% 105.98/14.54 (~ (((upairsetE) =>
% 105.98/14.54 (((upairsetIL) =>
% 105.98/14.54 (((upairsetIR) =>
% 105.98/14.54 (((emptyE1) =>
% 105.98/14.54 (((vacuousDall) =>
% 105.98/14.54 (((quantDeMorgan1) =>
% 105.98/14.54 (((quantDeMorgan2) =>
% 105.98/14.54 (((quantDeMorgan3) =>
% 105.98/14.54 (((quantDeMorgan4) =>
% 105.98/14.54 (((prop2setI) =>
% 105.98/14.54 (((prop2set2propI) =>
% 105.98/14.54 (((notdexE) =>
% 105.98/14.54 (((notdallE) =>
% 105.98/14.54 (((exuI1) =>
% 105.98/14.54 (((exuI3) =>
% 105.98/14.54 (((exuI2) =>
% 105.98/14.54 (((inCongP) =>
% 105.98/14.54 (((in__Cong) =>
% 105.98/14.55 (((exuE3u) =>
% 105.98/14.55 (((exu__Cong) =>
% 105.98/14.55 (((setadjoin__Cong) =>
% 105.98/14.55 (((powerset__Cong) =>
% 105.98/14.55 (((setunion__Cong) =>
% 105.98/14.55 (((exuEu) =>
% 105.98/14.55 (((descr__Cong) =>
% 105.98/14.55 (((dsetconstr__Cong) =>
% 105.98/14.55 (((subsetI1) =>
% 105.98/14.55 (((eqimpsubset2) =>
% 105.98/14.55 (((eqimpsubset1) =>
% 105.98/14.55 (((subsetI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (emptysetsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetE) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetE2) =>
% 105.98/14.55 ((
% 105.98/14.55 (notsubsetI) =>
% 105.98/14.55 ((
% 105.98/14.55 (notequalI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (notequalI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetRefl) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTrans) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subset2powerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetemptysetimpeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepInPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2IR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionEcases) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectI) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset5) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset3) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectER) =>
% 105.98/14.55 ((
% 105.98/14.55 (disjointsetsI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset4) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (bs114d) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusI) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusER) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusERneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusELneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusILneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusIRneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffE) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg2) =>
% 105.98/14.55 ((
% 105.98/14.55 (secondinupair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairiskpair) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairp) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2E) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairsubunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairinpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem3) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair1) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionE2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton1) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I2) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsuniq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (theprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstin) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR11) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR12) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR1) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairequniteq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemER) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempaircEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrI) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setOfPairsIsBReln) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrERa) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrER) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcImageSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (apProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (app) =>
% 105.98/14.55 ((
% 105.98/14.55 (infuncsetfunc) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcinfuncset) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall1) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp3) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcextLem) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp4) =>
% 105.98/14.55 ((
% 105.98/14.55 (subbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (eqbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq2) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2lamEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifp) =>
% 105.98/14.55 ((
% 105.98/14.55 (theeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrue) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueorfalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextT) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTI) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTELcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTERcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT1) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT2) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT3) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTnotintersectT) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementImpComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementSubsetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementInPowersetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (contraSubsetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTcontraSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTILcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTIRcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion2) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (intersectInPowersetIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpNotIn1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpInComplement1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTEcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementUnionInPowersetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule0) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_5) =>
% 105.98/14.55 ((
% 105.98/14.55 (breln1all2) =>
% 105.98/14.55 ((
% 105.98/14.55 (!!) @ (
% 105.98/14.55 (('#B') @ (
% 105.98/14.55 !!) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#S') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 '#S') @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 =>))) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#C') @ in)) @
% 105.98/14.55 breln1Set)))))) @
% 105.98/14.55 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl475])).
% 105.98/14.55 thf(zip_derived_cl496, plain,
% 105.98/14.55 (~ (((upairsetIL) =>
% 105.98/14.55 (((upairsetIR) =>
% 105.98/14.55 (((emptyE1) =>
% 105.98/14.55 (((vacuousDall) =>
% 105.98/14.55 (((quantDeMorgan1) =>
% 105.98/14.55 (((quantDeMorgan2) =>
% 105.98/14.55 (((quantDeMorgan3) =>
% 105.98/14.55 (((quantDeMorgan4) =>
% 105.98/14.55 (((prop2setI) =>
% 105.98/14.55 (((prop2set2propI) =>
% 105.98/14.55 (((notdexE) =>
% 105.98/14.55 (((notdallE) =>
% 105.98/14.55 (((exuI1) =>
% 105.98/14.55 (((exuI3) =>
% 105.98/14.55 (((exuI2) =>
% 105.98/14.55 (((inCongP) =>
% 105.98/14.55 (((in__Cong) =>
% 105.98/14.55 (((exuE3u) =>
% 105.98/14.55 (((exu__Cong) =>
% 105.98/14.55 (((setadjoin__Cong) =>
% 105.98/14.55 (((powerset__Cong) =>
% 105.98/14.55 (((setunion__Cong) =>
% 105.98/14.55 (((exuEu) =>
% 105.98/14.55 (((descr__Cong) =>
% 105.98/14.55 (((dsetconstr__Cong) =>
% 105.98/14.55 (((subsetI1) =>
% 105.98/14.55 (((eqimpsubset2) =>
% 105.98/14.55 (((eqimpsubset1) =>
% 105.98/14.55 (((subsetI2) =>
% 105.98/14.55 (((emptysetsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetE) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetE2) =>
% 105.98/14.55 ((
% 105.98/14.55 (notsubsetI) =>
% 105.98/14.55 ((
% 105.98/14.55 (notequalI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (notequalI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetRefl) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTrans) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subset2powerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetemptysetimpeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepInPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2IR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionEcases) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectI) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset5) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset3) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectER) =>
% 105.98/14.55 ((
% 105.98/14.55 (disjointsetsI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset4) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (bs114d) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusI) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusER) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusERneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusELneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusILneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusIRneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffE) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg2) =>
% 105.98/14.55 ((
% 105.98/14.55 (secondinupair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairiskpair) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairp) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2E) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairsubunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairinpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem3) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair1) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionE2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton1) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I2) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsuniq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (theprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstin) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR11) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR12) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR1) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairequniteq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemER) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempaircEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrI) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setOfPairsIsBReln) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrERa) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrER) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcImageSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (apProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (app) =>
% 105.98/14.55 ((
% 105.98/14.55 (infuncsetfunc) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcinfuncset) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall1) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp3) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcextLem) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp4) =>
% 105.98/14.55 ((
% 105.98/14.55 (subbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (eqbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq2) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2lamEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifp) =>
% 105.98/14.55 ((
% 105.98/14.55 (theeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrue) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueorfalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextT) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTI) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTELcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTERcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT1) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT2) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT3) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTnotintersectT) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementImpComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementSubsetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementInPowersetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (contraSubsetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTcontraSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTILcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTIRcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion2) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (intersectInPowersetIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpNotIn1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpInComplement1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTEcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementUnionInPowersetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule0) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_5) =>
% 105.98/14.55 ((
% 105.98/14.55 (breln1all2) =>
% 105.98/14.55 ((
% 105.98/14.55 (!!) @ (
% 105.98/14.55 (('#B') @ (
% 105.98/14.55 !!) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#S') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 '#S') @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 =>))) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#C') @ in)) @
% 105.98/14.55 breln1Set)))))) @
% 105.98/14.55 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
% 105.98/14.55 thf(zip_derived_cl507, plain,
% 105.98/14.55 (~ (((upairsetIR) =>
% 105.98/14.55 (((emptyE1) =>
% 105.98/14.55 (((vacuousDall) =>
% 105.98/14.55 (((quantDeMorgan1) =>
% 105.98/14.55 (((quantDeMorgan2) =>
% 105.98/14.55 (((quantDeMorgan3) =>
% 105.98/14.55 (((quantDeMorgan4) =>
% 105.98/14.55 (((prop2setI) =>
% 105.98/14.55 (((prop2set2propI) =>
% 105.98/14.55 (((notdexE) =>
% 105.98/14.55 (((notdallE) =>
% 105.98/14.55 (((exuI1) =>
% 105.98/14.55 (((exuI3) =>
% 105.98/14.55 (((exuI2) =>
% 105.98/14.55 (((inCongP) =>
% 105.98/14.55 (((in__Cong) =>
% 105.98/14.55 (((exuE3u) =>
% 105.98/14.55 (((exu__Cong) =>
% 105.98/14.55 (((setadjoin__Cong) =>
% 105.98/14.55 (((powerset__Cong) =>
% 105.98/14.55 (((setunion__Cong) =>
% 105.98/14.55 (((exuEu) =>
% 105.98/14.55 (((descr__Cong) =>
% 105.98/14.55 (((dsetconstr__Cong) =>
% 105.98/14.55 (((subsetI1) =>
% 105.98/14.55 (((eqimpsubset2) =>
% 105.98/14.55 (((eqimpsubset1) =>
% 105.98/14.55 (((subsetI2) =>
% 105.98/14.55 (((emptysetsubset) =>
% 105.98/14.55 (((subsetE) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetE2) =>
% 105.98/14.55 ((
% 105.98/14.55 (notsubsetI) =>
% 105.98/14.55 ((
% 105.98/14.55 (notequalI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (notequalI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetRefl) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTrans) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subset2powerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetemptysetimpeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepInPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2IR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionEcases) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectI) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset5) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset3) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectER) =>
% 105.98/14.55 ((
% 105.98/14.55 (disjointsetsI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset4) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (bs114d) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusI) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusER) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusERneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusELneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusILneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusIRneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffE) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg2) =>
% 105.98/14.55 ((
% 105.98/14.55 (secondinupair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairiskpair) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairp) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2E) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairsubunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairinpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem3) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair1) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionE2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton1) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I2) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsuniq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (theprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstin) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR11) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR12) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR1) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairequniteq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemER) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempaircEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrI) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setOfPairsIsBReln) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrERa) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrER) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcImageSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (apProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (app) =>
% 105.98/14.55 ((
% 105.98/14.55 (infuncsetfunc) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcinfuncset) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall1) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp3) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcextLem) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp4) =>
% 105.98/14.55 ((
% 105.98/14.55 (subbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (eqbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq2) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2lamEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifp) =>
% 105.98/14.55 ((
% 105.98/14.55 (theeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrue) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueorfalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextT) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTI) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTELcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTERcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT1) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT2) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT3) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTnotintersectT) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementImpComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementSubsetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementInPowersetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (contraSubsetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTcontraSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTILcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTIRcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion2) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (intersectInPowersetIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpNotIn1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpInComplement1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTEcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementUnionInPowersetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule0) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_5) =>
% 105.98/14.55 ((
% 105.98/14.55 (breln1all2) =>
% 105.98/14.55 ((
% 105.98/14.55 (!!) @ (
% 105.98/14.55 (('#B') @ (
% 105.98/14.55 !!) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#S') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 '#S') @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 =>))) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#C') @ in)) @
% 105.98/14.55 breln1Set)))))) @
% 105.98/14.55 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl496])).
% 105.98/14.55 thf(zip_derived_cl517, plain,
% 105.98/14.55 (~ (((emptyE1) =>
% 105.98/14.55 (((vacuousDall) =>
% 105.98/14.55 (((quantDeMorgan1) =>
% 105.98/14.55 (((quantDeMorgan2) =>
% 105.98/14.55 (((quantDeMorgan3) =>
% 105.98/14.55 (((quantDeMorgan4) =>
% 105.98/14.55 (((prop2setI) =>
% 105.98/14.55 (((prop2set2propI) =>
% 105.98/14.55 (((notdexE) =>
% 105.98/14.55 (((notdallE) =>
% 105.98/14.55 (((exuI1) =>
% 105.98/14.55 (((exuI3) =>
% 105.98/14.55 (((exuI2) =>
% 105.98/14.55 (((inCongP) =>
% 105.98/14.55 (((in__Cong) =>
% 105.98/14.55 (((exuE3u) =>
% 105.98/14.55 (((exu__Cong) =>
% 105.98/14.55 (((setadjoin__Cong) =>
% 105.98/14.55 (((powerset__Cong) =>
% 105.98/14.55 (((setunion__Cong) =>
% 105.98/14.55 (((exuEu) =>
% 105.98/14.55 (((descr__Cong) =>
% 105.98/14.55 (((dsetconstr__Cong) =>
% 105.98/14.55 (((subsetI1) =>
% 105.98/14.55 (((eqimpsubset2) =>
% 105.98/14.55 (((eqimpsubset1) =>
% 105.98/14.55 (((subsetI2) =>
% 105.98/14.55 (((emptysetsubset) =>
% 105.98/14.55 (((subsetE) =>
% 105.98/14.55 (((subsetE2) =>
% 105.98/14.55 ((
% 105.98/14.55 (notsubsetI) =>
% 105.98/14.55 ((
% 105.98/14.55 (notequalI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (notequalI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetRefl) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTrans) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subset2powerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetemptysetimpeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepInPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2IR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionEcases) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectI) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset5) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset3) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectER) =>
% 105.98/14.55 ((
% 105.98/14.55 (disjointsetsI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset4) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (bs114d) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusI) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusER) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusERneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusELneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusILneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusIRneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffE) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg2) =>
% 105.98/14.55 ((
% 105.98/14.55 (secondinupair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairiskpair) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairp) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2E) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairsubunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairinpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem3) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair1) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionE2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton1) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I2) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsuniq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (theprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstin) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR11) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR12) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR1) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairequniteq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemER) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempaircEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrI) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setOfPairsIsBReln) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrERa) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrER) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcImageSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (apProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (app) =>
% 105.98/14.55 ((
% 105.98/14.55 (infuncsetfunc) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcinfuncset) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall1) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp3) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcextLem) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp4) =>
% 105.98/14.55 ((
% 105.98/14.55 (subbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (eqbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq2) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2lamEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifp) =>
% 105.98/14.55 ((
% 105.98/14.55 (theeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrue) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueorfalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextT) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTI) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTELcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTERcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT1) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT2) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT3) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTnotintersectT) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementImpComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementSubsetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementInPowersetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (contraSubsetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTcontraSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTILcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTIRcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion2) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (intersectInPowersetIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpNotIn1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpInComplement1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTEcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementUnionInPowersetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule0) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_5) =>
% 105.98/14.55 ((
% 105.98/14.55 (breln1all2) =>
% 105.98/14.55 ((
% 105.98/14.55 (!!) @ (
% 105.98/14.55 (('#B') @ (
% 105.98/14.55 !!) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#S') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 '#S') @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 =>))) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#C') @ in)) @
% 105.98/14.55 breln1Set)))))) @
% 105.98/14.55 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl507])).
% 105.98/14.55 thf(zip_derived_cl528, plain,
% 105.98/14.55 (~ (((vacuousDall) =>
% 105.98/14.55 (((quantDeMorgan1) =>
% 105.98/14.55 (((quantDeMorgan2) =>
% 105.98/14.55 (((quantDeMorgan3) =>
% 105.98/14.55 (((quantDeMorgan4) =>
% 105.98/14.55 (((prop2setI) =>
% 105.98/14.55 (((prop2set2propI) =>
% 105.98/14.55 (((notdexE) =>
% 105.98/14.55 (((notdallE) =>
% 105.98/14.55 (((exuI1) =>
% 105.98/14.55 (((exuI3) =>
% 105.98/14.55 (((exuI2) =>
% 105.98/14.55 (((inCongP) =>
% 105.98/14.55 (((in__Cong) =>
% 105.98/14.55 (((exuE3u) =>
% 105.98/14.55 (((exu__Cong) =>
% 105.98/14.55 (((setadjoin__Cong) =>
% 105.98/14.55 (((powerset__Cong) =>
% 105.98/14.55 (((setunion__Cong) =>
% 105.98/14.55 (((exuEu) =>
% 105.98/14.55 (((descr__Cong) =>
% 105.98/14.55 (((dsetconstr__Cong) =>
% 105.98/14.55 (((subsetI1) =>
% 105.98/14.55 (((eqimpsubset2) =>
% 105.98/14.55 (((eqimpsubset1) =>
% 105.98/14.55 (((subsetI2) =>
% 105.98/14.55 (((emptysetsubset) =>
% 105.98/14.55 (((subsetE) =>
% 105.98/14.55 (((subsetE2) =>
% 105.98/14.55 (((notsubsetI) =>
% 105.98/14.55 ((
% 105.98/14.55 (notequalI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (notequalI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetRefl) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTrans) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subset2powerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetemptysetimpeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepInPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2IR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionEcases) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectI) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset5) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset3) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectER) =>
% 105.98/14.55 ((
% 105.98/14.55 (disjointsetsI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset4) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (bs114d) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusI) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusER) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusERneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusELneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusILneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusIRneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffE) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg2) =>
% 105.98/14.55 ((
% 105.98/14.55 (secondinupair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairiskpair) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairp) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2E) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairsubunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairinpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem3) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair1) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionE2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton1) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I2) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsuniq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (theprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstin) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR11) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR12) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR1) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairequniteq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemER) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempaircEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrI) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setOfPairsIsBReln) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrERa) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrER) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcImageSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (apProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (app) =>
% 105.98/14.55 ((
% 105.98/14.55 (infuncsetfunc) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcinfuncset) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall1) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp3) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcextLem) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp4) =>
% 105.98/14.55 ((
% 105.98/14.55 (subbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (eqbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq2) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2lamEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifp) =>
% 105.98/14.55 ((
% 105.98/14.55 (theeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrue) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueorfalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextT) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTI) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTELcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTERcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT1) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT2) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT3) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTnotintersectT) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementImpComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementSubsetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementInPowersetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (contraSubsetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTcontraSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTILcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTIRcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion2) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (intersectInPowersetIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpNotIn1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpInComplement1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTEcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementUnionInPowersetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule0) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_5) =>
% 105.98/14.55 ((
% 105.98/14.55 (breln1all2) =>
% 105.98/14.55 ((
% 105.98/14.55 (!!) @ (
% 105.98/14.55 (('#B') @ (
% 105.98/14.55 !!) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#S') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 '#S') @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 =>))) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#C') @ in)) @
% 105.98/14.55 breln1Set)))))) @
% 105.98/14.55 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl517])).
% 105.98/14.55 thf(zip_derived_cl537, plain,
% 105.98/14.55 (~ (((quantDeMorgan1) =>
% 105.98/14.55 (((quantDeMorgan2) =>
% 105.98/14.55 (((quantDeMorgan3) =>
% 105.98/14.55 (((quantDeMorgan4) =>
% 105.98/14.55 (((prop2setI) =>
% 105.98/14.55 (((prop2set2propI) =>
% 105.98/14.55 (((notdexE) =>
% 105.98/14.55 (((notdallE) =>
% 105.98/14.55 (((exuI1) =>
% 105.98/14.55 (((exuI3) =>
% 105.98/14.55 (((exuI2) =>
% 105.98/14.55 (((inCongP) =>
% 105.98/14.55 (((in__Cong) =>
% 105.98/14.55 (((exuE3u) =>
% 105.98/14.55 (((exu__Cong) =>
% 105.98/14.55 (((setadjoin__Cong) =>
% 105.98/14.55 (((powerset__Cong) =>
% 105.98/14.55 (((setunion__Cong) =>
% 105.98/14.55 (((exuEu) =>
% 105.98/14.55 (((descr__Cong) =>
% 105.98/14.55 (((dsetconstr__Cong) =>
% 105.98/14.55 (((subsetI1) =>
% 105.98/14.55 (((eqimpsubset2) =>
% 105.98/14.55 (((eqimpsubset1) =>
% 105.98/14.55 (((subsetI2) =>
% 105.98/14.55 (((emptysetsubset) =>
% 105.98/14.55 (((subsetE) =>
% 105.98/14.55 (((subsetE2) =>
% 105.98/14.55 (((notsubsetI) =>
% 105.98/14.55 (((notequalI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (notequalI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetRefl) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTrans) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subset2powerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetemptysetimpeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepInPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2IR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionEcases) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectI) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset5) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset3) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectER) =>
% 105.98/14.55 ((
% 105.98/14.55 (disjointsetsI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset4) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (bs114d) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusI) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusER) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusERneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusELneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusILneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusIRneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffE) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg2) =>
% 105.98/14.55 ((
% 105.98/14.55 (secondinupair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairiskpair) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairp) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2E) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairsubunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairinpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem3) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair1) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionE2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton1) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I2) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsuniq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (theprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstin) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR11) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR12) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR1) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairequniteq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemER) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempaircEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrI) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setOfPairsIsBReln) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrERa) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrER) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcImageSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (apProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (app) =>
% 105.98/14.55 ((
% 105.98/14.55 (infuncsetfunc) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcinfuncset) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall1) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp3) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcextLem) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp4) =>
% 105.98/14.55 ((
% 105.98/14.55 (subbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (eqbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq2) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2lamEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifp) =>
% 105.98/14.55 ((
% 105.98/14.55 (theeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrue) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueorfalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextT) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTI) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTELcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTERcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT1) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT2) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT3) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTnotintersectT) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementImpComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementSubsetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementInPowersetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (contraSubsetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTcontraSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTILcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTIRcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion2) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (intersectInPowersetIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpNotIn1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpInComplement1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTEcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementUnionInPowersetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule0) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_5) =>
% 105.98/14.55 ((
% 105.98/14.55 (breln1all2) =>
% 105.98/14.55 ((
% 105.98/14.55 (!!) @ (
% 105.98/14.55 (('#B') @ (
% 105.98/14.55 !!) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#S') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 '#S') @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 =>))) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#C') @ in)) @
% 105.98/14.55 breln1Set)))))) @
% 105.98/14.55 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])).
% 105.98/14.55 thf(zip_derived_cl546, plain,
% 105.98/14.55 (~ (((quantDeMorgan2) =>
% 105.98/14.55 (((quantDeMorgan3) =>
% 105.98/14.55 (((quantDeMorgan4) =>
% 105.98/14.55 (((prop2setI) =>
% 105.98/14.55 (((prop2set2propI) =>
% 105.98/14.55 (((notdexE) =>
% 105.98/14.55 (((notdallE) =>
% 105.98/14.55 (((exuI1) =>
% 105.98/14.55 (((exuI3) =>
% 105.98/14.55 (((exuI2) =>
% 105.98/14.55 (((inCongP) =>
% 105.98/14.55 (((in__Cong) =>
% 105.98/14.55 (((exuE3u) =>
% 105.98/14.55 (((exu__Cong) =>
% 105.98/14.55 (((setadjoin__Cong) =>
% 105.98/14.55 (((powerset__Cong) =>
% 105.98/14.55 (((setunion__Cong) =>
% 105.98/14.55 (((exuEu) =>
% 105.98/14.55 (((descr__Cong) =>
% 105.98/14.55 (((dsetconstr__Cong) =>
% 105.98/14.55 (((subsetI1) =>
% 105.98/14.55 (((eqimpsubset2) =>
% 105.98/14.55 (((eqimpsubset1) =>
% 105.98/14.55 (((subsetI2) =>
% 105.98/14.55 (((emptysetsubset) =>
% 105.98/14.55 (((subsetE) =>
% 105.98/14.55 (((subsetE2) =>
% 105.98/14.55 (((notsubsetI) =>
% 105.98/14.55 (((notequalI1) =>
% 105.98/14.55 (((notequalI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetRefl) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTrans) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subset2powerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetemptysetimpeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepInPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2IR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionEcases) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectI) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset5) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset3) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectER) =>
% 105.98/14.55 ((
% 105.98/14.55 (disjointsetsI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectRsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset4) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (bs114d) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusI) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusER) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusERneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusELneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusILneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusIRneg) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusLsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusSubset1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffE) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffI2) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg1) =>
% 105.98/14.55 ((
% 105.98/14.55 (symdiffIneg2) =>
% 105.98/14.55 ((
% 105.98/14.55 (secondinupair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairIR) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairiskpair) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairp) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletoninpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairset2E) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairsubunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairinpowunion) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ubforcartprodlem3) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair1) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempair) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionE2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton1) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setunionsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1I2) =>
% 105.98/14.55 ((
% 105.98/14.55 (singletonsuniq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (theprop) =>
% 105.98/14.55 ((
% 105.98/14.55 (kfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstin) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjL) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR11) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR12) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR1) =>
% 105.98/14.55 ((
% 105.98/14.55 (upairequniteq) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR2) =>
% 105.98/14.55 ((
% 105.98/14.55 (setukpairinjR) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndsingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ksndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (kpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndin) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemEL) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairmemER) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodmempaircEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodfstpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodsndpairEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (cartprodpairsurjEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrI) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setOfPairsIsBReln) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrERa) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL1) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrEL2) =>
% 105.98/14.55 ((
% 105.98/14.55 (dpsetconstrER) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcImageSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (apProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (app) =>
% 105.98/14.55 ((
% 105.98/14.55 (infuncsetfunc) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcinfuncset) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamProp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lamp) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2p) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall1) =>
% 105.98/14.55 ((
% 105.98/14.55 (brelnall2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ex1E2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp3) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcextLem) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcGraphProp4) =>
% 105.98/14.55 ((
% 105.98/14.55 (subbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (eqbreln) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext) =>
% 105.98/14.55 ((
% 105.98/14.55 (funcext2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq1) =>
% 105.98/14.55 ((
% 105.98/14.55 (ap2apEq2) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta1) =>
% 105.98/14.55 ((
% 105.98/14.55 (lam2lamEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (beta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (eta2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalseProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp1) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueProp2) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifSingleton) =>
% 105.98/14.55 ((
% 105.98/14.55 (ifp) =>
% 105.98/14.55 ((
% 105.98/14.55 (theeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrue) =>
% 105.98/14.55 ((
% 105.98/14.55 (iffalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (iftrueorfalse) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setminusT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementT_lem) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextT) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTI) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTELcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binintersectTERcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT1) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT2) =>
% 105.98/14.55 ((
% 105.98/14.55 (contrasubsetT3) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub1) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (doubleComplementEq) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTnotintersectT) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementImpComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementSubsetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementInPowersetComplementIntersect) =>
% 105.98/14.55 ((
% 105.98/14.55 (contraSubsetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementTcontraSubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTILcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTIRcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInUnion2) =>
% 105.98/14.55 ((
% 105.98/14.55 (inIntersectImpInIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (intersectInPowersetIntersectUnions) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpNotIn1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inComplementUnionImpInComplement1) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTE) =>
% 105.98/14.55 ((
% 105.98/14.55 (binunionTEcontra) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a1) =>
% 105.98/14.55 ((
% 105.98/14.55 (complementUnionInPowersetComplement) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan1) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2a) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b2) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2b) =>
% 105.98/14.55 ((
% 105.98/14.55 (demorgan2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule0) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz13rule4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_1) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_2) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_3) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_4) =>
% 105.98/14.55 ((
% 105.98/14.55 (woz1_5) =>
% 105.98/14.55 ((
% 105.98/14.55 (breln1all2) =>
% 105.98/14.55 ((
% 105.98/14.55 (!!) @ (
% 105.98/14.55 (('#B') @ (
% 105.98/14.55 !!) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#S') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 '#S') @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 =>))) @
% 105.98/14.55 (
% 105.98/14.55 (
% 105.98/14.55 ('#B') @ (
% 105.98/14.55 (
% 105.98/14.55 ('#C') @ in)) @
% 105.98/14.55 breln1Set)))))) @
% 105.98/14.55 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 105.98/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])).
% 105.98/14.55 thf(zip_derived_cl553, plain,
% 105.98/14.55 (~ (((quantDeMorgan3) =>
% 105.98/14.55 (((quantDeMorgan4) =>
% 105.98/14.55 (((prop2setI) =>
% 105.98/14.55 (((prop2set2propI) =>
% 105.98/14.55 (((notdexE) =>
% 105.98/14.55 (((notdallE) =>
% 105.98/14.55 (((exuI1) =>
% 105.98/14.55 (((exuI3) =>
% 105.98/14.55 (((exuI2) =>
% 105.98/14.55 (((inCongP) =>
% 105.98/14.55 (((in__Cong) =>
% 105.98/14.55 (((exuE3u) =>
% 105.98/14.55 (((exu__Cong) =>
% 105.98/14.55 (((setadjoin__Cong) =>
% 105.98/14.55 (((powerset__Cong) =>
% 105.98/14.55 (((setunion__Cong) =>
% 105.98/14.55 (((exuEu) =>
% 105.98/14.55 (((descr__Cong) =>
% 105.98/14.55 (((dsetconstr__Cong) =>
% 105.98/14.55 (((subsetI1) =>
% 105.98/14.55 (((eqimpsubset2) =>
% 105.98/14.55 (((eqimpsubset1) =>
% 105.98/14.55 (((subsetI2) =>
% 105.98/14.55 (((emptysetsubset) =>
% 105.98/14.55 (((subsetE) =>
% 105.98/14.55 (((subsetE2) =>
% 105.98/14.55 (((notsubsetI) =>
% 105.98/14.55 (((notequalI1) =>
% 105.98/14.55 (((notequalI2) =>
% 105.98/14.55 (((subsetRefl) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetTrans) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub) =>
% 105.98/14.55 ((
% 105.98/14.55 (setadjoinSub2) =>
% 105.98/14.55 ((
% 105.98/14.55 (subset2powerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (setextsub) =>
% 105.98/14.55 ((
% 105.98/14.55 (subsetemptysetimpeq) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetI1) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetE1) =>
% 105.98/14.55 ((
% 105.98/14.55 (inPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (powersetsubset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepInPowerset) =>
% 105.98/14.55 ((
% 105.98/14.55 (sepSubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionIL) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairset2IR) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionIR) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionEcases) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionE) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionLsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionRsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectI) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset5) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectEL) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectLsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset2) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset3) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectER) =>
% 106.27/14.55 ((
% 106.27/14.55 (disjointsetsI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectRsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset4) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset1) =>
% 106.27/14.55 ((
% 106.27/14.55 (bs114d) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusI) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusEL) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusER) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusSubset2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusERneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusELneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusILneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusIRneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusLsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusSubset1) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffE) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffI2) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffIneg1) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffIneg2) =>
% 106.27/14.55 ((
% 106.27/14.55 (secondinupair) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairIL) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairIR) =>
% 106.27/14.55 ((
% 106.27/14.55 (kpairiskpair) =>
% 106.27/14.55 ((
% 106.27/14.55 (kpairp) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletonsubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletoninpowerset) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletoninpowunion) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairset2E) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairsubunion) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairinpowunion) =>
% 106.27/14.55 ((
% 106.27/14.55 (ubforcartprodlem1) =>
% 106.27/14.55 ((
% 106.27/14.55 (ubforcartprodlem2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ubforcartprodlem3) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairin) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodmempair1) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodmempair) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionE2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionsingleton1) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionsingleton2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionsingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletonprop) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1E1) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1I) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1I2) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletonsuniq) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjL1) =>
% 106.27/14.55 ((
% 106.27/14.55 (kfstsingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (theprop) =>
% 106.27/14.55 ((
% 106.27/14.55 (kfstpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodfstin) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjL2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjL) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR11) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR12) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR1) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairequniteq) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR) =>
% 106.27/14.55 ((
% 106.27/14.55 (ksndsingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (ksndpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (kpairsurjEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodsndin) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairmemEL) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairmemER) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodmempaircEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodfstpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodsndpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairsurjEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrI) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrSub) =>
% 106.27/14.55 ((
% 106.27/14.55 (setOfPairsIsBReln) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrERa) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrEL1) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrEL2) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrER) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcImageSingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (apProp) =>
% 106.27/14.55 ((
% 106.27/14.55 (app) =>
% 106.27/14.55 ((
% 106.27/14.55 (infuncsetfunc) =>
% 106.27/14.55 ((
% 106.27/14.55 (ap2p) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcinfuncset) =>
% 106.27/14.55 ((
% 106.27/14.55 (lamProp) =>
% 106.27/14.55 ((
% 106.27/14.55 (lamp) =>
% 106.27/14.55 ((
% 106.27/14.55 (lam2p) =>
% 106.27/14.55 ((
% 106.27/14.55 (brelnall1) =>
% 106.27/14.55 ((
% 106.27/14.55 (brelnall2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1E2) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp1) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp3) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp2) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcextLem) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp4) =>
% 106.27/14.55 ((
% 106.27/14.55 (subbreln) =>
% 106.27/14.55 ((
% 106.27/14.55 (eqbreln) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcext) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcext2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ap2apEq1) =>
% 106.27/14.55 ((
% 106.27/14.55 (ap2apEq2) =>
% 106.27/14.55 ((
% 106.27/14.55 (beta1) =>
% 106.27/14.55 ((
% 106.27/14.55 (eta1) =>
% 106.27/14.55 ((
% 106.27/14.55 (lam2lamEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (beta2) =>
% 106.27/14.55 ((
% 106.27/14.55 (eta2) =>
% 106.27/14.55 ((
% 106.27/14.55 (iffalseProp1) =>
% 106.27/14.55 ((
% 106.27/14.55 (iffalseProp2) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrueProp1) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrueProp2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ifSingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (ifp) =>
% 106.27/14.55 ((
% 106.27/14.55 (theeq) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrue) =>
% 106.27/14.55 ((
% 106.27/14.55 (iffalse) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrueorfalse) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (setextT) =>
% 106.27/14.55 ((
% 106.27/14.55 (subsetTI) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetTI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetTE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectTELcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectTERcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT1) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT2) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT3) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementSub1) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementSub2) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTnotintersectT) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementImpComplementIntersect) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementSubsetComplementIntersect) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementInPowersetComplementIntersect) =>
% 106.27/14.55 ((
% 106.27/14.55 (contraSubsetComplement) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTcontraSubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionTILcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionTIRcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (inIntersectImpInUnion) =>
% 106.27/14.55 ((
% 106.27/14.55 (inIntersectImpInUnion2) =>
% 106.27/14.55 ((
% 106.27/14.55 (inIntersectImpInIntersectUnions) =>
% 106.27/14.55 ((
% 106.27/14.55 (intersectInPowersetIntersectUnions) =>
% 106.27/14.55 ((
% 106.27/14.55 (inComplementUnionImpNotIn1) =>
% 106.27/14.55 ((
% 106.27/14.55 (inComplementUnionImpInComplement1) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionTE) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionTEcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2a1) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementUnionInPowersetComplement) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2a2) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan1a) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan1b) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan1) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2a) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2b2) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2b) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule0) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule1) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule2) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule3) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule4) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_1) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_2) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_3) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_4) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_5) =>
% 106.27/14.55 ((
% 106.27/14.55 (breln1all2) =>
% 106.27/14.55 ((
% 106.27/14.55 (!!) @ (
% 106.27/14.55 (('#B') @ (
% 106.27/14.55 !!) @
% 106.27/14.55 (
% 106.27/14.55 (
% 106.27/14.55 ('#S') @ (
% 106.27/14.55 (
% 106.27/14.55 ('#B') @ (
% 106.27/14.55 '#S') @
% 106.27/14.55 (
% 106.27/14.55 (
% 106.27/14.55 ('#B') @ (
% 106.27/14.55 (
% 106.27/14.55 ('#B') @ (
% 106.27/14.55 =>))) @
% 106.27/14.55 (
% 106.27/14.55 (
% 106.27/14.55 ('#B') @ (
% 106.27/14.55 (
% 106.27/14.55 ('#C') @ in)) @
% 106.27/14.55 breln1Set)))))) @
% 106.27/14.55 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl546])).
% 106.27/14.55 thf(zip_derived_cl561, plain,
% 106.27/14.55 (~ (((quantDeMorgan4) =>
% 106.27/14.55 (((prop2setI) =>
% 106.27/14.55 (((prop2set2propI) =>
% 106.27/14.55 (((notdexE) =>
% 106.27/14.55 (((notdallE) =>
% 106.27/14.55 (((exuI1) =>
% 106.27/14.55 (((exuI3) =>
% 106.27/14.55 (((exuI2) =>
% 106.27/14.55 (((inCongP) =>
% 106.27/14.55 (((in__Cong) =>
% 106.27/14.55 (((exuE3u) =>
% 106.27/14.55 (((exu__Cong) =>
% 106.27/14.55 (((setadjoin__Cong) =>
% 106.27/14.55 (((powerset__Cong) =>
% 106.27/14.55 (((setunion__Cong) =>
% 106.27/14.55 (((exuEu) =>
% 106.27/14.55 (((descr__Cong) =>
% 106.27/14.55 (((dsetconstr__Cong) =>
% 106.27/14.55 (((subsetI1) =>
% 106.27/14.55 (((eqimpsubset2) =>
% 106.27/14.55 (((eqimpsubset1) =>
% 106.27/14.55 (((subsetI2) =>
% 106.27/14.55 (((emptysetsubset) =>
% 106.27/14.55 (((subsetE) =>
% 106.27/14.55 (((subsetE2) =>
% 106.27/14.55 (((notsubsetI) =>
% 106.27/14.55 (((notequalI1) =>
% 106.27/14.55 (((notequalI2) =>
% 106.27/14.55 (((subsetRefl) =>
% 106.27/14.55 (((subsetTrans) =>
% 106.27/14.55 ((
% 106.27/14.55 (setadjoinSub) =>
% 106.27/14.55 ((
% 106.27/14.55 (setadjoinSub2) =>
% 106.27/14.55 ((
% 106.27/14.55 (subset2powerset) =>
% 106.27/14.55 ((
% 106.27/14.55 (setextsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (subsetemptysetimpeq) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (inPowerset) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetsubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (sepInPowerset) =>
% 106.27/14.55 ((
% 106.27/14.55 (sepSubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionIL) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairset2IR) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionIR) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionEcases) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionE) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionLsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionRsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectI) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset5) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectEL) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectLsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset2) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset3) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectER) =>
% 106.27/14.55 ((
% 106.27/14.55 (disjointsetsI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectRsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset4) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset1) =>
% 106.27/14.55 ((
% 106.27/14.55 (bs114d) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusI) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusEL) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusER) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusSubset2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusERneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusELneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusILneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusIRneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusLsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusSubset1) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffE) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffI2) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffIneg1) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffIneg2) =>
% 106.27/14.55 ((
% 106.27/14.55 (secondinupair) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairIL) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairIR) =>
% 106.27/14.55 ((
% 106.27/14.55 (kpairiskpair) =>
% 106.27/14.55 ((
% 106.27/14.55 (kpairp) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletonsubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletoninpowerset) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletoninpowunion) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairset2E) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairsubunion) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairinpowunion) =>
% 106.27/14.55 ((
% 106.27/14.55 (ubforcartprodlem1) =>
% 106.27/14.55 ((
% 106.27/14.55 (ubforcartprodlem2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ubforcartprodlem3) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairin) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodmempair1) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodmempair) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionE2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionsingleton1) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionsingleton2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionsingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletonprop) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1E1) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1I) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1I2) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletonsuniq) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjL1) =>
% 106.27/14.55 ((
% 106.27/14.55 (kfstsingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (theprop) =>
% 106.27/14.55 ((
% 106.27/14.55 (kfstpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodfstin) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjL2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjL) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR11) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR12) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR1) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairequniteq) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR) =>
% 106.27/14.55 ((
% 106.27/14.55 (ksndsingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (ksndpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (kpairsurjEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodsndin) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairmemEL) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairmemER) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodmempaircEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodfstpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodsndpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairsurjEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrI) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrSub) =>
% 106.27/14.55 ((
% 106.27/14.55 (setOfPairsIsBReln) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrERa) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrEL1) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrEL2) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrER) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcImageSingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (apProp) =>
% 106.27/14.55 ((
% 106.27/14.55 (app) =>
% 106.27/14.55 ((
% 106.27/14.55 (infuncsetfunc) =>
% 106.27/14.55 ((
% 106.27/14.55 (ap2p) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcinfuncset) =>
% 106.27/14.55 ((
% 106.27/14.55 (lamProp) =>
% 106.27/14.55 ((
% 106.27/14.55 (lamp) =>
% 106.27/14.55 ((
% 106.27/14.55 (lam2p) =>
% 106.27/14.55 ((
% 106.27/14.55 (brelnall1) =>
% 106.27/14.55 ((
% 106.27/14.55 (brelnall2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1E2) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp1) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp3) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp2) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcextLem) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp4) =>
% 106.27/14.55 ((
% 106.27/14.55 (subbreln) =>
% 106.27/14.55 ((
% 106.27/14.55 (eqbreln) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcext) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcext2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ap2apEq1) =>
% 106.27/14.55 ((
% 106.27/14.55 (ap2apEq2) =>
% 106.27/14.55 ((
% 106.27/14.55 (beta1) =>
% 106.27/14.55 ((
% 106.27/14.55 (eta1) =>
% 106.27/14.55 ((
% 106.27/14.55 (lam2lamEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (beta2) =>
% 106.27/14.55 ((
% 106.27/14.55 (eta2) =>
% 106.27/14.55 ((
% 106.27/14.55 (iffalseProp1) =>
% 106.27/14.55 ((
% 106.27/14.55 (iffalseProp2) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrueProp1) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrueProp2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ifSingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (ifp) =>
% 106.27/14.55 ((
% 106.27/14.55 (theeq) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrue) =>
% 106.27/14.55 ((
% 106.27/14.55 (iffalse) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrueorfalse) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (setextT) =>
% 106.27/14.55 ((
% 106.27/14.55 (subsetTI) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetTI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetTE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectTELcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectTERcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT1) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT2) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT3) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementSub1) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementSub2) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTnotintersectT) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementImpComplementIntersect) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementSubsetComplementIntersect) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementInPowersetComplementIntersect) =>
% 106.27/14.55 ((
% 106.27/14.55 (contraSubsetComplement) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTcontraSubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionTILcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionTIRcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (inIntersectImpInUnion) =>
% 106.27/14.55 ((
% 106.27/14.55 (inIntersectImpInUnion2) =>
% 106.27/14.55 ((
% 106.27/14.55 (inIntersectImpInIntersectUnions) =>
% 106.27/14.55 ((
% 106.27/14.55 (intersectInPowersetIntersectUnions) =>
% 106.27/14.55 ((
% 106.27/14.55 (inComplementUnionImpNotIn1) =>
% 106.27/14.55 ((
% 106.27/14.55 (inComplementUnionImpInComplement1) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionTE) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionTEcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2a1) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementUnionInPowersetComplement) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2a2) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan1a) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan1b) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan1) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2a) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2b2) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2b) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule0) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule1) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule2) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule3) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule4) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_1) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_2) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_3) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_4) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_5) =>
% 106.27/14.55 ((
% 106.27/14.55 (breln1all2) =>
% 106.27/14.55 ((
% 106.27/14.55 (!!) @ (
% 106.27/14.55 (('#B') @ (
% 106.27/14.55 !!) @
% 106.27/14.55 (
% 106.27/14.55 (
% 106.27/14.55 ('#S') @ (
% 106.27/14.55 (
% 106.27/14.55 ('#B') @ (
% 106.27/14.55 '#S') @
% 106.27/14.55 (
% 106.27/14.55 (
% 106.27/14.55 ('#B') @ (
% 106.27/14.55 (
% 106.27/14.55 ('#B') @ (
% 106.27/14.55 =>))) @
% 106.27/14.55 (
% 106.27/14.55 (
% 106.27/14.55 ('#B') @ (
% 106.27/14.55 (
% 106.27/14.55 ('#C') @ in)) @
% 106.27/14.55 breln1Set)))))) @
% 106.27/14.55 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl553])).
% 106.27/14.55 thf(zip_derived_cl570, plain,
% 106.27/14.55 (~ (((prop2setI) =>
% 106.27/14.55 (((prop2set2propI) =>
% 106.27/14.55 (((notdexE) =>
% 106.27/14.55 (((notdallE) =>
% 106.27/14.55 (((exuI1) =>
% 106.27/14.55 (((exuI3) =>
% 106.27/14.55 (((exuI2) =>
% 106.27/14.55 (((inCongP) =>
% 106.27/14.55 (((in__Cong) =>
% 106.27/14.55 (((exuE3u) =>
% 106.27/14.55 (((exu__Cong) =>
% 106.27/14.55 (((setadjoin__Cong) =>
% 106.27/14.55 (((powerset__Cong) =>
% 106.27/14.55 (((setunion__Cong) =>
% 106.27/14.55 (((exuEu) =>
% 106.27/14.55 (((descr__Cong) =>
% 106.27/14.55 (((dsetconstr__Cong) =>
% 106.27/14.55 (((subsetI1) =>
% 106.27/14.55 (((eqimpsubset2) =>
% 106.27/14.55 (((eqimpsubset1) =>
% 106.27/14.55 (((subsetI2) =>
% 106.27/14.55 (((emptysetsubset) =>
% 106.27/14.55 (((subsetE) =>
% 106.27/14.55 (((subsetE2) =>
% 106.27/14.55 (((notsubsetI) =>
% 106.27/14.55 (((notequalI1) =>
% 106.27/14.55 (((notequalI2) =>
% 106.27/14.55 (((subsetRefl) =>
% 106.27/14.55 (((subsetTrans) =>
% 106.27/14.55 (((setadjoinSub) =>
% 106.27/14.55 ((
% 106.27/14.55 (setadjoinSub2) =>
% 106.27/14.55 ((
% 106.27/14.55 (subset2powerset) =>
% 106.27/14.55 ((
% 106.27/14.55 (setextsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (subsetemptysetimpeq) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (inPowerset) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetsubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (sepInPowerset) =>
% 106.27/14.55 ((
% 106.27/14.55 (sepSubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionIL) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairset2IR) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionIR) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionEcases) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionE) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionLsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionRsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectI) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset5) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectEL) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectLsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset2) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset3) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectER) =>
% 106.27/14.55 ((
% 106.27/14.55 (disjointsetsI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectRsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset4) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset1) =>
% 106.27/14.55 ((
% 106.27/14.55 (bs114d) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusI) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusEL) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusER) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusSubset2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusERneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusELneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusILneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusIRneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusLsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusSubset1) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffE) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffI2) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffIneg1) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffIneg2) =>
% 106.27/14.55 ((
% 106.27/14.55 (secondinupair) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairIL) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairIR) =>
% 106.27/14.55 ((
% 106.27/14.55 (kpairiskpair) =>
% 106.27/14.55 ((
% 106.27/14.55 (kpairp) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletonsubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletoninpowerset) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletoninpowunion) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairset2E) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairsubunion) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairinpowunion) =>
% 106.27/14.55 ((
% 106.27/14.55 (ubforcartprodlem1) =>
% 106.27/14.55 ((
% 106.27/14.55 (ubforcartprodlem2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ubforcartprodlem3) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairin) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodmempair1) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodmempair) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionE2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionsingleton1) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionsingleton2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionsingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletonprop) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1E1) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1I) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1I2) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletonsuniq) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjL1) =>
% 106.27/14.55 ((
% 106.27/14.55 (kfstsingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (theprop) =>
% 106.27/14.55 ((
% 106.27/14.55 (kfstpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodfstin) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjL2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjL) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR11) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR12) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR1) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairequniteq) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR) =>
% 106.27/14.55 ((
% 106.27/14.55 (ksndsingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (ksndpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (kpairsurjEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodsndin) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairmemEL) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairmemER) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodmempaircEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodfstpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodsndpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairsurjEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrI) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrSub) =>
% 106.27/14.55 ((
% 106.27/14.55 (setOfPairsIsBReln) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrERa) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrEL1) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrEL2) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrER) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcImageSingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (apProp) =>
% 106.27/14.55 ((
% 106.27/14.55 (app) =>
% 106.27/14.55 ((
% 106.27/14.55 (infuncsetfunc) =>
% 106.27/14.55 ((
% 106.27/14.55 (ap2p) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcinfuncset) =>
% 106.27/14.55 ((
% 106.27/14.55 (lamProp) =>
% 106.27/14.55 ((
% 106.27/14.55 (lamp) =>
% 106.27/14.55 ((
% 106.27/14.55 (lam2p) =>
% 106.27/14.55 ((
% 106.27/14.55 (brelnall1) =>
% 106.27/14.55 ((
% 106.27/14.55 (brelnall2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1E2) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp1) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp3) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp2) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcextLem) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp4) =>
% 106.27/14.55 ((
% 106.27/14.55 (subbreln) =>
% 106.27/14.55 ((
% 106.27/14.55 (eqbreln) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcext) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcext2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ap2apEq1) =>
% 106.27/14.55 ((
% 106.27/14.55 (ap2apEq2) =>
% 106.27/14.55 ((
% 106.27/14.55 (beta1) =>
% 106.27/14.55 ((
% 106.27/14.55 (eta1) =>
% 106.27/14.55 ((
% 106.27/14.55 (lam2lamEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (beta2) =>
% 106.27/14.55 ((
% 106.27/14.55 (eta2) =>
% 106.27/14.55 ((
% 106.27/14.55 (iffalseProp1) =>
% 106.27/14.55 ((
% 106.27/14.55 (iffalseProp2) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrueProp1) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrueProp2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ifSingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (ifp) =>
% 106.27/14.55 ((
% 106.27/14.55 (theeq) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrue) =>
% 106.27/14.55 ((
% 106.27/14.55 (iffalse) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrueorfalse) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (setextT) =>
% 106.27/14.55 ((
% 106.27/14.55 (subsetTI) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetTI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetTE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectTELcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectTERcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT1) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT2) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT3) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementSub1) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementSub2) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTnotintersectT) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementImpComplementIntersect) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementSubsetComplementIntersect) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementInPowersetComplementIntersect) =>
% 106.27/14.55 ((
% 106.27/14.55 (contraSubsetComplement) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTcontraSubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionTILcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionTIRcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (inIntersectImpInUnion) =>
% 106.27/14.55 ((
% 106.27/14.55 (inIntersectImpInUnion2) =>
% 106.27/14.55 ((
% 106.27/14.55 (inIntersectImpInIntersectUnions) =>
% 106.27/14.55 ((
% 106.27/14.55 (intersectInPowersetIntersectUnions) =>
% 106.27/14.55 ((
% 106.27/14.55 (inComplementUnionImpNotIn1) =>
% 106.27/14.55 ((
% 106.27/14.55 (inComplementUnionImpInComplement1) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionTE) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionTEcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2a1) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementUnionInPowersetComplement) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2a2) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan1a) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan1b) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan1) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2a) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2b2) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2b) =>
% 106.27/14.55 ((
% 106.27/14.55 (demorgan2) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule0) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule1) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule2) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule3) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz13rule4) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_1) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_2) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_3) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_4) =>
% 106.27/14.55 ((
% 106.27/14.55 (woz1_5) =>
% 106.27/14.55 ((
% 106.27/14.55 (breln1all2) =>
% 106.27/14.55 ((
% 106.27/14.55 (!!) @ (
% 106.27/14.55 (('#B') @ (
% 106.27/14.55 !!) @
% 106.27/14.55 (
% 106.27/14.55 (
% 106.27/14.55 ('#S') @ (
% 106.27/14.55 (
% 106.27/14.55 ('#B') @ (
% 106.27/14.55 '#S') @
% 106.27/14.55 (
% 106.27/14.55 (
% 106.27/14.55 ('#B') @ (
% 106.27/14.55 (
% 106.27/14.55 ('#B') @ (
% 106.27/14.55 =>))) @
% 106.27/14.55 (
% 106.27/14.55 (
% 106.27/14.55 ('#B') @ (
% 106.27/14.55 (
% 106.27/14.55 ('#C') @ in)) @
% 106.27/14.55 breln1Set)))))) @
% 106.27/14.55 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])).
% 106.27/14.55 thf(zip_derived_cl578, plain,
% 106.27/14.55 (~ (((prop2set2propI) =>
% 106.27/14.55 (((notdexE) =>
% 106.27/14.55 (((notdallE) =>
% 106.27/14.55 (((exuI1) =>
% 106.27/14.55 (((exuI3) =>
% 106.27/14.55 (((exuI2) =>
% 106.27/14.55 (((inCongP) =>
% 106.27/14.55 (((in__Cong) =>
% 106.27/14.55 (((exuE3u) =>
% 106.27/14.55 (((exu__Cong) =>
% 106.27/14.55 (((setadjoin__Cong) =>
% 106.27/14.55 (((powerset__Cong) =>
% 106.27/14.55 (((setunion__Cong) =>
% 106.27/14.55 (((exuEu) =>
% 106.27/14.55 (((descr__Cong) =>
% 106.27/14.55 (((dsetconstr__Cong) =>
% 106.27/14.55 (((subsetI1) =>
% 106.27/14.55 (((eqimpsubset2) =>
% 106.27/14.55 (((eqimpsubset1) =>
% 106.27/14.55 (((subsetI2) =>
% 106.27/14.55 (((emptysetsubset) =>
% 106.27/14.55 (((subsetE) =>
% 106.27/14.55 (((subsetE2) =>
% 106.27/14.55 (((notsubsetI) =>
% 106.27/14.55 (((notequalI1) =>
% 106.27/14.55 (((notequalI2) =>
% 106.27/14.55 (((subsetRefl) =>
% 106.27/14.55 (((subsetTrans) =>
% 106.27/14.55 (((setadjoinSub) =>
% 106.27/14.55 (((setadjoinSub2) =>
% 106.27/14.55 ((
% 106.27/14.55 (subset2powerset) =>
% 106.27/14.55 ((
% 106.27/14.55 (setextsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (subsetemptysetimpeq) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (inPowerset) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetsubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (sepInPowerset) =>
% 106.27/14.55 ((
% 106.27/14.55 (sepSubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionIL) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairset2IR) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionIR) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionEcases) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionE) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionLsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionRsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectI) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset5) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectEL) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectLsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset2) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset3) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectER) =>
% 106.27/14.55 ((
% 106.27/14.55 (disjointsetsI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectRsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset4) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectSubset1) =>
% 106.27/14.55 ((
% 106.27/14.55 (bs114d) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusI) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusEL) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusER) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusSubset2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusERneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusELneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusILneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusIRneg) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusLsub) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusSubset1) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffE) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffI2) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffIneg1) =>
% 106.27/14.55 ((
% 106.27/14.55 (symdiffIneg2) =>
% 106.27/14.55 ((
% 106.27/14.55 (secondinupair) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairIL) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairIR) =>
% 106.27/14.55 ((
% 106.27/14.55 (kpairiskpair) =>
% 106.27/14.55 ((
% 106.27/14.55 (kpairp) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletonsubset) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletoninpowerset) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletoninpowunion) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairset2E) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairsubunion) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairinpowunion) =>
% 106.27/14.55 ((
% 106.27/14.55 (ubforcartprodlem1) =>
% 106.27/14.55 ((
% 106.27/14.55 (ubforcartprodlem2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ubforcartprodlem3) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairin) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodmempair1) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodmempair) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionE2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionsingleton1) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionsingleton2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setunionsingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletonprop) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1E1) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1I) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1I2) =>
% 106.27/14.55 ((
% 106.27/14.55 (singletonsuniq) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjL1) =>
% 106.27/14.55 ((
% 106.27/14.55 (kfstsingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (theprop) =>
% 106.27/14.55 ((
% 106.27/14.55 (kfstpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodfstin) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjL2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjL) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR11) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR12) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR1) =>
% 106.27/14.55 ((
% 106.27/14.55 (upairequniteq) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR2) =>
% 106.27/14.55 ((
% 106.27/14.55 (setukpairinjR) =>
% 106.27/14.55 ((
% 106.27/14.55 (ksndsingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (ksndpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (kpairsurjEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodsndin) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairmemEL) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairmemER) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodmempaircEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodfstpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodsndpairEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (cartprodpairsurjEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrI) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrSub) =>
% 106.27/14.55 ((
% 106.27/14.55 (setOfPairsIsBReln) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrERa) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrEL1) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrEL2) =>
% 106.27/14.55 ((
% 106.27/14.55 (dpsetconstrER) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcImageSingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (apProp) =>
% 106.27/14.55 ((
% 106.27/14.55 (app) =>
% 106.27/14.55 ((
% 106.27/14.55 (infuncsetfunc) =>
% 106.27/14.55 ((
% 106.27/14.55 (ap2p) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcinfuncset) =>
% 106.27/14.55 ((
% 106.27/14.55 (lamProp) =>
% 106.27/14.55 ((
% 106.27/14.55 (lamp) =>
% 106.27/14.55 ((
% 106.27/14.55 (lam2p) =>
% 106.27/14.55 ((
% 106.27/14.55 (brelnall1) =>
% 106.27/14.55 ((
% 106.27/14.55 (brelnall2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ex1E2) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp1) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp3) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp2) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcextLem) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcGraphProp4) =>
% 106.27/14.55 ((
% 106.27/14.55 (subbreln) =>
% 106.27/14.55 ((
% 106.27/14.55 (eqbreln) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcext) =>
% 106.27/14.55 ((
% 106.27/14.55 (funcext2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ap2apEq1) =>
% 106.27/14.55 ((
% 106.27/14.55 (ap2apEq2) =>
% 106.27/14.55 ((
% 106.27/14.55 (beta1) =>
% 106.27/14.55 ((
% 106.27/14.55 (eta1) =>
% 106.27/14.55 ((
% 106.27/14.55 (lam2lamEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (beta2) =>
% 106.27/14.55 ((
% 106.27/14.55 (eta2) =>
% 106.27/14.55 ((
% 106.27/14.55 (iffalseProp1) =>
% 106.27/14.55 ((
% 106.27/14.55 (iffalseProp2) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrueProp1) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrueProp2) =>
% 106.27/14.55 ((
% 106.27/14.55 (ifSingleton) =>
% 106.27/14.55 ((
% 106.27/14.55 (ifp) =>
% 106.27/14.55 ((
% 106.27/14.55 (theeq) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrue) =>
% 106.27/14.55 ((
% 106.27/14.55 (iffalse) =>
% 106.27/14.55 ((
% 106.27/14.55 (iftrueorfalse) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (binunionT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (setminusT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementT_lem) =>
% 106.27/14.55 ((
% 106.27/14.55 (setextT) =>
% 106.27/14.55 ((
% 106.27/14.55 (subsetTI) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetTI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (powersetTE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectTELcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (binintersectTERcontra) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT1) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT2) =>
% 106.27/14.55 ((
% 106.27/14.55 (contrasubsetT3) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementI1) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementE1) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementSub1) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementSub2) =>
% 106.27/14.55 ((
% 106.27/14.55 (doubleComplementEq) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementTnotintersectT) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementImpComplementIntersect) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementSubsetComplementIntersect) =>
% 106.27/14.55 ((
% 106.27/14.55 (complementInPowersetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (contraSubsetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTcontraSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTILcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTIRcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion2) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (intersectInPowersetIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpNotIn1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpInComplement1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTEcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementUnionInPowersetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule0) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_5) =>
% 106.27/14.56 ((
% 106.27/14.56 (breln1all2) =>
% 106.27/14.56 ((
% 106.27/14.56 (!!) @ (
% 106.27/14.56 (('#B') @ (
% 106.27/14.56 !!) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#S') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 '#S') @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 =>))) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#C') @ in)) @
% 106.27/14.56 breln1Set)))))) @
% 106.27/14.56 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl570])).
% 106.27/14.56 thf(zip_derived_cl586, plain,
% 106.27/14.56 (~ (((notdexE) =>
% 106.27/14.56 (((notdallE) =>
% 106.27/14.56 (((exuI1) =>
% 106.27/14.56 (((exuI3) =>
% 106.27/14.56 (((exuI2) =>
% 106.27/14.56 (((inCongP) =>
% 106.27/14.56 (((in__Cong) =>
% 106.27/14.56 (((exuE3u) =>
% 106.27/14.56 (((exu__Cong) =>
% 106.27/14.56 (((setadjoin__Cong) =>
% 106.27/14.56 (((powerset__Cong) =>
% 106.27/14.56 (((setunion__Cong) =>
% 106.27/14.56 (((exuEu) =>
% 106.27/14.56 (((descr__Cong) =>
% 106.27/14.56 (((dsetconstr__Cong) =>
% 106.27/14.56 (((subsetI1) =>
% 106.27/14.56 (((eqimpsubset2) =>
% 106.27/14.56 (((eqimpsubset1) =>
% 106.27/14.56 (((subsetI2) =>
% 106.27/14.56 (((emptysetsubset) =>
% 106.27/14.56 (((subsetE) =>
% 106.27/14.56 (((subsetE2) =>
% 106.27/14.56 (((notsubsetI) =>
% 106.27/14.56 (((notequalI1) =>
% 106.27/14.56 (((notequalI2) =>
% 106.27/14.56 (((subsetRefl) =>
% 106.27/14.56 (((subsetTrans) =>
% 106.27/14.56 (((setadjoinSub) =>
% 106.27/14.56 (((setadjoinSub2) =>
% 106.27/14.56 (((subset2powerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (setextsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (subsetemptysetimpeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepInPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2IR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionEcases) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectI) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset5) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset3) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectER) =>
% 106.27/14.56 ((
% 106.27/14.56 (disjointsetsI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset4) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (bs114d) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusI) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusER) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusERneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusELneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusILneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusIRneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffE) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI2) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg2) =>
% 106.27/14.56 ((
% 106.27/14.56 (secondinupair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairiskpair) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairp) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2E) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairsubunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairinpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem3) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair1) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionE2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton1) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I2) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsuniq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (theprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstin) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR11) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR12) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR1) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairequniteq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemER) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempaircEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrI) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrSub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setOfPairsIsBReln) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrERa) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrER) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcImageSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (apProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (app) =>
% 106.27/14.56 ((
% 106.27/14.56 (infuncsetfunc) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcinfuncset) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall1) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp3) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcextLem) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp4) =>
% 106.27/14.56 ((
% 106.27/14.56 (subbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (eqbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq2) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2lamEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifp) =>
% 106.27/14.56 ((
% 106.27/14.56 (theeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrue) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueorfalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setextT) =>
% 106.27/14.56 ((
% 106.27/14.56 (subsetTI) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTELcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTERcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT1) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT2) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT3) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub2) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTnotintersectT) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementImpComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementSubsetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementInPowersetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (contraSubsetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTcontraSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTILcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTIRcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion2) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (intersectInPowersetIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpNotIn1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpInComplement1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTEcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementUnionInPowersetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule0) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_5) =>
% 106.27/14.56 ((
% 106.27/14.56 (breln1all2) =>
% 106.27/14.56 ((
% 106.27/14.56 (!!) @ (
% 106.27/14.56 (('#B') @ (
% 106.27/14.56 !!) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#S') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 '#S') @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 =>))) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#C') @ in)) @
% 106.27/14.56 breln1Set)))))) @
% 106.27/14.56 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 106.27/14.56 thf(zip_derived_cl595, plain,
% 106.27/14.56 (~ (((notdallE) =>
% 106.27/14.56 (((exuI1) =>
% 106.27/14.56 (((exuI3) =>
% 106.27/14.56 (((exuI2) =>
% 106.27/14.56 (((inCongP) =>
% 106.27/14.56 (((in__Cong) =>
% 106.27/14.56 (((exuE3u) =>
% 106.27/14.56 (((exu__Cong) =>
% 106.27/14.56 (((setadjoin__Cong) =>
% 106.27/14.56 (((powerset__Cong) =>
% 106.27/14.56 (((setunion__Cong) =>
% 106.27/14.56 (((exuEu) =>
% 106.27/14.56 (((descr__Cong) =>
% 106.27/14.56 (((dsetconstr__Cong) =>
% 106.27/14.56 (((subsetI1) =>
% 106.27/14.56 (((eqimpsubset2) =>
% 106.27/14.56 (((eqimpsubset1) =>
% 106.27/14.56 (((subsetI2) =>
% 106.27/14.56 (((emptysetsubset) =>
% 106.27/14.56 (((subsetE) =>
% 106.27/14.56 (((subsetE2) =>
% 106.27/14.56 (((notsubsetI) =>
% 106.27/14.56 (((notequalI1) =>
% 106.27/14.56 (((notequalI2) =>
% 106.27/14.56 (((subsetRefl) =>
% 106.27/14.56 (((subsetTrans) =>
% 106.27/14.56 (((setadjoinSub) =>
% 106.27/14.56 (((setadjoinSub2) =>
% 106.27/14.56 (((subset2powerset) =>
% 106.27/14.56 (((setextsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (subsetemptysetimpeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepInPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2IR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionEcases) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectI) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset5) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset3) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectER) =>
% 106.27/14.56 ((
% 106.27/14.56 (disjointsetsI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset4) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (bs114d) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusI) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusER) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusERneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusELneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusILneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusIRneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffE) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI2) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg2) =>
% 106.27/14.56 ((
% 106.27/14.56 (secondinupair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairiskpair) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairp) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2E) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairsubunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairinpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem3) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair1) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionE2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton1) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I2) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsuniq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (theprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstin) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR11) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR12) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR1) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairequniteq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemER) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempaircEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrI) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrSub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setOfPairsIsBReln) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrERa) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrER) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcImageSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (apProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (app) =>
% 106.27/14.56 ((
% 106.27/14.56 (infuncsetfunc) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcinfuncset) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall1) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp3) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcextLem) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp4) =>
% 106.27/14.56 ((
% 106.27/14.56 (subbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (eqbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq2) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2lamEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifp) =>
% 106.27/14.56 ((
% 106.27/14.56 (theeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrue) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueorfalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setextT) =>
% 106.27/14.56 ((
% 106.27/14.56 (subsetTI) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTELcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTERcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT1) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT2) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT3) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub2) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTnotintersectT) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementImpComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementSubsetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementInPowersetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (contraSubsetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTcontraSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTILcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTIRcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion2) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (intersectInPowersetIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpNotIn1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpInComplement1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTEcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementUnionInPowersetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule0) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_5) =>
% 106.27/14.56 ((
% 106.27/14.56 (breln1all2) =>
% 106.27/14.56 ((
% 106.27/14.56 (!!) @ (
% 106.27/14.56 (('#B') @ (
% 106.27/14.56 !!) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#S') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 '#S') @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 =>))) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#C') @ in)) @
% 106.27/14.56 breln1Set)))))) @
% 106.27/14.56 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl586])).
% 106.27/14.56 thf(zip_derived_cl606, plain,
% 106.27/14.56 (~ (((exuI1) =>
% 106.27/14.56 (((exuI3) =>
% 106.27/14.56 (((exuI2) =>
% 106.27/14.56 (((inCongP) =>
% 106.27/14.56 (((in__Cong) =>
% 106.27/14.56 (((exuE3u) =>
% 106.27/14.56 (((exu__Cong) =>
% 106.27/14.56 (((setadjoin__Cong) =>
% 106.27/14.56 (((powerset__Cong) =>
% 106.27/14.56 (((setunion__Cong) =>
% 106.27/14.56 (((exuEu) =>
% 106.27/14.56 (((descr__Cong) =>
% 106.27/14.56 (((dsetconstr__Cong) =>
% 106.27/14.56 (((subsetI1) =>
% 106.27/14.56 (((eqimpsubset2) =>
% 106.27/14.56 (((eqimpsubset1) =>
% 106.27/14.56 (((subsetI2) =>
% 106.27/14.56 (((emptysetsubset) =>
% 106.27/14.56 (((subsetE) =>
% 106.27/14.56 (((subsetE2) =>
% 106.27/14.56 (((notsubsetI) =>
% 106.27/14.56 (((notequalI1) =>
% 106.27/14.56 (((notequalI2) =>
% 106.27/14.56 (((subsetRefl) =>
% 106.27/14.56 (((subsetTrans) =>
% 106.27/14.56 (((setadjoinSub) =>
% 106.27/14.56 (((setadjoinSub2) =>
% 106.27/14.56 (((subset2powerset) =>
% 106.27/14.56 (((setextsub) =>
% 106.27/14.56 (((subsetemptysetimpeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepInPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2IR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionEcases) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectI) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset5) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset3) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectER) =>
% 106.27/14.56 ((
% 106.27/14.56 (disjointsetsI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset4) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (bs114d) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusI) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusER) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusERneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusELneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusILneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusIRneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffE) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI2) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg2) =>
% 106.27/14.56 ((
% 106.27/14.56 (secondinupair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairiskpair) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairp) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2E) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairsubunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairinpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem3) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair1) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionE2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton1) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I2) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsuniq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (theprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstin) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR11) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR12) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR1) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairequniteq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemER) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempaircEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrI) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrSub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setOfPairsIsBReln) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrERa) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrER) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcImageSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (apProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (app) =>
% 106.27/14.56 ((
% 106.27/14.56 (infuncsetfunc) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcinfuncset) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall1) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp3) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcextLem) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp4) =>
% 106.27/14.56 ((
% 106.27/14.56 (subbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (eqbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq2) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2lamEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifp) =>
% 106.27/14.56 ((
% 106.27/14.56 (theeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrue) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueorfalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setextT) =>
% 106.27/14.56 ((
% 106.27/14.56 (subsetTI) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTELcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTERcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT1) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT2) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT3) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub2) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTnotintersectT) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementImpComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementSubsetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementInPowersetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (contraSubsetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTcontraSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTILcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTIRcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion2) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (intersectInPowersetIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpNotIn1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpInComplement1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTEcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementUnionInPowersetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule0) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_5) =>
% 106.27/14.56 ((
% 106.27/14.56 (breln1all2) =>
% 106.27/14.56 ((
% 106.27/14.56 (!!) @ (
% 106.27/14.56 (('#B') @ (
% 106.27/14.56 !!) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#S') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 '#S') @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 =>))) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#C') @ in)) @
% 106.27/14.56 breln1Set)))))) @
% 106.27/14.56 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])).
% 106.27/14.56 thf(zip_derived_cl619, plain,
% 106.27/14.56 (~ (((exuI3) =>
% 106.27/14.56 (((exuI2) =>
% 106.27/14.56 (((inCongP) =>
% 106.27/14.56 (((in__Cong) =>
% 106.27/14.56 (((exuE3u) =>
% 106.27/14.56 (((exu__Cong) =>
% 106.27/14.56 (((setadjoin__Cong) =>
% 106.27/14.56 (((powerset__Cong) =>
% 106.27/14.56 (((setunion__Cong) =>
% 106.27/14.56 (((exuEu) =>
% 106.27/14.56 (((descr__Cong) =>
% 106.27/14.56 (((dsetconstr__Cong) =>
% 106.27/14.56 (((subsetI1) =>
% 106.27/14.56 (((eqimpsubset2) =>
% 106.27/14.56 (((eqimpsubset1) =>
% 106.27/14.56 (((subsetI2) =>
% 106.27/14.56 (((emptysetsubset) =>
% 106.27/14.56 (((subsetE) =>
% 106.27/14.56 (((subsetE2) =>
% 106.27/14.56 (((notsubsetI) =>
% 106.27/14.56 (((notequalI1) =>
% 106.27/14.56 (((notequalI2) =>
% 106.27/14.56 (((subsetRefl) =>
% 106.27/14.56 (((subsetTrans) =>
% 106.27/14.56 (((setadjoinSub) =>
% 106.27/14.56 (((setadjoinSub2) =>
% 106.27/14.56 (((subset2powerset) =>
% 106.27/14.56 (((setextsub) =>
% 106.27/14.56 (((subsetemptysetimpeq) =>
% 106.27/14.56 (((powersetI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepInPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2IR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionEcases) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectI) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset5) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset3) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectER) =>
% 106.27/14.56 ((
% 106.27/14.56 (disjointsetsI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset4) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (bs114d) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusI) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusER) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusERneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusELneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusILneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusIRneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffE) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI2) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg2) =>
% 106.27/14.56 ((
% 106.27/14.56 (secondinupair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairiskpair) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairp) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2E) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairsubunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairinpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem3) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair1) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionE2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton1) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I2) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsuniq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (theprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstin) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR11) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR12) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR1) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairequniteq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemER) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempaircEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrI) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrSub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setOfPairsIsBReln) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrERa) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrER) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcImageSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (apProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (app) =>
% 106.27/14.56 ((
% 106.27/14.56 (infuncsetfunc) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcinfuncset) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall1) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp3) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcextLem) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp4) =>
% 106.27/14.56 ((
% 106.27/14.56 (subbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (eqbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq2) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2lamEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifp) =>
% 106.27/14.56 ((
% 106.27/14.56 (theeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrue) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueorfalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setextT) =>
% 106.27/14.56 ((
% 106.27/14.56 (subsetTI) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTELcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTERcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT1) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT2) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT3) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub2) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTnotintersectT) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementImpComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementSubsetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementInPowersetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (contraSubsetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTcontraSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTILcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTIRcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion2) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (intersectInPowersetIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpNotIn1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpInComplement1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTEcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementUnionInPowersetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule0) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_5) =>
% 106.27/14.56 ((
% 106.27/14.56 (breln1all2) =>
% 106.27/14.56 ((
% 106.27/14.56 (!!) @ (
% 106.27/14.56 (('#B') @ (
% 106.27/14.56 !!) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#S') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 '#S') @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 =>))) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#C') @ in)) @
% 106.27/14.56 breln1Set)))))) @
% 106.27/14.56 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])).
% 106.27/14.56 thf(zip_derived_cl630, plain,
% 106.27/14.56 (~ (((exuI2) =>
% 106.27/14.56 (((inCongP) =>
% 106.27/14.56 (((in__Cong) =>
% 106.27/14.56 (((exuE3u) =>
% 106.27/14.56 (((exu__Cong) =>
% 106.27/14.56 (((setadjoin__Cong) =>
% 106.27/14.56 (((powerset__Cong) =>
% 106.27/14.56 (((setunion__Cong) =>
% 106.27/14.56 (((exuEu) =>
% 106.27/14.56 (((descr__Cong) =>
% 106.27/14.56 (((dsetconstr__Cong) =>
% 106.27/14.56 (((subsetI1) =>
% 106.27/14.56 (((eqimpsubset2) =>
% 106.27/14.56 (((eqimpsubset1) =>
% 106.27/14.56 (((subsetI2) =>
% 106.27/14.56 (((emptysetsubset) =>
% 106.27/14.56 (((subsetE) =>
% 106.27/14.56 (((subsetE2) =>
% 106.27/14.56 (((notsubsetI) =>
% 106.27/14.56 (((notequalI1) =>
% 106.27/14.56 (((notequalI2) =>
% 106.27/14.56 (((subsetRefl) =>
% 106.27/14.56 (((subsetTrans) =>
% 106.27/14.56 (((setadjoinSub) =>
% 106.27/14.56 (((setadjoinSub2) =>
% 106.27/14.56 (((subset2powerset) =>
% 106.27/14.56 (((setextsub) =>
% 106.27/14.56 (((subsetemptysetimpeq) =>
% 106.27/14.56 (((powersetI1) =>
% 106.27/14.56 (((powersetE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepInPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2IR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionEcases) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectI) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset5) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset3) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectER) =>
% 106.27/14.56 ((
% 106.27/14.56 (disjointsetsI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset4) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (bs114d) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusI) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusER) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusERneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusELneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusILneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusIRneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffE) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI2) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg2) =>
% 106.27/14.56 ((
% 106.27/14.56 (secondinupair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairiskpair) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairp) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2E) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairsubunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairinpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem3) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair1) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionE2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton1) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I2) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsuniq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (theprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstin) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR11) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR12) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR1) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairequniteq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemER) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempaircEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrI) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrSub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setOfPairsIsBReln) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrERa) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrER) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcImageSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (apProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (app) =>
% 106.27/14.56 ((
% 106.27/14.56 (infuncsetfunc) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcinfuncset) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall1) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp3) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcextLem) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp4) =>
% 106.27/14.56 ((
% 106.27/14.56 (subbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (eqbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq2) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2lamEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifp) =>
% 106.27/14.56 ((
% 106.27/14.56 (theeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrue) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueorfalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setextT) =>
% 106.27/14.56 ((
% 106.27/14.56 (subsetTI) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTELcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTERcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT1) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT2) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT3) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub2) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTnotintersectT) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementImpComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementSubsetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementInPowersetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (contraSubsetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTcontraSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTILcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTIRcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion2) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (intersectInPowersetIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpNotIn1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpInComplement1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTEcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementUnionInPowersetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule0) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_5) =>
% 106.27/14.56 ((
% 106.27/14.56 (breln1all2) =>
% 106.27/14.56 ((
% 106.27/14.56 (!!) @ (
% 106.27/14.56 (('#B') @ (
% 106.27/14.56 !!) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#S') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 '#S') @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 =>))) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#C') @ in)) @
% 106.27/14.56 breln1Set)))))) @
% 106.27/14.56 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl619])).
% 106.27/14.56 thf(zip_derived_cl640, plain,
% 106.27/14.56 (~ (((inCongP) =>
% 106.27/14.56 (((in__Cong) =>
% 106.27/14.56 (((exuE3u) =>
% 106.27/14.56 (((exu__Cong) =>
% 106.27/14.56 (((setadjoin__Cong) =>
% 106.27/14.56 (((powerset__Cong) =>
% 106.27/14.56 (((setunion__Cong) =>
% 106.27/14.56 (((exuEu) =>
% 106.27/14.56 (((descr__Cong) =>
% 106.27/14.56 (((dsetconstr__Cong) =>
% 106.27/14.56 (((subsetI1) =>
% 106.27/14.56 (((eqimpsubset2) =>
% 106.27/14.56 (((eqimpsubset1) =>
% 106.27/14.56 (((subsetI2) =>
% 106.27/14.56 (((emptysetsubset) =>
% 106.27/14.56 (((subsetE) =>
% 106.27/14.56 (((subsetE2) =>
% 106.27/14.56 (((notsubsetI) =>
% 106.27/14.56 (((notequalI1) =>
% 106.27/14.56 (((notequalI2) =>
% 106.27/14.56 (((subsetRefl) =>
% 106.27/14.56 (((subsetTrans) =>
% 106.27/14.56 (((setadjoinSub) =>
% 106.27/14.56 (((setadjoinSub2) =>
% 106.27/14.56 (((subset2powerset) =>
% 106.27/14.56 (((setextsub) =>
% 106.27/14.56 (((subsetemptysetimpeq) =>
% 106.27/14.56 (((powersetI1) =>
% 106.27/14.56 (((powersetE1) =>
% 106.27/14.56 (((inPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepInPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2IR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionEcases) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectI) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset5) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset3) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectER) =>
% 106.27/14.56 ((
% 106.27/14.56 (disjointsetsI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset4) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (bs114d) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusI) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusER) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusERneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusELneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusILneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusIRneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffE) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI2) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg2) =>
% 106.27/14.56 ((
% 106.27/14.56 (secondinupair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairiskpair) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairp) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2E) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairsubunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairinpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem3) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair1) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionE2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton1) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I2) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsuniq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (theprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstin) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR11) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR12) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR1) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairequniteq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemER) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempaircEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrI) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrSub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setOfPairsIsBReln) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrERa) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrER) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcImageSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (apProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (app) =>
% 106.27/14.56 ((
% 106.27/14.56 (infuncsetfunc) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcinfuncset) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall1) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp3) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcextLem) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp4) =>
% 106.27/14.56 ((
% 106.27/14.56 (subbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (eqbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq2) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2lamEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifp) =>
% 106.27/14.56 ((
% 106.27/14.56 (theeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrue) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueorfalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setextT) =>
% 106.27/14.56 ((
% 106.27/14.56 (subsetTI) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTELcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTERcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT1) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT2) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT3) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub2) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTnotintersectT) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementImpComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementSubsetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementInPowersetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (contraSubsetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTcontraSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTILcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTIRcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion2) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (intersectInPowersetIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpNotIn1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpInComplement1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTEcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementUnionInPowersetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule0) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_5) =>
% 106.27/14.56 ((
% 106.27/14.56 (breln1all2) =>
% 106.27/14.56 ((
% 106.27/14.56 (!!) @ (
% 106.27/14.56 (('#B') @ (
% 106.27/14.56 !!) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#S') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 '#S') @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 =>))) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#C') @ in)) @
% 106.27/14.56 breln1Set)))))) @
% 106.27/14.56 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl630])).
% 106.27/14.56 thf(zip_derived_cl650, plain,
% 106.27/14.56 (~ (((in__Cong) =>
% 106.27/14.56 (((exuE3u) =>
% 106.27/14.56 (((exu__Cong) =>
% 106.27/14.56 (((setadjoin__Cong) =>
% 106.27/14.56 (((powerset__Cong) =>
% 106.27/14.56 (((setunion__Cong) =>
% 106.27/14.56 (((exuEu) =>
% 106.27/14.56 (((descr__Cong) =>
% 106.27/14.56 (((dsetconstr__Cong) =>
% 106.27/14.56 (((subsetI1) =>
% 106.27/14.56 (((eqimpsubset2) =>
% 106.27/14.56 (((eqimpsubset1) =>
% 106.27/14.56 (((subsetI2) =>
% 106.27/14.56 (((emptysetsubset) =>
% 106.27/14.56 (((subsetE) =>
% 106.27/14.56 (((subsetE2) =>
% 106.27/14.56 (((notsubsetI) =>
% 106.27/14.56 (((notequalI1) =>
% 106.27/14.56 (((notequalI2) =>
% 106.27/14.56 (((subsetRefl) =>
% 106.27/14.56 (((subsetTrans) =>
% 106.27/14.56 (((setadjoinSub) =>
% 106.27/14.56 (((setadjoinSub2) =>
% 106.27/14.56 (((subset2powerset) =>
% 106.27/14.56 (((setextsub) =>
% 106.27/14.56 (((subsetemptysetimpeq) =>
% 106.27/14.56 (((powersetI1) =>
% 106.27/14.56 (((powersetE1) =>
% 106.27/14.56 (((inPowerset) =>
% 106.27/14.56 (((powersetsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepInPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2IR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionEcases) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectI) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset5) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset3) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectER) =>
% 106.27/14.56 ((
% 106.27/14.56 (disjointsetsI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset4) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (bs114d) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusI) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusER) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusERneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusELneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusILneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusIRneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffE) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI2) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg2) =>
% 106.27/14.56 ((
% 106.27/14.56 (secondinupair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairiskpair) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairp) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2E) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairsubunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairinpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem3) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair1) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionE2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton1) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I2) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsuniq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (theprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstin) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR11) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR12) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR1) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairequniteq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemER) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempaircEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrI) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrSub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setOfPairsIsBReln) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrERa) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrER) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcImageSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (apProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (app) =>
% 106.27/14.56 ((
% 106.27/14.56 (infuncsetfunc) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcinfuncset) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall1) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp3) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcextLem) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp4) =>
% 106.27/14.56 ((
% 106.27/14.56 (subbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (eqbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq2) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2lamEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifp) =>
% 106.27/14.56 ((
% 106.27/14.56 (theeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrue) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueorfalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setextT) =>
% 106.27/14.56 ((
% 106.27/14.56 (subsetTI) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTELcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTERcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT1) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT2) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT3) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub2) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTnotintersectT) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementImpComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementSubsetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementInPowersetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (contraSubsetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTcontraSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTILcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTIRcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion2) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (intersectInPowersetIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpNotIn1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpInComplement1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTEcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementUnionInPowersetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule0) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_5) =>
% 106.27/14.56 ((
% 106.27/14.56 (breln1all2) =>
% 106.27/14.56 ((
% 106.27/14.56 (!!) @ (
% 106.27/14.56 (('#B') @ (
% 106.27/14.56 !!) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#S') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 '#S') @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 =>))) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#C') @ in)) @
% 106.27/14.56 breln1Set)))))) @
% 106.27/14.56 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
% 106.27/14.56 thf(zip_derived_cl660, plain,
% 106.27/14.56 (~ (((exuE3u) =>
% 106.27/14.56 (((exu__Cong) =>
% 106.27/14.56 (((setadjoin__Cong) =>
% 106.27/14.56 (((powerset__Cong) =>
% 106.27/14.56 (((setunion__Cong) =>
% 106.27/14.56 (((exuEu) =>
% 106.27/14.56 (((descr__Cong) =>
% 106.27/14.56 (((dsetconstr__Cong) =>
% 106.27/14.56 (((subsetI1) =>
% 106.27/14.56 (((eqimpsubset2) =>
% 106.27/14.56 (((eqimpsubset1) =>
% 106.27/14.56 (((subsetI2) =>
% 106.27/14.56 (((emptysetsubset) =>
% 106.27/14.56 (((subsetE) =>
% 106.27/14.56 (((subsetE2) =>
% 106.27/14.56 (((notsubsetI) =>
% 106.27/14.56 (((notequalI1) =>
% 106.27/14.56 (((notequalI2) =>
% 106.27/14.56 (((subsetRefl) =>
% 106.27/14.56 (((subsetTrans) =>
% 106.27/14.56 (((setadjoinSub) =>
% 106.27/14.56 (((setadjoinSub2) =>
% 106.27/14.56 (((subset2powerset) =>
% 106.27/14.56 (((setextsub) =>
% 106.27/14.56 (((subsetemptysetimpeq) =>
% 106.27/14.56 (((powersetI1) =>
% 106.27/14.56 (((powersetE1) =>
% 106.27/14.56 (((inPowerset) =>
% 106.27/14.56 (((powersetsubset) =>
% 106.27/14.56 (((sepInPowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (sepSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2IR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionEcases) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectI) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset5) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset3) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectER) =>
% 106.27/14.56 ((
% 106.27/14.56 (disjointsetsI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset4) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (bs114d) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusI) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusER) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusERneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusELneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusILneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusIRneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffE) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI2) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg2) =>
% 106.27/14.56 ((
% 106.27/14.56 (secondinupair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairiskpair) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairp) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2E) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairsubunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairinpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem3) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair1) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionE2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton1) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I2) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsuniq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (theprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstin) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR11) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR12) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR1) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairequniteq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemER) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempaircEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrI) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrSub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setOfPairsIsBReln) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrERa) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrER) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcImageSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (apProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (app) =>
% 106.27/14.56 ((
% 106.27/14.56 (infuncsetfunc) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcinfuncset) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall1) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp3) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcextLem) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp4) =>
% 106.27/14.56 ((
% 106.27/14.56 (subbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (eqbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq2) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2lamEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifp) =>
% 106.27/14.56 ((
% 106.27/14.56 (theeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrue) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueorfalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setextT) =>
% 106.27/14.56 ((
% 106.27/14.56 (subsetTI) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTELcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTERcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT1) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT2) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT3) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub2) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTnotintersectT) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementImpComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementSubsetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementInPowersetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (contraSubsetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTcontraSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTILcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTIRcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion2) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (intersectInPowersetIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpNotIn1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpInComplement1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTEcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementUnionInPowersetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule0) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_5) =>
% 106.27/14.56 ((
% 106.27/14.56 (breln1all2) =>
% 106.27/14.56 ((
% 106.27/14.56 (!!) @ (
% 106.27/14.56 (('#B') @ (
% 106.27/14.56 !!) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#S') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 '#S') @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 =>))) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#C') @ in)) @
% 106.27/14.56 breln1Set)))))) @
% 106.27/14.56 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
% 106.27/14.56 thf(zip_derived_cl672, plain,
% 106.27/14.56 (~ (((exu__Cong) =>
% 106.27/14.56 (((setadjoin__Cong) =>
% 106.27/14.56 (((powerset__Cong) =>
% 106.27/14.56 (((setunion__Cong) =>
% 106.27/14.56 (((exuEu) =>
% 106.27/14.56 (((descr__Cong) =>
% 106.27/14.56 (((dsetconstr__Cong) =>
% 106.27/14.56 (((subsetI1) =>
% 106.27/14.56 (((eqimpsubset2) =>
% 106.27/14.56 (((eqimpsubset1) =>
% 106.27/14.56 (((subsetI2) =>
% 106.27/14.56 (((emptysetsubset) =>
% 106.27/14.56 (((subsetE) =>
% 106.27/14.56 (((subsetE2) =>
% 106.27/14.56 (((notsubsetI) =>
% 106.27/14.56 (((notequalI1) =>
% 106.27/14.56 (((notequalI2) =>
% 106.27/14.56 (((subsetRefl) =>
% 106.27/14.56 (((subsetTrans) =>
% 106.27/14.56 (((setadjoinSub) =>
% 106.27/14.56 (((setadjoinSub2) =>
% 106.27/14.56 (((subset2powerset) =>
% 106.27/14.56 (((setextsub) =>
% 106.27/14.56 (((subsetemptysetimpeq) =>
% 106.27/14.56 (((powersetI1) =>
% 106.27/14.56 (((powersetE1) =>
% 106.27/14.56 (((inPowerset) =>
% 106.27/14.56 (((powersetsubset) =>
% 106.27/14.56 (((sepInPowerset) =>
% 106.27/14.56 (((sepSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2IR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionEcases) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectI) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset5) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset3) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectER) =>
% 106.27/14.56 ((
% 106.27/14.56 (disjointsetsI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset4) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (bs114d) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusI) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusER) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusERneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusELneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusILneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusIRneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffE) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI2) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg2) =>
% 106.27/14.56 ((
% 106.27/14.56 (secondinupair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairiskpair) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairp) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2E) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairsubunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairinpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem3) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair1) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionE2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton1) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I2) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsuniq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (theprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstin) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR11) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR12) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR1) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairequniteq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemER) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempaircEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrI) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrSub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setOfPairsIsBReln) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrERa) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrER) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcImageSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (apProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (app) =>
% 106.27/14.56 ((
% 106.27/14.56 (infuncsetfunc) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcinfuncset) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall1) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp3) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcextLem) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp4) =>
% 106.27/14.56 ((
% 106.27/14.56 (subbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (eqbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq2) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2lamEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifp) =>
% 106.27/14.56 ((
% 106.27/14.56 (theeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrue) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueorfalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setextT) =>
% 106.27/14.56 ((
% 106.27/14.56 (subsetTI) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTELcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTERcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT1) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT2) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT3) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub2) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTnotintersectT) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementImpComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementSubsetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementInPowersetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (contraSubsetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTcontraSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTILcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTIRcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion2) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (intersectInPowersetIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpNotIn1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpInComplement1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTEcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementUnionInPowersetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule0) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_5) =>
% 106.27/14.56 ((
% 106.27/14.56 (breln1all2) =>
% 106.27/14.56 ((
% 106.27/14.56 (!!) @ (
% 106.27/14.56 (('#B') @ (
% 106.27/14.56 !!) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#S') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 '#S') @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 =>))) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#C') @ in)) @
% 106.27/14.56 breln1Set)))))) @
% 106.27/14.56 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])).
% 106.27/14.56 thf(zip_derived_cl685, plain,
% 106.27/14.56 (~ (((setadjoin__Cong) =>
% 106.27/14.56 (((powerset__Cong) =>
% 106.27/14.56 (((setunion__Cong) =>
% 106.27/14.56 (((exuEu) =>
% 106.27/14.56 (((descr__Cong) =>
% 106.27/14.56 (((dsetconstr__Cong) =>
% 106.27/14.56 (((subsetI1) =>
% 106.27/14.56 (((eqimpsubset2) =>
% 106.27/14.56 (((eqimpsubset1) =>
% 106.27/14.56 (((subsetI2) =>
% 106.27/14.56 (((emptysetsubset) =>
% 106.27/14.56 (((subsetE) =>
% 106.27/14.56 (((subsetE2) =>
% 106.27/14.56 (((notsubsetI) =>
% 106.27/14.56 (((notequalI1) =>
% 106.27/14.56 (((notequalI2) =>
% 106.27/14.56 (((subsetRefl) =>
% 106.27/14.56 (((subsetTrans) =>
% 106.27/14.56 (((setadjoinSub) =>
% 106.27/14.56 (((setadjoinSub2) =>
% 106.27/14.56 (((subset2powerset) =>
% 106.27/14.56 (((setextsub) =>
% 106.27/14.56 (((subsetemptysetimpeq) =>
% 106.27/14.56 (((powersetI1) =>
% 106.27/14.56 (((powersetE1) =>
% 106.27/14.56 (((inPowerset) =>
% 106.27/14.56 (((powersetsubset) =>
% 106.27/14.56 (((sepInPowerset) =>
% 106.27/14.56 (((sepSubset) =>
% 106.27/14.56 (((binunionIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2IR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionEcases) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectI) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset5) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset3) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectER) =>
% 106.27/14.56 ((
% 106.27/14.56 (disjointsetsI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset4) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (bs114d) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusI) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusER) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusERneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusELneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusILneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusIRneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffE) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI2) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg2) =>
% 106.27/14.56 ((
% 106.27/14.56 (secondinupair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairiskpair) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairp) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2E) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairsubunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairinpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem3) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair1) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionE2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton1) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I2) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsuniq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (theprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstin) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR11) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR12) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR1) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairequniteq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemER) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempaircEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrI) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrSub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setOfPairsIsBReln) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrERa) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrER) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcImageSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (apProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (app) =>
% 106.27/14.56 ((
% 106.27/14.56 (infuncsetfunc) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcinfuncset) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall1) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp3) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcextLem) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp4) =>
% 106.27/14.56 ((
% 106.27/14.56 (subbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (eqbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq2) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2lamEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifp) =>
% 106.27/14.56 ((
% 106.27/14.56 (theeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrue) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueorfalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setextT) =>
% 106.27/14.56 ((
% 106.27/14.56 (subsetTI) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTELcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTERcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT1) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT2) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT3) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub2) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTnotintersectT) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementImpComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementSubsetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementInPowersetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (contraSubsetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTcontraSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTILcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTIRcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion2) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (intersectInPowersetIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpNotIn1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpInComplement1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTEcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementUnionInPowersetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule0) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_5) =>
% 106.27/14.56 ((
% 106.27/14.56 (breln1all2) =>
% 106.27/14.56 ((
% 106.27/14.56 (!!) @ (
% 106.27/14.56 (('#B') @ (
% 106.27/14.56 !!) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#S') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 '#S') @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 =>))) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#C') @ in)) @
% 106.27/14.56 breln1Set)))))) @
% 106.27/14.56 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])).
% 106.27/14.56 thf(zip_derived_cl699, plain,
% 106.27/14.56 (~ (((powerset__Cong) =>
% 106.27/14.56 (((setunion__Cong) =>
% 106.27/14.56 (((exuEu) =>
% 106.27/14.56 (((descr__Cong) =>
% 106.27/14.56 (((dsetconstr__Cong) =>
% 106.27/14.56 (((subsetI1) =>
% 106.27/14.56 (((eqimpsubset2) =>
% 106.27/14.56 (((eqimpsubset1) =>
% 106.27/14.56 (((subsetI2) =>
% 106.27/14.56 (((emptysetsubset) =>
% 106.27/14.56 (((subsetE) =>
% 106.27/14.56 (((subsetE2) =>
% 106.27/14.56 (((notsubsetI) =>
% 106.27/14.56 (((notequalI1) =>
% 106.27/14.56 (((notequalI2) =>
% 106.27/14.56 (((subsetRefl) =>
% 106.27/14.56 (((subsetTrans) =>
% 106.27/14.56 (((setadjoinSub) =>
% 106.27/14.56 (((setadjoinSub2) =>
% 106.27/14.56 (((subset2powerset) =>
% 106.27/14.56 (((setextsub) =>
% 106.27/14.56 (((subsetemptysetimpeq) =>
% 106.27/14.56 (((powersetI1) =>
% 106.27/14.56 (((powersetE1) =>
% 106.27/14.56 (((inPowerset) =>
% 106.27/14.56 (((powersetsubset) =>
% 106.27/14.56 (((sepInPowerset) =>
% 106.27/14.56 (((sepSubset) =>
% 106.27/14.56 (((binunionIL) =>
% 106.27/14.56 (((upairset2IR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionEcases) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectI) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset5) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset3) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectER) =>
% 106.27/14.56 ((
% 106.27/14.56 (disjointsetsI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset4) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (bs114d) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusI) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusER) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusERneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusELneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusILneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusIRneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffE) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI2) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg2) =>
% 106.27/14.56 ((
% 106.27/14.56 (secondinupair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairiskpair) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairp) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2E) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairsubunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairinpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem3) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair1) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionE2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton1) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I2) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsuniq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (theprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstin) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR11) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR12) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR1) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairequniteq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemER) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempaircEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrI) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrSub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setOfPairsIsBReln) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrERa) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrEL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (dpsetconstrER) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcImageSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (apProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (app) =>
% 106.27/14.56 ((
% 106.27/14.56 (infuncsetfunc) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcinfuncset) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamProp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lamp) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2p) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall1) =>
% 106.27/14.56 ((
% 106.27/14.56 (brelnall2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp3) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcextLem) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcGraphProp4) =>
% 106.27/14.56 ((
% 106.27/14.56 (subbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (eqbreln) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext) =>
% 106.27/14.56 ((
% 106.27/14.56 (funcext2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ap2apEq2) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta1) =>
% 106.27/14.56 ((
% 106.27/14.56 (lam2lamEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (beta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (eta2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalseProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp1) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueProp2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifSingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ifp) =>
% 106.27/14.56 ((
% 106.27/14.56 (theeq) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrue) =>
% 106.27/14.56 ((
% 106.27/14.56 (iffalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (iftrueorfalse) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementT_lem) =>
% 106.27/14.56 ((
% 106.27/14.56 (setextT) =>
% 106.27/14.56 ((
% 106.27/14.56 (subsetTI) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (powersetTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTELcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectTERcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT1) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT2) =>
% 106.27/14.56 ((
% 106.27/14.56 (contrasubsetT3) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementE1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub1) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementSub2) =>
% 106.27/14.56 ((
% 106.27/14.56 (doubleComplementEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTnotintersectT) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementImpComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementSubsetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementInPowersetComplementIntersect) =>
% 106.27/14.56 ((
% 106.27/14.56 (contraSubsetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementTcontraSubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTILcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTIRcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInUnion2) =>
% 106.27/14.56 ((
% 106.27/14.56 (inIntersectImpInIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (intersectInPowersetIntersectUnions) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpNotIn1) =>
% 106.27/14.56 ((
% 106.27/14.56 (inComplementUnionImpInComplement1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionTEcontra) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a1) =>
% 106.27/14.56 ((
% 106.27/14.56 (complementUnionInPowersetComplement) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan1) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2a) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b2) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2b) =>
% 106.27/14.56 ((
% 106.27/14.56 (demorgan2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule0) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz13rule4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_1) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_2) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_3) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_4) =>
% 106.27/14.56 ((
% 106.27/14.56 (woz1_5) =>
% 106.27/14.56 ((
% 106.27/14.56 (breln1all2) =>
% 106.27/14.56 ((
% 106.27/14.56 (!!) @ (
% 106.27/14.56 (('#B') @ (
% 106.27/14.56 !!) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#S') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 '#S') @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 =>))) @
% 106.27/14.56 (
% 106.27/14.56 (
% 106.27/14.56 ('#B') @ (
% 106.27/14.56 (
% 106.27/14.56 ('#C') @ in)) @
% 106.27/14.56 breln1Set)))))) @
% 106.27/14.56 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl685])).
% 106.27/14.56 thf(zip_derived_cl714, plain,
% 106.27/14.56 (~ (((setunion__Cong) =>
% 106.27/14.56 (((exuEu) =>
% 106.27/14.56 (((descr__Cong) =>
% 106.27/14.56 (((dsetconstr__Cong) =>
% 106.27/14.56 (((subsetI1) =>
% 106.27/14.56 (((eqimpsubset2) =>
% 106.27/14.56 (((eqimpsubset1) =>
% 106.27/14.56 (((subsetI2) =>
% 106.27/14.56 (((emptysetsubset) =>
% 106.27/14.56 (((subsetE) =>
% 106.27/14.56 (((subsetE2) =>
% 106.27/14.56 (((notsubsetI) =>
% 106.27/14.56 (((notequalI1) =>
% 106.27/14.56 (((notequalI2) =>
% 106.27/14.56 (((subsetRefl) =>
% 106.27/14.56 (((subsetTrans) =>
% 106.27/14.56 (((setadjoinSub) =>
% 106.27/14.56 (((setadjoinSub2) =>
% 106.27/14.56 (((subset2powerset) =>
% 106.27/14.56 (((setextsub) =>
% 106.27/14.56 (((subsetemptysetimpeq) =>
% 106.27/14.56 (((powersetI1) =>
% 106.27/14.56 (((powersetE1) =>
% 106.27/14.56 (((inPowerset) =>
% 106.27/14.56 (((powersetsubset) =>
% 106.27/14.56 (((sepInPowerset) =>
% 106.27/14.56 (((sepSubset) =>
% 106.27/14.56 (((binunionIL) =>
% 106.27/14.56 (((upairset2IR) =>
% 106.27/14.56 (((binunionIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionEcases) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionE) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binunionRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectI) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset5) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset3) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectER) =>
% 106.27/14.56 ((
% 106.27/14.56 (disjointsetsI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectRsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset4) =>
% 106.27/14.56 ((
% 106.27/14.56 (binintersectSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (bs114d) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusI) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusER) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusERneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusELneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusILneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusIRneg) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusLsub) =>
% 106.27/14.56 ((
% 106.27/14.56 (setminusSubset1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffE) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffI2) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg1) =>
% 106.27/14.56 ((
% 106.27/14.56 (symdiffIneg2) =>
% 106.27/14.56 ((
% 106.27/14.56 (secondinupair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairIR) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairiskpair) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairp) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsubset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowerset) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletoninpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairset2E) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairsubunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairinpowunion) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem2) =>
% 106.27/14.56 ((
% 106.27/14.56 (ubforcartprodlem3) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair1) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempair) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionE2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton1) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setunionsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1E1) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I) =>
% 106.27/14.56 ((
% 106.27/14.56 (ex1I2) =>
% 106.27/14.56 ((
% 106.27/14.56 (singletonsuniq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL1) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (theprop) =>
% 106.27/14.56 ((
% 106.27/14.56 (kfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstin) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjL) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR11) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR12) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR1) =>
% 106.27/14.56 ((
% 106.27/14.56 (upairequniteq) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR2) =>
% 106.27/14.56 ((
% 106.27/14.56 (setukpairinjR) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndsingleton) =>
% 106.27/14.56 ((
% 106.27/14.56 (ksndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (kpairsurjEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndin) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemEL) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairmemER) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodmempaircEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodfstpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodsndpairEq) =>
% 106.27/14.56 ((
% 106.27/14.56 (cartprodpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrI) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrSub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setOfPairsIsBReln) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrERa) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrER) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcImageSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (apProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (app) =>
% 106.27/14.57 ((
% 106.27/14.57 (infuncsetfunc) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcinfuncset) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall1) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp3) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcextLem) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp4) =>
% 106.27/14.57 ((
% 106.27/14.57 (subbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (eqbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq2) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2lamEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifp) =>
% 106.27/14.57 ((
% 106.27/14.57 (theeq) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrue) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueorfalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setextT) =>
% 106.27/14.57 ((
% 106.27/14.57 (subsetTI) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTELcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTERcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT1) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT2) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT3) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub2) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTnotintersectT) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementImpComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementSubsetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementInPowersetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (contraSubsetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTcontraSubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTILcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTIRcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion2) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (intersectInPowersetIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpNotIn1) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpInComplement1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTEcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementUnionInPowersetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule0) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_5) =>
% 106.27/14.57 ((
% 106.27/14.57 (breln1all2) =>
% 106.27/14.57 ((
% 106.27/14.57 (!!) @ (
% 106.27/14.57 (('#B') @ (
% 106.27/14.57 !!) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#S') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 '#S') @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 =>))) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#C') @ in)) @
% 106.27/14.57 breln1Set)))))) @
% 106.27/14.57 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl699])).
% 106.27/14.57 thf(zip_derived_cl731, plain,
% 106.27/14.57 (~ (((exuEu) =>
% 106.27/14.57 (((descr__Cong) =>
% 106.27/14.57 (((dsetconstr__Cong) =>
% 106.27/14.57 (((subsetI1) =>
% 106.27/14.57 (((eqimpsubset2) =>
% 106.27/14.57 (((eqimpsubset1) =>
% 106.27/14.57 (((subsetI2) =>
% 106.27/14.57 (((emptysetsubset) =>
% 106.27/14.57 (((subsetE) =>
% 106.27/14.57 (((subsetE2) =>
% 106.27/14.57 (((notsubsetI) =>
% 106.27/14.57 (((notequalI1) =>
% 106.27/14.57 (((notequalI2) =>
% 106.27/14.57 (((subsetRefl) =>
% 106.27/14.57 (((subsetTrans) =>
% 106.27/14.57 (((setadjoinSub) =>
% 106.27/14.57 (((setadjoinSub2) =>
% 106.27/14.57 (((subset2powerset) =>
% 106.27/14.57 (((setextsub) =>
% 106.27/14.57 (((subsetemptysetimpeq) =>
% 106.27/14.57 (((powersetI1) =>
% 106.27/14.57 (((powersetE1) =>
% 106.27/14.57 (((inPowerset) =>
% 106.27/14.57 (((powersetsubset) =>
% 106.27/14.57 (((sepInPowerset) =>
% 106.27/14.57 (((sepSubset) =>
% 106.27/14.57 (((binunionIL) =>
% 106.27/14.57 (((upairset2IR) =>
% 106.27/14.57 (((binunionIR) =>
% 106.27/14.57 (((binunionEcases) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectI) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset5) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset3) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectER) =>
% 106.27/14.57 ((
% 106.27/14.57 (disjointsetsI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset4) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (bs114d) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusI) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusER) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusERneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusELneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusILneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusIRneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffE) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI2) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg2) =>
% 106.27/14.57 ((
% 106.27/14.57 (secondinupair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIR) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairiskpair) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairp) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowerset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairset2E) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairsubunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairinpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem3) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair1) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionE2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton1) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I2) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsuniq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (theprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstin) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR11) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR12) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR1) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairequniteq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemER) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempaircEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrI) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrSub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setOfPairsIsBReln) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrERa) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrER) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcImageSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (apProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (app) =>
% 106.27/14.57 ((
% 106.27/14.57 (infuncsetfunc) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcinfuncset) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall1) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp3) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcextLem) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp4) =>
% 106.27/14.57 ((
% 106.27/14.57 (subbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (eqbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq2) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2lamEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifp) =>
% 106.27/14.57 ((
% 106.27/14.57 (theeq) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrue) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueorfalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setextT) =>
% 106.27/14.57 ((
% 106.27/14.57 (subsetTI) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTELcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTERcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT1) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT2) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT3) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub2) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTnotintersectT) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementImpComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementSubsetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementInPowersetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (contraSubsetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTcontraSubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTILcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTIRcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion2) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (intersectInPowersetIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpNotIn1) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpInComplement1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTEcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementUnionInPowersetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule0) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_5) =>
% 106.27/14.57 ((
% 106.27/14.57 (breln1all2) =>
% 106.27/14.57 ((
% 106.27/14.57 (!!) @ (
% 106.27/14.57 (('#B') @ (
% 106.27/14.57 !!) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#S') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 '#S') @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 =>))) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#C') @ in)) @
% 106.27/14.57 breln1Set)))))) @
% 106.27/14.57 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl714])).
% 106.27/14.57 thf(zip_derived_cl749, plain,
% 106.27/14.57 (~ (((descr__Cong) =>
% 106.27/14.57 (((dsetconstr__Cong) =>
% 106.27/14.57 (((subsetI1) =>
% 106.27/14.57 (((eqimpsubset2) =>
% 106.27/14.57 (((eqimpsubset1) =>
% 106.27/14.57 (((subsetI2) =>
% 106.27/14.57 (((emptysetsubset) =>
% 106.27/14.57 (((subsetE) =>
% 106.27/14.57 (((subsetE2) =>
% 106.27/14.57 (((notsubsetI) =>
% 106.27/14.57 (((notequalI1) =>
% 106.27/14.57 (((notequalI2) =>
% 106.27/14.57 (((subsetRefl) =>
% 106.27/14.57 (((subsetTrans) =>
% 106.27/14.57 (((setadjoinSub) =>
% 106.27/14.57 (((setadjoinSub2) =>
% 106.27/14.57 (((subset2powerset) =>
% 106.27/14.57 (((setextsub) =>
% 106.27/14.57 (((subsetemptysetimpeq) =>
% 106.27/14.57 (((powersetI1) =>
% 106.27/14.57 (((powersetE1) =>
% 106.27/14.57 (((inPowerset) =>
% 106.27/14.57 (((powersetsubset) =>
% 106.27/14.57 (((sepInPowerset) =>
% 106.27/14.57 (((sepSubset) =>
% 106.27/14.57 (((binunionIL) =>
% 106.27/14.57 (((upairset2IR) =>
% 106.27/14.57 (((binunionIR) =>
% 106.27/14.57 (((binunionEcases) =>
% 106.27/14.57 (((binunionE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectI) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset5) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset3) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectER) =>
% 106.27/14.57 ((
% 106.27/14.57 (disjointsetsI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset4) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (bs114d) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusI) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusER) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusERneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusELneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusILneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusIRneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffE) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI2) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg2) =>
% 106.27/14.57 ((
% 106.27/14.57 (secondinupair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIR) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairiskpair) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairp) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowerset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairset2E) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairsubunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairinpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem3) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair1) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionE2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton1) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I2) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsuniq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (theprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstin) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR11) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR12) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR1) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairequniteq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemER) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempaircEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrI) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrSub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setOfPairsIsBReln) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrERa) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrER) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcImageSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (apProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (app) =>
% 106.27/14.57 ((
% 106.27/14.57 (infuncsetfunc) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcinfuncset) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall1) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp3) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcextLem) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp4) =>
% 106.27/14.57 ((
% 106.27/14.57 (subbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (eqbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq2) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2lamEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifp) =>
% 106.27/14.57 ((
% 106.27/14.57 (theeq) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrue) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueorfalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setextT) =>
% 106.27/14.57 ((
% 106.27/14.57 (subsetTI) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTELcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTERcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT1) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT2) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT3) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub2) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTnotintersectT) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementImpComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementSubsetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementInPowersetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (contraSubsetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTcontraSubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTILcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTIRcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion2) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (intersectInPowersetIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpNotIn1) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpInComplement1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTEcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementUnionInPowersetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule0) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_5) =>
% 106.27/14.57 ((
% 106.27/14.57 (breln1all2) =>
% 106.27/14.57 ((
% 106.27/14.57 (!!) @ (
% 106.27/14.57 (('#B') @ (
% 106.27/14.57 !!) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#S') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 '#S') @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 =>))) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#C') @ in)) @
% 106.27/14.57 breln1Set)))))) @
% 106.27/14.57 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl731])).
% 106.27/14.57 thf(zip_derived_cl769, plain,
% 106.27/14.57 (~ (((dsetconstr__Cong) =>
% 106.27/14.57 (((subsetI1) =>
% 106.27/14.57 (((eqimpsubset2) =>
% 106.27/14.57 (((eqimpsubset1) =>
% 106.27/14.57 (((subsetI2) =>
% 106.27/14.57 (((emptysetsubset) =>
% 106.27/14.57 (((subsetE) =>
% 106.27/14.57 (((subsetE2) =>
% 106.27/14.57 (((notsubsetI) =>
% 106.27/14.57 (((notequalI1) =>
% 106.27/14.57 (((notequalI2) =>
% 106.27/14.57 (((subsetRefl) =>
% 106.27/14.57 (((subsetTrans) =>
% 106.27/14.57 (((setadjoinSub) =>
% 106.27/14.57 (((setadjoinSub2) =>
% 106.27/14.57 (((subset2powerset) =>
% 106.27/14.57 (((setextsub) =>
% 106.27/14.57 (((subsetemptysetimpeq) =>
% 106.27/14.57 (((powersetI1) =>
% 106.27/14.57 (((powersetE1) =>
% 106.27/14.57 (((inPowerset) =>
% 106.27/14.57 (((powersetsubset) =>
% 106.27/14.57 (((sepInPowerset) =>
% 106.27/14.57 (((sepSubset) =>
% 106.27/14.57 (((binunionIL) =>
% 106.27/14.57 (((upairset2IR) =>
% 106.27/14.57 (((binunionIR) =>
% 106.27/14.57 (((binunionEcases) =>
% 106.27/14.57 (((binunionE) =>
% 106.27/14.57 (((binunionLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectI) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset5) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset3) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectER) =>
% 106.27/14.57 ((
% 106.27/14.57 (disjointsetsI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset4) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (bs114d) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusI) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusER) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusERneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusELneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusILneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusIRneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffE) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI2) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg2) =>
% 106.27/14.57 ((
% 106.27/14.57 (secondinupair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIR) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairiskpair) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairp) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowerset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairset2E) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairsubunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairinpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem3) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair1) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionE2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton1) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I2) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsuniq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (theprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstin) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR11) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR12) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR1) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairequniteq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemER) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempaircEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrI) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrSub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setOfPairsIsBReln) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrERa) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrER) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcImageSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (apProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (app) =>
% 106.27/14.57 ((
% 106.27/14.57 (infuncsetfunc) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcinfuncset) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall1) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp3) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcextLem) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp4) =>
% 106.27/14.57 ((
% 106.27/14.57 (subbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (eqbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq2) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2lamEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifp) =>
% 106.27/14.57 ((
% 106.27/14.57 (theeq) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrue) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueorfalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setextT) =>
% 106.27/14.57 ((
% 106.27/14.57 (subsetTI) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTELcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTERcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT1) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT2) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT3) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub2) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTnotintersectT) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementImpComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementSubsetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementInPowersetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (contraSubsetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTcontraSubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTILcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTIRcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion2) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (intersectInPowersetIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpNotIn1) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpInComplement1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTEcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementUnionInPowersetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule0) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_5) =>
% 106.27/14.57 ((
% 106.27/14.57 (breln1all2) =>
% 106.27/14.57 ((
% 106.27/14.57 (!!) @ (
% 106.27/14.57 (('#B') @ (
% 106.27/14.57 !!) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#S') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 '#S') @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 =>))) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#C') @ in)) @
% 106.27/14.57 breln1Set)))))) @
% 106.27/14.57 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl749])).
% 106.27/14.57 thf(zip_derived_cl789, plain,
% 106.27/14.57 (~ (((subsetI1) =>
% 106.27/14.57 (((eqimpsubset2) =>
% 106.27/14.57 (((eqimpsubset1) =>
% 106.27/14.57 (((subsetI2) =>
% 106.27/14.57 (((emptysetsubset) =>
% 106.27/14.57 (((subsetE) =>
% 106.27/14.57 (((subsetE2) =>
% 106.27/14.57 (((notsubsetI) =>
% 106.27/14.57 (((notequalI1) =>
% 106.27/14.57 (((notequalI2) =>
% 106.27/14.57 (((subsetRefl) =>
% 106.27/14.57 (((subsetTrans) =>
% 106.27/14.57 (((setadjoinSub) =>
% 106.27/14.57 (((setadjoinSub2) =>
% 106.27/14.57 (((subset2powerset) =>
% 106.27/14.57 (((setextsub) =>
% 106.27/14.57 (((subsetemptysetimpeq) =>
% 106.27/14.57 (((powersetI1) =>
% 106.27/14.57 (((powersetE1) =>
% 106.27/14.57 (((inPowerset) =>
% 106.27/14.57 (((powersetsubset) =>
% 106.27/14.57 (((sepInPowerset) =>
% 106.27/14.57 (((sepSubset) =>
% 106.27/14.57 (((binunionIL) =>
% 106.27/14.57 (((upairset2IR) =>
% 106.27/14.57 (((binunionIR) =>
% 106.27/14.57 (((binunionEcases) =>
% 106.27/14.57 (((binunionE) =>
% 106.27/14.57 (((binunionLsub) =>
% 106.27/14.57 (((binunionRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectI) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset5) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset3) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectER) =>
% 106.27/14.57 ((
% 106.27/14.57 (disjointsetsI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset4) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (bs114d) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusI) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusER) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusERneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusELneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusILneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusIRneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffE) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI2) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg2) =>
% 106.27/14.57 ((
% 106.27/14.57 (secondinupair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIR) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairiskpair) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairp) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowerset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairset2E) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairsubunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairinpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem3) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair1) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionE2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton1) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I2) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsuniq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (theprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstin) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR11) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR12) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR1) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairequniteq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemER) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempaircEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrI) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrSub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setOfPairsIsBReln) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrERa) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrER) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcImageSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (apProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (app) =>
% 106.27/14.57 ((
% 106.27/14.57 (infuncsetfunc) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcinfuncset) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall1) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp3) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcextLem) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp4) =>
% 106.27/14.57 ((
% 106.27/14.57 (subbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (eqbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq2) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2lamEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifp) =>
% 106.27/14.57 ((
% 106.27/14.57 (theeq) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrue) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueorfalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setextT) =>
% 106.27/14.57 ((
% 106.27/14.57 (subsetTI) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTELcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTERcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT1) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT2) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT3) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub2) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTnotintersectT) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementImpComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementSubsetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementInPowersetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (contraSubsetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTcontraSubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTILcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTIRcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion2) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (intersectInPowersetIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpNotIn1) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpInComplement1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTEcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementUnionInPowersetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule0) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_5) =>
% 106.27/14.57 ((
% 106.27/14.57 (breln1all2) =>
% 106.27/14.57 ((
% 106.27/14.57 (!!) @ (
% 106.27/14.57 (('#B') @ (
% 106.27/14.57 !!) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#S') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 '#S') @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 =>))) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#C') @ in)) @
% 106.27/14.57 breln1Set)))))) @
% 106.27/14.57 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl769])).
% 106.27/14.57 thf(zip_derived_cl807, plain,
% 106.27/14.57 (~ (((eqimpsubset2) =>
% 106.27/14.57 (((eqimpsubset1) =>
% 106.27/14.57 (((subsetI2) =>
% 106.27/14.57 (((emptysetsubset) =>
% 106.27/14.57 (((subsetE) =>
% 106.27/14.57 (((subsetE2) =>
% 106.27/14.57 (((notsubsetI) =>
% 106.27/14.57 (((notequalI1) =>
% 106.27/14.57 (((notequalI2) =>
% 106.27/14.57 (((subsetRefl) =>
% 106.27/14.57 (((subsetTrans) =>
% 106.27/14.57 (((setadjoinSub) =>
% 106.27/14.57 (((setadjoinSub2) =>
% 106.27/14.57 (((subset2powerset) =>
% 106.27/14.57 (((setextsub) =>
% 106.27/14.57 (((subsetemptysetimpeq) =>
% 106.27/14.57 (((powersetI1) =>
% 106.27/14.57 (((powersetE1) =>
% 106.27/14.57 (((inPowerset) =>
% 106.27/14.57 (((powersetsubset) =>
% 106.27/14.57 (((sepInPowerset) =>
% 106.27/14.57 (((sepSubset) =>
% 106.27/14.57 (((binunionIL) =>
% 106.27/14.57 (((upairset2IR) =>
% 106.27/14.57 (((binunionIR) =>
% 106.27/14.57 (((binunionEcases) =>
% 106.27/14.57 (((binunionE) =>
% 106.27/14.57 (((binunionLsub) =>
% 106.27/14.57 (((binunionRsub) =>
% 106.27/14.57 (((binintersectI) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset5) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset3) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectER) =>
% 106.27/14.57 ((
% 106.27/14.57 (disjointsetsI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset4) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (bs114d) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusI) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusER) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusERneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusELneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusILneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusIRneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffE) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI2) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg2) =>
% 106.27/14.57 ((
% 106.27/14.57 (secondinupair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIR) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairiskpair) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairp) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowerset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairset2E) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairsubunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairinpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem3) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair1) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionE2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton1) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I2) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsuniq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (theprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstin) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR11) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR12) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR1) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairequniteq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemER) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempaircEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrI) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrSub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setOfPairsIsBReln) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrERa) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrER) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcImageSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (apProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (app) =>
% 106.27/14.57 ((
% 106.27/14.57 (infuncsetfunc) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcinfuncset) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall1) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp3) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcextLem) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp4) =>
% 106.27/14.57 ((
% 106.27/14.57 (subbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (eqbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq2) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2lamEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifp) =>
% 106.27/14.57 ((
% 106.27/14.57 (theeq) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrue) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueorfalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setextT) =>
% 106.27/14.57 ((
% 106.27/14.57 (subsetTI) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTELcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTERcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT1) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT2) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT3) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub2) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTnotintersectT) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementImpComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementSubsetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementInPowersetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (contraSubsetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTcontraSubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTILcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTIRcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion2) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (intersectInPowersetIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpNotIn1) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpInComplement1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTEcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementUnionInPowersetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule0) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_5) =>
% 106.27/14.57 ((
% 106.27/14.57 (breln1all2) =>
% 106.27/14.57 ((
% 106.27/14.57 (!!) @ (
% 106.27/14.57 (('#B') @ (
% 106.27/14.57 !!) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#S') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 '#S') @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 =>))) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#C') @ in)) @
% 106.27/14.57 breln1Set)))))) @
% 106.27/14.57 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl789])).
% 106.27/14.57 thf(zip_derived_cl824, plain,
% 106.27/14.57 (~ (((eqimpsubset1) =>
% 106.27/14.57 (((subsetI2) =>
% 106.27/14.57 (((emptysetsubset) =>
% 106.27/14.57 (((subsetE) =>
% 106.27/14.57 (((subsetE2) =>
% 106.27/14.57 (((notsubsetI) =>
% 106.27/14.57 (((notequalI1) =>
% 106.27/14.57 (((notequalI2) =>
% 106.27/14.57 (((subsetRefl) =>
% 106.27/14.57 (((subsetTrans) =>
% 106.27/14.57 (((setadjoinSub) =>
% 106.27/14.57 (((setadjoinSub2) =>
% 106.27/14.57 (((subset2powerset) =>
% 106.27/14.57 (((setextsub) =>
% 106.27/14.57 (((subsetemptysetimpeq) =>
% 106.27/14.57 (((powersetI1) =>
% 106.27/14.57 (((powersetE1) =>
% 106.27/14.57 (((inPowerset) =>
% 106.27/14.57 (((powersetsubset) =>
% 106.27/14.57 (((sepInPowerset) =>
% 106.27/14.57 (((sepSubset) =>
% 106.27/14.57 (((binunionIL) =>
% 106.27/14.57 (((upairset2IR) =>
% 106.27/14.57 (((binunionIR) =>
% 106.27/14.57 (((binunionEcases) =>
% 106.27/14.57 (((binunionE) =>
% 106.27/14.57 (((binunionLsub) =>
% 106.27/14.57 (((binunionRsub) =>
% 106.27/14.57 (((binintersectI) =>
% 106.27/14.57 (((binintersectSubset5) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset3) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectER) =>
% 106.27/14.57 ((
% 106.27/14.57 (disjointsetsI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset4) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (bs114d) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusI) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusER) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusERneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusELneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusILneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusIRneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffE) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI2) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg2) =>
% 106.27/14.57 ((
% 106.27/14.57 (secondinupair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIR) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairiskpair) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairp) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowerset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairset2E) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairsubunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairinpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem3) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair1) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionE2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton1) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I2) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsuniq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (theprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstin) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR11) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR12) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR1) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairequniteq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemER) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempaircEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrI) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrSub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setOfPairsIsBReln) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrERa) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrER) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcImageSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (apProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (app) =>
% 106.27/14.57 ((
% 106.27/14.57 (infuncsetfunc) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcinfuncset) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall1) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp3) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcextLem) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp4) =>
% 106.27/14.57 ((
% 106.27/14.57 (subbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (eqbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq2) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2lamEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifp) =>
% 106.27/14.57 ((
% 106.27/14.57 (theeq) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrue) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueorfalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setextT) =>
% 106.27/14.57 ((
% 106.27/14.57 (subsetTI) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTELcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTERcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT1) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT2) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT3) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub2) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTnotintersectT) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementImpComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementSubsetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementInPowersetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (contraSubsetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTcontraSubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTILcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTIRcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion2) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (intersectInPowersetIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpNotIn1) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpInComplement1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTEcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementUnionInPowersetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule0) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_5) =>
% 106.27/14.57 ((
% 106.27/14.57 (breln1all2) =>
% 106.27/14.57 ((
% 106.27/14.57 (!!) @ (
% 106.27/14.57 (('#B') @ (
% 106.27/14.57 !!) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#S') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 '#S') @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 =>))) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#C') @ in)) @
% 106.27/14.57 breln1Set)))))) @
% 106.27/14.57 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl807])).
% 106.27/14.57 thf(zip_derived_cl838, plain,
% 106.27/14.57 (~ (((subsetI2) =>
% 106.27/14.57 (((emptysetsubset) =>
% 106.27/14.57 (((subsetE) =>
% 106.27/14.57 (((subsetE2) =>
% 106.27/14.57 (((notsubsetI) =>
% 106.27/14.57 (((notequalI1) =>
% 106.27/14.57 (((notequalI2) =>
% 106.27/14.57 (((subsetRefl) =>
% 106.27/14.57 (((subsetTrans) =>
% 106.27/14.57 (((setadjoinSub) =>
% 106.27/14.57 (((setadjoinSub2) =>
% 106.27/14.57 (((subset2powerset) =>
% 106.27/14.57 (((setextsub) =>
% 106.27/14.57 (((subsetemptysetimpeq) =>
% 106.27/14.57 (((powersetI1) =>
% 106.27/14.57 (((powersetE1) =>
% 106.27/14.57 (((inPowerset) =>
% 106.27/14.57 (((powersetsubset) =>
% 106.27/14.57 (((sepInPowerset) =>
% 106.27/14.57 (((sepSubset) =>
% 106.27/14.57 (((binunionIL) =>
% 106.27/14.57 (((upairset2IR) =>
% 106.27/14.57 (((binunionIR) =>
% 106.27/14.57 (((binunionEcases) =>
% 106.27/14.57 (((binunionE) =>
% 106.27/14.57 (((binunionLsub) =>
% 106.27/14.57 (((binunionRsub) =>
% 106.27/14.57 (((binintersectI) =>
% 106.27/14.57 (((binintersectSubset5) =>
% 106.27/14.57 (((binintersectEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset3) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectER) =>
% 106.27/14.57 ((
% 106.27/14.57 (disjointsetsI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset4) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (bs114d) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusI) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusER) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusERneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusELneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusILneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusIRneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffE) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI2) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg2) =>
% 106.27/14.57 ((
% 106.27/14.57 (secondinupair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIR) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairiskpair) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairp) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowerset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairset2E) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairsubunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairinpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem3) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair1) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionE2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton1) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I2) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsuniq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (theprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstin) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR11) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR12) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR1) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairequniteq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemER) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempaircEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrI) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrSub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setOfPairsIsBReln) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrERa) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrER) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcImageSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (apProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (app) =>
% 106.27/14.57 ((
% 106.27/14.57 (infuncsetfunc) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcinfuncset) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall1) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp3) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcextLem) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp4) =>
% 106.27/14.57 ((
% 106.27/14.57 (subbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (eqbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq2) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2lamEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifp) =>
% 106.27/14.57 ((
% 106.27/14.57 (theeq) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrue) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueorfalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setextT) =>
% 106.27/14.57 ((
% 106.27/14.57 (subsetTI) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTELcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTERcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT1) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT2) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT3) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub2) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTnotintersectT) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementImpComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementSubsetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementInPowersetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (contraSubsetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTcontraSubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTILcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTIRcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion2) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (intersectInPowersetIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpNotIn1) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpInComplement1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTEcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementUnionInPowersetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule0) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_5) =>
% 106.27/14.57 ((
% 106.27/14.57 (breln1all2) =>
% 106.27/14.57 ((
% 106.27/14.57 (!!) @ (
% 106.27/14.57 (('#B') @ (
% 106.27/14.57 !!) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#S') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 '#S') @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 =>))) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#C') @ in)) @
% 106.27/14.57 breln1Set)))))) @
% 106.27/14.57 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl824])).
% 106.27/14.57 thf(zip_derived_cl850, plain,
% 106.27/14.57 (~ (((emptysetsubset) =>
% 106.27/14.57 (((subsetE) =>
% 106.27/14.57 (((subsetE2) =>
% 106.27/14.57 (((notsubsetI) =>
% 106.27/14.57 (((notequalI1) =>
% 106.27/14.57 (((notequalI2) =>
% 106.27/14.57 (((subsetRefl) =>
% 106.27/14.57 (((subsetTrans) =>
% 106.27/14.57 (((setadjoinSub) =>
% 106.27/14.57 (((setadjoinSub2) =>
% 106.27/14.57 (((subset2powerset) =>
% 106.27/14.57 (((setextsub) =>
% 106.27/14.57 (((subsetemptysetimpeq) =>
% 106.27/14.57 (((powersetI1) =>
% 106.27/14.57 (((powersetE1) =>
% 106.27/14.57 (((inPowerset) =>
% 106.27/14.57 (((powersetsubset) =>
% 106.27/14.57 (((sepInPowerset) =>
% 106.27/14.57 (((sepSubset) =>
% 106.27/14.57 (((binunionIL) =>
% 106.27/14.57 (((upairset2IR) =>
% 106.27/14.57 (((binunionIR) =>
% 106.27/14.57 (((binunionEcases) =>
% 106.27/14.57 (((binunionE) =>
% 106.27/14.57 (((binunionLsub) =>
% 106.27/14.57 (((binunionRsub) =>
% 106.27/14.57 (((binintersectI) =>
% 106.27/14.57 (((binintersectSubset5) =>
% 106.27/14.57 (((binintersectEL) =>
% 106.27/14.57 (((binintersectLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset3) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectER) =>
% 106.27/14.57 ((
% 106.27/14.57 (disjointsetsI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset4) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (bs114d) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusI) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusER) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusERneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusELneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusILneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusIRneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffE) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI2) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg2) =>
% 106.27/14.57 ((
% 106.27/14.57 (secondinupair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIR) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairiskpair) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairp) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowerset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairset2E) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairsubunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairinpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem3) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair1) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionE2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton1) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I2) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsuniq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (theprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstin) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR11) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR12) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR1) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairequniteq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemER) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempaircEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrI) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrSub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setOfPairsIsBReln) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrERa) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrER) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcImageSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (apProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (app) =>
% 106.27/14.57 ((
% 106.27/14.57 (infuncsetfunc) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcinfuncset) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall1) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp3) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcextLem) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp4) =>
% 106.27/14.57 ((
% 106.27/14.57 (subbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (eqbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq2) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2lamEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifp) =>
% 106.27/14.57 ((
% 106.27/14.57 (theeq) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrue) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueorfalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setextT) =>
% 106.27/14.57 ((
% 106.27/14.57 (subsetTI) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTELcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTERcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT1) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT2) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT3) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub2) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTnotintersectT) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementImpComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementSubsetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementInPowersetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (contraSubsetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTcontraSubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTILcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTIRcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion2) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (intersectInPowersetIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpNotIn1) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpInComplement1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTEcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementUnionInPowersetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule0) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_5) =>
% 106.27/14.57 ((
% 106.27/14.57 (breln1all2) =>
% 106.27/14.57 ((
% 106.27/14.57 (!!) @ (
% 106.27/14.57 (('#B') @ (
% 106.27/14.57 !!) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#S') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 '#S') @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 =>))) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#C') @ in)) @
% 106.27/14.57 breln1Set)))))) @
% 106.27/14.57 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl838])).
% 106.27/14.57 thf(zip_derived_cl863, plain,
% 106.27/14.57 (~ (((subsetE) =>
% 106.27/14.57 (((subsetE2) =>
% 106.27/14.57 (((notsubsetI) =>
% 106.27/14.57 (((notequalI1) =>
% 106.27/14.57 (((notequalI2) =>
% 106.27/14.57 (((subsetRefl) =>
% 106.27/14.57 (((subsetTrans) =>
% 106.27/14.57 (((setadjoinSub) =>
% 106.27/14.57 (((setadjoinSub2) =>
% 106.27/14.57 (((subset2powerset) =>
% 106.27/14.57 (((setextsub) =>
% 106.27/14.57 (((subsetemptysetimpeq) =>
% 106.27/14.57 (((powersetI1) =>
% 106.27/14.57 (((powersetE1) =>
% 106.27/14.57 (((inPowerset) =>
% 106.27/14.57 (((powersetsubset) =>
% 106.27/14.57 (((sepInPowerset) =>
% 106.27/14.57 (((sepSubset) =>
% 106.27/14.57 (((binunionIL) =>
% 106.27/14.57 (((upairset2IR) =>
% 106.27/14.57 (((binunionIR) =>
% 106.27/14.57 (((binunionEcases) =>
% 106.27/14.57 (((binunionE) =>
% 106.27/14.57 (((binunionLsub) =>
% 106.27/14.57 (((binunionRsub) =>
% 106.27/14.57 (((binintersectI) =>
% 106.27/14.57 (((binintersectSubset5) =>
% 106.27/14.57 (((binintersectEL) =>
% 106.27/14.57 (((binintersectLsub) =>
% 106.27/14.57 (((binintersectSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset3) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectER) =>
% 106.27/14.57 ((
% 106.27/14.57 (disjointsetsI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset4) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (bs114d) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusI) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusER) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusERneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusELneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusILneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusIRneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffE) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI2) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg2) =>
% 106.27/14.57 ((
% 106.27/14.57 (secondinupair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIR) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairiskpair) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairp) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowerset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairset2E) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairsubunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairinpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem3) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair1) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionE2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton1) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I2) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsuniq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (theprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstin) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR11) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR12) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR1) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairequniteq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemER) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempaircEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrI) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrSub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setOfPairsIsBReln) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrERa) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrER) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcImageSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (apProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (app) =>
% 106.27/14.57 ((
% 106.27/14.57 (infuncsetfunc) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcinfuncset) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall1) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp3) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcextLem) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp4) =>
% 106.27/14.57 ((
% 106.27/14.57 (subbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (eqbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq2) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2lamEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifp) =>
% 106.27/14.57 ((
% 106.27/14.57 (theeq) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrue) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueorfalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setextT) =>
% 106.27/14.57 ((
% 106.27/14.57 (subsetTI) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTELcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTERcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT1) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT2) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT3) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub2) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTnotintersectT) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementImpComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementSubsetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementInPowersetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (contraSubsetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTcontraSubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTILcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTIRcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion2) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (intersectInPowersetIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpNotIn1) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpInComplement1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTEcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementUnionInPowersetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule0) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_5) =>
% 106.27/14.57 ((
% 106.27/14.57 (breln1all2) =>
% 106.27/14.57 ((
% 106.27/14.57 (!!) @ (
% 106.27/14.57 (('#B') @ (
% 106.27/14.57 !!) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#S') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 '#S') @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 =>))) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#C') @ in)) @
% 106.27/14.57 breln1Set)))))) @
% 106.27/14.57 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl850])).
% 106.27/14.57 thf(zip_derived_cl878, plain,
% 106.27/14.57 (~ (((subsetE2) =>
% 106.27/14.57 (((notsubsetI) =>
% 106.27/14.57 (((notequalI1) =>
% 106.27/14.57 (((notequalI2) =>
% 106.27/14.57 (((subsetRefl) =>
% 106.27/14.57 (((subsetTrans) =>
% 106.27/14.57 (((setadjoinSub) =>
% 106.27/14.57 (((setadjoinSub2) =>
% 106.27/14.57 (((subset2powerset) =>
% 106.27/14.57 (((setextsub) =>
% 106.27/14.57 (((subsetemptysetimpeq) =>
% 106.27/14.57 (((powersetI1) =>
% 106.27/14.57 (((powersetE1) =>
% 106.27/14.57 (((inPowerset) =>
% 106.27/14.57 (((powersetsubset) =>
% 106.27/14.57 (((sepInPowerset) =>
% 106.27/14.57 (((sepSubset) =>
% 106.27/14.57 (((binunionIL) =>
% 106.27/14.57 (((upairset2IR) =>
% 106.27/14.57 (((binunionIR) =>
% 106.27/14.57 (((binunionEcases) =>
% 106.27/14.57 (((binunionE) =>
% 106.27/14.57 (((binunionLsub) =>
% 106.27/14.57 (((binunionRsub) =>
% 106.27/14.57 (((binintersectI) =>
% 106.27/14.57 (((binintersectSubset5) =>
% 106.27/14.57 (((binintersectEL) =>
% 106.27/14.57 (((binintersectLsub) =>
% 106.27/14.57 (((binintersectSubset2) =>
% 106.27/14.57 (((binintersectSubset3) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectER) =>
% 106.27/14.57 ((
% 106.27/14.57 (disjointsetsI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset4) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (bs114d) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusI) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusER) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusERneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusELneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusILneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusIRneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffE) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI2) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg2) =>
% 106.27/14.57 ((
% 106.27/14.57 (secondinupair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIR) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairiskpair) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairp) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowerset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairset2E) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairsubunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairinpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem3) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair1) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionE2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton1) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I2) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsuniq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (theprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstin) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR11) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR12) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR1) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairequniteq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemER) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempaircEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrI) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrSub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setOfPairsIsBReln) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrERa) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrER) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcImageSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (apProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (app) =>
% 106.27/14.57 ((
% 106.27/14.57 (infuncsetfunc) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcinfuncset) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall1) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp3) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcextLem) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp4) =>
% 106.27/14.57 ((
% 106.27/14.57 (subbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (eqbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq2) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2lamEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifp) =>
% 106.27/14.57 ((
% 106.27/14.57 (theeq) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrue) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueorfalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setextT) =>
% 106.27/14.57 ((
% 106.27/14.57 (subsetTI) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTELcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTERcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT1) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT2) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT3) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub2) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTnotintersectT) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementImpComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementSubsetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementInPowersetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (contraSubsetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTcontraSubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTILcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTIRcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion2) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (intersectInPowersetIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpNotIn1) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpInComplement1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTEcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementUnionInPowersetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule0) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_5) =>
% 106.27/14.57 ((
% 106.27/14.57 (breln1all2) =>
% 106.27/14.57 ((
% 106.27/14.57 (!!) @ (
% 106.27/14.57 (('#B') @ (
% 106.27/14.57 !!) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#S') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 '#S') @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 =>))) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#C') @ in)) @
% 106.27/14.57 breln1Set)))))) @
% 106.27/14.57 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl863])).
% 106.27/14.57 thf(zip_derived_cl896, plain,
% 106.27/14.57 (~ (((notsubsetI) =>
% 106.27/14.57 (((notequalI1) =>
% 106.27/14.57 (((notequalI2) =>
% 106.27/14.57 (((subsetRefl) =>
% 106.27/14.57 (((subsetTrans) =>
% 106.27/14.57 (((setadjoinSub) =>
% 106.27/14.57 (((setadjoinSub2) =>
% 106.27/14.57 (((subset2powerset) =>
% 106.27/14.57 (((setextsub) =>
% 106.27/14.57 (((subsetemptysetimpeq) =>
% 106.27/14.57 (((powersetI1) =>
% 106.27/14.57 (((powersetE1) =>
% 106.27/14.57 (((inPowerset) =>
% 106.27/14.57 (((powersetsubset) =>
% 106.27/14.57 (((sepInPowerset) =>
% 106.27/14.57 (((sepSubset) =>
% 106.27/14.57 (((binunionIL) =>
% 106.27/14.57 (((upairset2IR) =>
% 106.27/14.57 (((binunionIR) =>
% 106.27/14.57 (((binunionEcases) =>
% 106.27/14.57 (((binunionE) =>
% 106.27/14.57 (((binunionLsub) =>
% 106.27/14.57 (((binunionRsub) =>
% 106.27/14.57 (((binintersectI) =>
% 106.27/14.57 (((binintersectSubset5) =>
% 106.27/14.57 (((binintersectEL) =>
% 106.27/14.57 (((binintersectLsub) =>
% 106.27/14.57 (((binintersectSubset2) =>
% 106.27/14.57 (((binintersectSubset3) =>
% 106.27/14.57 (((binintersectER) =>
% 106.27/14.57 ((
% 106.27/14.57 (disjointsetsI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset4) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (bs114d) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusI) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusER) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusERneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusELneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusILneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusIRneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffE) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI2) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg2) =>
% 106.27/14.57 ((
% 106.27/14.57 (secondinupair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIR) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairiskpair) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairp) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowerset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairset2E) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairsubunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairinpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem3) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair1) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionE2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton1) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I2) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsuniq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (theprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstin) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR11) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR12) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR1) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairequniteq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemER) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempaircEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrI) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrSub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setOfPairsIsBReln) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrERa) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrER) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcImageSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (apProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (app) =>
% 106.27/14.57 ((
% 106.27/14.57 (infuncsetfunc) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcinfuncset) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall1) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp3) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcextLem) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp4) =>
% 106.27/14.57 ((
% 106.27/14.57 (subbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (eqbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq2) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2lamEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifp) =>
% 106.27/14.57 ((
% 106.27/14.57 (theeq) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrue) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueorfalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setextT) =>
% 106.27/14.57 ((
% 106.27/14.57 (subsetTI) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTELcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectTERcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT1) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT2) =>
% 106.27/14.57 ((
% 106.27/14.57 (contrasubsetT3) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementE1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub1) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementSub2) =>
% 106.27/14.57 ((
% 106.27/14.57 (doubleComplementEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTnotintersectT) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementImpComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementSubsetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementInPowersetComplementIntersect) =>
% 106.27/14.57 ((
% 106.27/14.57 (contraSubsetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementTcontraSubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTILcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTIRcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInUnion2) =>
% 106.27/14.57 ((
% 106.27/14.57 (inIntersectImpInIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (intersectInPowersetIntersectUnions) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpNotIn1) =>
% 106.27/14.57 ((
% 106.27/14.57 (inComplementUnionImpInComplement1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTE) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionTEcontra) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a1) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementUnionInPowersetComplement) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan1) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2a) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b2) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2b) =>
% 106.27/14.57 ((
% 106.27/14.57 (demorgan2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule0) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz13rule4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_1) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_2) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_3) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_4) =>
% 106.27/14.57 ((
% 106.27/14.57 (woz1_5) =>
% 106.27/14.57 ((
% 106.27/14.57 (breln1all2) =>
% 106.27/14.57 ((
% 106.27/14.57 (!!) @ (
% 106.27/14.57 (('#B') @ (
% 106.27/14.57 !!) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#S') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 '#S') @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 =>))) @
% 106.27/14.57 (
% 106.27/14.57 (
% 106.27/14.57 ('#B') @ (
% 106.27/14.57 (
% 106.27/14.57 ('#C') @ in)) @
% 106.27/14.57 breln1Set)))))) @
% 106.27/14.57 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl878])).
% 106.27/14.57 thf(zip_derived_cl909, plain,
% 106.27/14.57 (~ (((notequalI1) =>
% 106.27/14.57 (((notequalI2) =>
% 106.27/14.57 (((subsetRefl) =>
% 106.27/14.57 (((subsetTrans) =>
% 106.27/14.57 (((setadjoinSub) =>
% 106.27/14.57 (((setadjoinSub2) =>
% 106.27/14.57 (((subset2powerset) =>
% 106.27/14.57 (((setextsub) =>
% 106.27/14.57 (((subsetemptysetimpeq) =>
% 106.27/14.57 (((powersetI1) =>
% 106.27/14.57 (((powersetE1) =>
% 106.27/14.57 (((inPowerset) =>
% 106.27/14.57 (((powersetsubset) =>
% 106.27/14.57 (((sepInPowerset) =>
% 106.27/14.57 (((sepSubset) =>
% 106.27/14.57 (((binunionIL) =>
% 106.27/14.57 (((upairset2IR) =>
% 106.27/14.57 (((binunionIR) =>
% 106.27/14.57 (((binunionEcases) =>
% 106.27/14.57 (((binunionE) =>
% 106.27/14.57 (((binunionLsub) =>
% 106.27/14.57 (((binunionRsub) =>
% 106.27/14.57 (((binintersectI) =>
% 106.27/14.57 (((binintersectSubset5) =>
% 106.27/14.57 (((binintersectEL) =>
% 106.27/14.57 (((binintersectLsub) =>
% 106.27/14.57 (((binintersectSubset2) =>
% 106.27/14.57 (((binintersectSubset3) =>
% 106.27/14.57 (((binintersectER) =>
% 106.27/14.57 (((disjointsetsI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectRsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset4) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (bs114d) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusI) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusER) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusERneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusELneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusILneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusIRneg) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusLsub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusSubset1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffE) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffI2) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg1) =>
% 106.27/14.57 ((
% 106.27/14.57 (symdiffIneg2) =>
% 106.27/14.57 ((
% 106.27/14.57 (secondinupair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairIR) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairiskpair) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairp) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsubset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowerset) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletoninpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairset2E) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairsubunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairinpowunion) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ubforcartprodlem3) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair1) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempair) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionE2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton1) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setunionsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1I2) =>
% 106.27/14.57 ((
% 106.27/14.57 (singletonsuniq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (theprop) =>
% 106.27/14.57 ((
% 106.27/14.57 (kfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstin) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjL) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR11) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR12) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR1) =>
% 106.27/14.57 ((
% 106.27/14.57 (upairequniteq) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR2) =>
% 106.27/14.57 ((
% 106.27/14.57 (setukpairinjR) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndsingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ksndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (kpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndin) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemEL) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairmemER) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodmempaircEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodfstpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodsndpairEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (cartprodpairsurjEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrI) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrSub) =>
% 106.27/14.57 ((
% 106.27/14.57 (setOfPairsIsBReln) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrERa) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL1) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrEL2) =>
% 106.27/14.57 ((
% 106.27/14.57 (dpsetconstrER) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcImageSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (apProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (app) =>
% 106.27/14.57 ((
% 106.27/14.57 (infuncsetfunc) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcinfuncset) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamProp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lamp) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2p) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall1) =>
% 106.27/14.57 ((
% 106.27/14.57 (brelnall2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ex1E2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp3) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcextLem) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcGraphProp4) =>
% 106.27/14.57 ((
% 106.27/14.57 (subbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (eqbreln) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext) =>
% 106.27/14.57 ((
% 106.27/14.57 (funcext2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq1) =>
% 106.27/14.57 ((
% 106.27/14.57 (ap2apEq2) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta1) =>
% 106.27/14.57 ((
% 106.27/14.57 (lam2lamEq) =>
% 106.27/14.57 ((
% 106.27/14.57 (beta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (eta2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalseProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp1) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueProp2) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifSingleton) =>
% 106.27/14.57 ((
% 106.27/14.57 (ifp) =>
% 106.27/14.57 ((
% 106.27/14.57 (theeq) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrue) =>
% 106.27/14.57 ((
% 106.27/14.57 (iffalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (iftrueorfalse) =>
% 106.27/14.57 ((
% 106.27/14.57 (binintersectT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (binunionT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setminusT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (complementT_lem) =>
% 106.27/14.57 ((
% 106.27/14.57 (setextT) =>
% 106.27/14.57 ((
% 106.27/14.57 (subsetTI) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTI1) =>
% 106.27/14.57 ((
% 106.27/14.57 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl896])).
% 106.27/14.58 thf(zip_derived_cl924, plain,
% 106.27/14.58 (~ (((notequalI2) =>
% 106.27/14.58 (((subsetRefl) =>
% 106.27/14.58 (((subsetTrans) =>
% 106.27/14.58 (((setadjoinSub) =>
% 106.27/14.58 (((setadjoinSub2) =>
% 106.27/14.58 (((subset2powerset) =>
% 106.27/14.58 (((setextsub) =>
% 106.27/14.58 (((subsetemptysetimpeq) =>
% 106.27/14.58 (((powersetI1) =>
% 106.27/14.58 (((powersetE1) =>
% 106.27/14.58 (((inPowerset) =>
% 106.27/14.58 (((powersetsubset) =>
% 106.27/14.58 (((sepInPowerset) =>
% 106.27/14.58 (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectSubset4) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (bs114d) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusI) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusER) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusERneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusELneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusILneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusIRneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusLsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffE) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI2) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg2) =>
% 106.27/14.58 ((
% 106.27/14.58 (secondinupair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIR) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairiskpair) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairp) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowerset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairset2E) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairsubunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairinpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem3) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair1) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionE2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton1) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I2) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsuniq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (theprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstin) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR11) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR12) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR1) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairequniteq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemER) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempaircEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrI) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrSub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setOfPairsIsBReln) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrERa) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrER) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcImageSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (apProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (app) =>
% 106.27/14.58 ((
% 106.27/14.58 (infuncsetfunc) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcinfuncset) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall1) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp3) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcextLem) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp4) =>
% 106.27/14.58 ((
% 106.27/14.58 (subbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (eqbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq2) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2lamEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifp) =>
% 106.27/14.58 ((
% 106.27/14.58 (theeq) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrue) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueorfalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setextT) =>
% 106.27/14.58 ((
% 106.27/14.58 (subsetTI) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl909])).
% 106.27/14.58 thf(zip_derived_cl938, plain,
% 106.27/14.58 (~ (((subsetRefl) =>
% 106.27/14.58 (((subsetTrans) =>
% 106.27/14.58 (((setadjoinSub) =>
% 106.27/14.58 (((setadjoinSub2) =>
% 106.27/14.58 (((subset2powerset) =>
% 106.27/14.58 (((setextsub) =>
% 106.27/14.58 (((subsetemptysetimpeq) =>
% 106.27/14.58 (((powersetI1) =>
% 106.27/14.58 (((powersetE1) =>
% 106.27/14.58 (((inPowerset) =>
% 106.27/14.58 (((powersetsubset) =>
% 106.27/14.58 (((sepInPowerset) =>
% 106.27/14.58 (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 (((binintersectSubset4) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (bs114d) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusI) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusER) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusERneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusELneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusILneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusIRneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusLsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffE) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI2) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg2) =>
% 106.27/14.58 ((
% 106.27/14.58 (secondinupair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIR) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairiskpair) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairp) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowerset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairset2E) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairsubunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairinpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem3) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair1) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionE2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton1) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I2) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsuniq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (theprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstin) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR11) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR12) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR1) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairequniteq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemER) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempaircEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrI) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrSub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setOfPairsIsBReln) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrERa) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrER) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcImageSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (apProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (app) =>
% 106.27/14.58 ((
% 106.27/14.58 (infuncsetfunc) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcinfuncset) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall1) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp3) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcextLem) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp4) =>
% 106.27/14.58 ((
% 106.27/14.58 (subbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (eqbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq2) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2lamEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifp) =>
% 106.27/14.58 ((
% 106.27/14.58 (theeq) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrue) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueorfalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setextT) =>
% 106.27/14.58 ((
% 106.27/14.58 (subsetTI) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl924])).
% 106.27/14.58 thf(zip_derived_cl952, plain,
% 106.27/14.58 (~ (((subsetTrans) =>
% 106.27/14.58 (((setadjoinSub) =>
% 106.27/14.58 (((setadjoinSub2) =>
% 106.27/14.58 (((subset2powerset) =>
% 106.27/14.58 (((setextsub) =>
% 106.27/14.58 (((subsetemptysetimpeq) =>
% 106.27/14.58 (((powersetI1) =>
% 106.27/14.58 (((powersetE1) =>
% 106.27/14.58 (((inPowerset) =>
% 106.27/14.58 (((powersetsubset) =>
% 106.27/14.58 (((sepInPowerset) =>
% 106.27/14.58 (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 (((binintersectSubset4) =>
% 106.27/14.58 (((binintersectSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (bs114d) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusI) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusER) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusERneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusELneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusILneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusIRneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusLsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffE) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI2) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg2) =>
% 106.27/14.58 ((
% 106.27/14.58 (secondinupair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIR) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairiskpair) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairp) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowerset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairset2E) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairsubunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairinpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem3) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair1) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionE2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton1) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I2) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsuniq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (theprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstin) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR11) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR12) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR1) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairequniteq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemER) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempaircEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrI) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrSub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setOfPairsIsBReln) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrERa) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrER) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcImageSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (apProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (app) =>
% 106.27/14.58 ((
% 106.27/14.58 (infuncsetfunc) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcinfuncset) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall1) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp3) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcextLem) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp4) =>
% 106.27/14.58 ((
% 106.27/14.58 (subbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (eqbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq2) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2lamEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifp) =>
% 106.27/14.58 ((
% 106.27/14.58 (theeq) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrue) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueorfalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setextT) =>
% 106.27/14.58 ((
% 106.27/14.58 (subsetTI) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl938])).
% 106.27/14.58 thf(zip_derived_cl967, plain,
% 106.27/14.58 (~ (((setadjoinSub) =>
% 106.27/14.58 (((setadjoinSub2) =>
% 106.27/14.58 (((subset2powerset) =>
% 106.27/14.58 (((setextsub) =>
% 106.27/14.58 (((subsetemptysetimpeq) =>
% 106.27/14.58 (((powersetI1) =>
% 106.27/14.58 (((powersetE1) =>
% 106.27/14.58 (((inPowerset) =>
% 106.27/14.58 (((powersetsubset) =>
% 106.27/14.58 (((sepInPowerset) =>
% 106.27/14.58 (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 (((binintersectSubset4) =>
% 106.27/14.58 (((binintersectSubset1) =>
% 106.27/14.58 (((bs114d) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusI) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusER) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusERneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusELneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusILneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusIRneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusLsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffE) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI2) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg2) =>
% 106.27/14.58 ((
% 106.27/14.58 (secondinupair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIR) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairiskpair) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairp) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowerset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairset2E) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairsubunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairinpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem3) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair1) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionE2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton1) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I2) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsuniq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (theprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstin) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR11) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR12) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR1) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairequniteq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemER) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempaircEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrI) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrSub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setOfPairsIsBReln) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrERa) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrER) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcImageSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (apProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (app) =>
% 106.27/14.58 ((
% 106.27/14.58 (infuncsetfunc) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcinfuncset) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall1) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp3) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcextLem) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp4) =>
% 106.27/14.58 ((
% 106.27/14.58 (subbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (eqbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq2) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2lamEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifp) =>
% 106.27/14.58 ((
% 106.27/14.58 (theeq) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrue) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueorfalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setextT) =>
% 106.27/14.58 ((
% 106.27/14.58 (subsetTI) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl952])).
% 106.27/14.58 thf(zip_derived_cl984, plain,
% 106.27/14.58 (~ (((setadjoinSub2) =>
% 106.27/14.58 (((subset2powerset) =>
% 106.27/14.58 (((setextsub) =>
% 106.27/14.58 (((subsetemptysetimpeq) =>
% 106.27/14.58 (((powersetI1) =>
% 106.27/14.58 (((powersetE1) =>
% 106.27/14.58 (((inPowerset) =>
% 106.27/14.58 (((powersetsubset) =>
% 106.27/14.58 (((sepInPowerset) =>
% 106.27/14.58 (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 (((binintersectSubset4) =>
% 106.27/14.58 (((binintersectSubset1) =>
% 106.27/14.58 (((bs114d) =>
% 106.27/14.58 (((setminusI) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusER) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusERneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusELneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusILneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusIRneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusLsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffE) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI2) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg2) =>
% 106.27/14.58 ((
% 106.27/14.58 (secondinupair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIR) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairiskpair) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairp) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowerset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairset2E) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairsubunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairinpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem3) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair1) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionE2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton1) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I2) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsuniq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (theprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstin) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR11) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR12) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR1) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairequniteq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemER) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempaircEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrI) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrSub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setOfPairsIsBReln) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrERa) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrER) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcImageSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (apProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (app) =>
% 106.27/14.58 ((
% 106.27/14.58 (infuncsetfunc) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcinfuncset) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall1) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp3) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcextLem) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp4) =>
% 106.27/14.58 ((
% 106.27/14.58 (subbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (eqbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq2) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2lamEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifp) =>
% 106.27/14.58 ((
% 106.27/14.58 (theeq) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrue) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueorfalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setextT) =>
% 106.27/14.58 ((
% 106.27/14.58 (subsetTI) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl967])).
% 106.27/14.58 thf(zip_derived_cl1000, plain,
% 106.27/14.58 (~ (((subset2powerset) =>
% 106.27/14.58 (((setextsub) =>
% 106.27/14.58 (((subsetemptysetimpeq) =>
% 106.27/14.58 (((powersetI1) =>
% 106.27/14.58 (((powersetE1) =>
% 106.27/14.58 (((inPowerset) =>
% 106.27/14.58 (((powersetsubset) =>
% 106.27/14.58 (((sepInPowerset) =>
% 106.27/14.58 (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 (((binintersectSubset4) =>
% 106.27/14.58 (((binintersectSubset1) =>
% 106.27/14.58 (((bs114d) =>
% 106.27/14.58 (((setminusI) =>
% 106.27/14.58 (((setminusEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusER) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusERneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusELneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusILneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusIRneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusLsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffE) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI2) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg2) =>
% 106.27/14.58 ((
% 106.27/14.58 (secondinupair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIR) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairiskpair) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairp) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowerset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairset2E) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairsubunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairinpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem3) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair1) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionE2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton1) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I2) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsuniq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (theprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstin) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR11) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR12) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR1) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairequniteq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemER) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempaircEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrI) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrSub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setOfPairsIsBReln) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrERa) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrER) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcImageSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (apProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (app) =>
% 106.27/14.58 ((
% 106.27/14.58 (infuncsetfunc) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcinfuncset) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall1) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp3) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcextLem) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp4) =>
% 106.27/14.58 ((
% 106.27/14.58 (subbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (eqbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq2) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2lamEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifp) =>
% 106.27/14.58 ((
% 106.27/14.58 (theeq) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrue) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueorfalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setextT) =>
% 106.27/14.58 ((
% 106.27/14.58 (subsetTI) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl984])).
% 106.27/14.58 thf(zip_derived_cl1015, plain,
% 106.27/14.58 (~ (((setextsub) =>
% 106.27/14.58 (((subsetemptysetimpeq) =>
% 106.27/14.58 (((powersetI1) =>
% 106.27/14.58 (((powersetE1) =>
% 106.27/14.58 (((inPowerset) =>
% 106.27/14.58 (((powersetsubset) =>
% 106.27/14.58 (((sepInPowerset) =>
% 106.27/14.58 (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 (((binintersectSubset4) =>
% 106.27/14.58 (((binintersectSubset1) =>
% 106.27/14.58 (((bs114d) =>
% 106.27/14.58 (((setminusI) =>
% 106.27/14.58 (((setminusEL) =>
% 106.27/14.58 (((setminusER) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusERneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusELneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusILneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusIRneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusLsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffE) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI2) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg2) =>
% 106.27/14.58 ((
% 106.27/14.58 (secondinupair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIR) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairiskpair) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairp) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowerset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairset2E) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairsubunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairinpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem3) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair1) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionE2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton1) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I2) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsuniq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (theprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstin) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR11) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR12) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR1) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairequniteq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemER) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempaircEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrI) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrSub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setOfPairsIsBReln) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrERa) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrER) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcImageSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (apProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (app) =>
% 106.27/14.58 ((
% 106.27/14.58 (infuncsetfunc) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcinfuncset) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall1) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp3) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcextLem) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp4) =>
% 106.27/14.58 ((
% 106.27/14.58 (subbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (eqbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq2) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2lamEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifp) =>
% 106.27/14.58 ((
% 106.27/14.58 (theeq) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrue) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueorfalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setextT) =>
% 106.27/14.58 ((
% 106.27/14.58 (subsetTI) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])).
% 106.27/14.58 thf(zip_derived_cl1027, plain,
% 106.27/14.58 (~ (((subsetemptysetimpeq) =>
% 106.27/14.58 (((powersetI1) =>
% 106.27/14.58 (((powersetE1) =>
% 106.27/14.58 (((inPowerset) =>
% 106.27/14.58 (((powersetsubset) =>
% 106.27/14.58 (((sepInPowerset) =>
% 106.27/14.58 (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 (((binintersectSubset4) =>
% 106.27/14.58 (((binintersectSubset1) =>
% 106.27/14.58 (((bs114d) =>
% 106.27/14.58 (((setminusI) =>
% 106.27/14.58 (((setminusEL) =>
% 106.27/14.58 (((setminusER) =>
% 106.27/14.58 (((setminusSubset2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusERneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusELneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusILneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusIRneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusLsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffE) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI2) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg2) =>
% 106.27/14.58 ((
% 106.27/14.58 (secondinupair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIR) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairiskpair) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairp) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowerset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairset2E) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairsubunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairinpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem3) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair1) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionE2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton1) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I2) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsuniq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (theprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstin) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR11) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR12) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR1) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairequniteq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemER) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempaircEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrI) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrSub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setOfPairsIsBReln) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrERa) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrER) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcImageSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (apProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (app) =>
% 106.27/14.58 ((
% 106.27/14.58 (infuncsetfunc) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcinfuncset) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall1) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp3) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcextLem) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp4) =>
% 106.27/14.58 ((
% 106.27/14.58 (subbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (eqbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq2) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2lamEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifp) =>
% 106.27/14.58 ((
% 106.27/14.58 (theeq) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrue) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueorfalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setextT) =>
% 106.27/14.58 ((
% 106.27/14.58 (subsetTI) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1015])).
% 106.27/14.58 thf(zip_derived_cl1039, plain,
% 106.27/14.58 (~ (((powersetI1) =>
% 106.27/14.58 (((powersetE1) =>
% 106.27/14.58 (((inPowerset) =>
% 106.27/14.58 (((powersetsubset) =>
% 106.27/14.58 (((sepInPowerset) =>
% 106.27/14.58 (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 (((binintersectSubset4) =>
% 106.27/14.58 (((binintersectSubset1) =>
% 106.27/14.58 (((bs114d) =>
% 106.27/14.58 (((setminusI) =>
% 106.27/14.58 (((setminusEL) =>
% 106.27/14.58 (((setminusER) =>
% 106.27/14.58 (((setminusSubset2) =>
% 106.27/14.58 (((setminusERneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusELneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusILneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusIRneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusLsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffE) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI2) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg2) =>
% 106.27/14.58 ((
% 106.27/14.58 (secondinupair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIR) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairiskpair) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairp) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowerset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairset2E) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairsubunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairinpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem3) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair1) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionE2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton1) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I2) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsuniq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (theprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstin) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR11) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR12) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR1) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairequniteq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemER) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempaircEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrI) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrSub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setOfPairsIsBReln) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrERa) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrER) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcImageSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (apProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (app) =>
% 106.27/14.58 ((
% 106.27/14.58 (infuncsetfunc) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcinfuncset) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall1) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp3) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcextLem) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp4) =>
% 106.27/14.58 ((
% 106.27/14.58 (subbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (eqbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq2) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2lamEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifp) =>
% 106.27/14.58 ((
% 106.27/14.58 (theeq) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrue) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueorfalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setextT) =>
% 106.27/14.58 ((
% 106.27/14.58 (subsetTI) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1027])).
% 106.27/14.58 thf(zip_derived_cl1055, plain,
% 106.27/14.58 (~ (((powersetE1) =>
% 106.27/14.58 (((inPowerset) =>
% 106.27/14.58 (((powersetsubset) =>
% 106.27/14.58 (((sepInPowerset) =>
% 106.27/14.58 (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 (((binintersectSubset4) =>
% 106.27/14.58 (((binintersectSubset1) =>
% 106.27/14.58 (((bs114d) =>
% 106.27/14.58 (((setminusI) =>
% 106.27/14.58 (((setminusEL) =>
% 106.27/14.58 (((setminusER) =>
% 106.27/14.58 (((setminusSubset2) =>
% 106.27/14.58 (((setminusERneg) =>
% 106.27/14.58 (((setminusELneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusILneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusIRneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusLsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffE) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI2) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg2) =>
% 106.27/14.58 ((
% 106.27/14.58 (secondinupair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIR) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairiskpair) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairp) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowerset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairset2E) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairsubunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairinpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem3) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair1) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionE2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton1) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I2) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsuniq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (theprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstin) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR11) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR12) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR1) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairequniteq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemER) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempaircEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrI) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrSub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setOfPairsIsBReln) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrERa) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrER) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcImageSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (apProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (app) =>
% 106.27/14.58 ((
% 106.27/14.58 (infuncsetfunc) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcinfuncset) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall1) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp3) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcextLem) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp4) =>
% 106.27/14.58 ((
% 106.27/14.58 (subbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (eqbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq2) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2lamEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifp) =>
% 106.27/14.58 ((
% 106.27/14.58 (theeq) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrue) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueorfalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setextT) =>
% 106.27/14.58 ((
% 106.27/14.58 (subsetTI) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1039])).
% 106.27/14.58 thf(zip_derived_cl1067, plain,
% 106.27/14.58 (~ (((inPowerset) =>
% 106.27/14.58 (((powersetsubset) =>
% 106.27/14.58 (((sepInPowerset) =>
% 106.27/14.58 (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 (((binintersectSubset4) =>
% 106.27/14.58 (((binintersectSubset1) =>
% 106.27/14.58 (((bs114d) =>
% 106.27/14.58 (((setminusI) =>
% 106.27/14.58 (((setminusEL) =>
% 106.27/14.58 (((setminusER) =>
% 106.27/14.58 (((setminusSubset2) =>
% 106.27/14.58 (((setminusERneg) =>
% 106.27/14.58 (((setminusELneg) =>
% 106.27/14.58 (((setminusILneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusIRneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusLsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffE) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI2) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg2) =>
% 106.27/14.58 ((
% 106.27/14.58 (secondinupair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIR) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairiskpair) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairp) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowerset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairset2E) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairsubunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairinpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem3) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair1) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionE2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton1) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I2) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsuniq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (theprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstin) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR11) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR12) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR1) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairequniteq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemER) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempaircEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrI) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrSub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setOfPairsIsBReln) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrERa) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrER) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcImageSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (apProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (app) =>
% 106.27/14.58 ((
% 106.27/14.58 (infuncsetfunc) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcinfuncset) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall1) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp3) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcextLem) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp4) =>
% 106.27/14.58 ((
% 106.27/14.58 (subbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (eqbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq2) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2lamEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifp) =>
% 106.27/14.58 ((
% 106.27/14.58 (theeq) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrue) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueorfalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setextT) =>
% 106.27/14.58 ((
% 106.27/14.58 (subsetTI) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1055])).
% 106.27/14.58 thf(zip_derived_cl1074, plain,
% 106.27/14.58 (~ (((powersetsubset) =>
% 106.27/14.58 (((sepInPowerset) =>
% 106.27/14.58 (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 (((binintersectSubset4) =>
% 106.27/14.58 (((binintersectSubset1) =>
% 106.27/14.58 (((bs114d) =>
% 106.27/14.58 (((setminusI) =>
% 106.27/14.58 (((setminusEL) =>
% 106.27/14.58 (((setminusER) =>
% 106.27/14.58 (((setminusSubset2) =>
% 106.27/14.58 (((setminusERneg) =>
% 106.27/14.58 (((setminusELneg) =>
% 106.27/14.58 (((setminusILneg) =>
% 106.27/14.58 (((setminusIRneg) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusLsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffE) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI2) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg2) =>
% 106.27/14.58 ((
% 106.27/14.58 (secondinupair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIR) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairiskpair) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairp) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowerset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairset2E) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairsubunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairinpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem3) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair1) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionE2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton1) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I2) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsuniq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (theprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstin) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR11) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR12) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR1) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairequniteq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemER) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempaircEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrI) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrSub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setOfPairsIsBReln) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrERa) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrER) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcImageSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (apProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (app) =>
% 106.27/14.58 ((
% 106.27/14.58 (infuncsetfunc) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcinfuncset) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall1) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp3) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcextLem) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp4) =>
% 106.27/14.58 ((
% 106.27/14.58 (subbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (eqbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq2) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2lamEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifp) =>
% 106.27/14.58 ((
% 106.27/14.58 (theeq) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrue) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueorfalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setextT) =>
% 106.27/14.58 ((
% 106.27/14.58 (subsetTI) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1067])).
% 106.27/14.58 thf(zip_derived_cl1082, plain,
% 106.27/14.58 (~ (((sepInPowerset) =>
% 106.27/14.58 (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 (((binintersectSubset4) =>
% 106.27/14.58 (((binintersectSubset1) =>
% 106.27/14.58 (((bs114d) =>
% 106.27/14.58 (((setminusI) =>
% 106.27/14.58 (((setminusEL) =>
% 106.27/14.58 (((setminusER) =>
% 106.27/14.58 (((setminusSubset2) =>
% 106.27/14.58 (((setminusERneg) =>
% 106.27/14.58 (((setminusELneg) =>
% 106.27/14.58 (((setminusILneg) =>
% 106.27/14.58 (((setminusIRneg) =>
% 106.27/14.58 (((setminusLsub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusSubset1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffE) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffI2) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg1) =>
% 106.27/14.58 ((
% 106.27/14.58 (symdiffIneg2) =>
% 106.27/14.58 ((
% 106.27/14.58 (secondinupair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairIR) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairiskpair) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairp) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowerset) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletoninpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairset2E) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairsubunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairinpowunion) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ubforcartprodlem3) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair1) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempair) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionE2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton1) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setunionsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1I2) =>
% 106.27/14.58 ((
% 106.27/14.58 (singletonsuniq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (theprop) =>
% 106.27/14.58 ((
% 106.27/14.58 (kfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstin) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjL) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR11) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR12) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR1) =>
% 106.27/14.58 ((
% 106.27/14.58 (upairequniteq) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR2) =>
% 106.27/14.58 ((
% 106.27/14.58 (setukpairinjR) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndsingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ksndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (kpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndin) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemEL) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairmemER) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodmempaircEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodfstpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodsndpairEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (cartprodpairsurjEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrI) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrSub) =>
% 106.27/14.58 ((
% 106.27/14.58 (setOfPairsIsBReln) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrERa) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL1) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrEL2) =>
% 106.27/14.58 ((
% 106.27/14.58 (dpsetconstrER) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcImageSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (apProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (app) =>
% 106.27/14.58 ((
% 106.27/14.58 (infuncsetfunc) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcinfuncset) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamProp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lamp) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2p) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall1) =>
% 106.27/14.58 ((
% 106.27/14.58 (brelnall2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ex1E2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp3) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcextLem) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcGraphProp4) =>
% 106.27/14.58 ((
% 106.27/14.58 (subbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (eqbreln) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext) =>
% 106.27/14.58 ((
% 106.27/14.58 (funcext2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq1) =>
% 106.27/14.58 ((
% 106.27/14.58 (ap2apEq2) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta1) =>
% 106.27/14.58 ((
% 106.27/14.58 (lam2lamEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (beta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (eta2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalseProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp1) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueProp2) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifSingleton) =>
% 106.27/14.58 ((
% 106.27/14.58 (ifp) =>
% 106.27/14.58 ((
% 106.27/14.58 (theeq) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrue) =>
% 106.27/14.58 ((
% 106.27/14.58 (iffalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (iftrueorfalse) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setminusT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementT_lem) =>
% 106.27/14.58 ((
% 106.27/14.58 (setextT) =>
% 106.27/14.58 ((
% 106.27/14.58 (subsetTI) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (powersetTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTELcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binintersectTERcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT1) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT2) =>
% 106.27/14.58 ((
% 106.27/14.58 (contrasubsetT3) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementI1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementE1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub1) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementSub2) =>
% 106.27/14.58 ((
% 106.27/14.58 (doubleComplementEq) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTnotintersectT) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementImpComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementSubsetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementInPowersetComplementIntersect) =>
% 106.27/14.58 ((
% 106.27/14.58 (contraSubsetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementTcontraSubset) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTILcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTIRcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInUnion2) =>
% 106.27/14.58 ((
% 106.27/14.58 (inIntersectImpInIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (intersectInPowersetIntersectUnions) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpNotIn1) =>
% 106.27/14.58 ((
% 106.27/14.58 (inComplementUnionImpInComplement1) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTE) =>
% 106.27/14.58 ((
% 106.27/14.58 (binunionTEcontra) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a1) =>
% 106.27/14.58 ((
% 106.27/14.58 (complementUnionInPowersetComplement) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan1) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2a) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b2) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2b) =>
% 106.27/14.58 ((
% 106.27/14.58 (demorgan2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule0) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz13rule4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_1) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_2) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_3) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_4) =>
% 106.27/14.58 ((
% 106.27/14.58 (woz1_5) =>
% 106.27/14.58 ((
% 106.27/14.58 (breln1all2) =>
% 106.27/14.58 ((
% 106.27/14.58 (!!) @ (
% 106.27/14.58 (('#B') @ (
% 106.27/14.58 !!) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#S') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 '#S') @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 =>))) @
% 106.27/14.58 (
% 106.27/14.58 (
% 106.27/14.58 ('#B') @ (
% 106.27/14.58 (
% 106.27/14.58 ('#C') @ in)) @
% 106.27/14.58 breln1Set)))))) @
% 106.27/14.58 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1074])).
% 106.27/14.58 thf(zip_derived_cl1090, plain,
% 106.27/14.58 (~ (((sepSubset) =>
% 106.27/14.58 (((binunionIL) =>
% 106.27/14.58 (((upairset2IR) =>
% 106.27/14.58 (((binunionIR) =>
% 106.27/14.58 (((binunionEcases) =>
% 106.27/14.58 (((binunionE) =>
% 106.27/14.58 (((binunionLsub) =>
% 106.27/14.58 (((binunionRsub) =>
% 106.27/14.58 (((binintersectI) =>
% 106.27/14.58 (((binintersectSubset5) =>
% 106.27/14.58 (((binintersectEL) =>
% 106.27/14.58 (((binintersectLsub) =>
% 106.27/14.58 (((binintersectSubset2) =>
% 106.27/14.58 (((binintersectSubset3) =>
% 106.27/14.58 (((binintersectER) =>
% 106.27/14.58 (((disjointsetsI1) =>
% 106.27/14.58 (((binintersectRsub) =>
% 106.27/14.58 (((binintersectSubset4) =>
% 106.27/14.58 (((binintersectSubset1) =>
% 106.27/14.58 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffE) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffI2) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffIneg1) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffIneg2) =>
% 106.27/14.59 ((
% 106.27/14.59 (secondinupair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIR) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairiskpair) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairp) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowerset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])).
% 106.27/14.59 thf(zip_derived_cl1096, plain,
% 106.27/14.59 (~ (((binunionIL) =>
% 106.27/14.59 (((upairset2IR) =>
% 106.27/14.59 (((binunionIR) =>
% 106.27/14.59 (((binunionEcases) =>
% 106.27/14.59 (((binunionE) =>
% 106.27/14.59 (((binunionLsub) =>
% 106.27/14.59 (((binunionRsub) =>
% 106.27/14.59 (((binintersectI) =>
% 106.27/14.59 (((binintersectSubset5) =>
% 106.27/14.59 (((binintersectEL) =>
% 106.27/14.59 (((binintersectLsub) =>
% 106.27/14.59 (((binintersectSubset2) =>
% 106.27/14.59 (((binintersectSubset3) =>
% 106.27/14.59 (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffI2) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffIneg1) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffIneg2) =>
% 106.27/14.59 ((
% 106.27/14.59 (secondinupair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIR) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairiskpair) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairp) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowerset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
% 106.27/14.59 thf(zip_derived_cl1102, plain,
% 106.27/14.59 (~ (((upairset2IR) =>
% 106.27/14.59 (((binunionIR) =>
% 106.27/14.59 (((binunionEcases) =>
% 106.27/14.59 (((binunionE) =>
% 106.27/14.59 (((binunionLsub) =>
% 106.27/14.59 (((binunionRsub) =>
% 106.27/14.59 (((binintersectI) =>
% 106.27/14.59 (((binintersectSubset5) =>
% 106.27/14.59 (((binintersectEL) =>
% 106.27/14.59 (((binintersectLsub) =>
% 106.27/14.59 (((binintersectSubset2) =>
% 106.27/14.59 (((binintersectSubset3) =>
% 106.27/14.59 (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 (((symdiffI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffI2) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffIneg1) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffIneg2) =>
% 106.27/14.59 ((
% 106.27/14.59 (secondinupair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIR) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairiskpair) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairp) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowerset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])).
% 106.27/14.59 thf(zip_derived_cl1109, plain,
% 106.27/14.59 (~ (((binunionIR) =>
% 106.27/14.59 (((binunionEcases) =>
% 106.27/14.59 (((binunionE) =>
% 106.27/14.59 (((binunionLsub) =>
% 106.27/14.59 (((binunionRsub) =>
% 106.27/14.59 (((binintersectI) =>
% 106.27/14.59 (((binintersectSubset5) =>
% 106.27/14.59 (((binintersectEL) =>
% 106.27/14.59 (((binintersectLsub) =>
% 106.27/14.59 (((binintersectSubset2) =>
% 106.27/14.59 (((binintersectSubset3) =>
% 106.27/14.59 (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 (((symdiffI1) =>
% 106.27/14.59 (((symdiffI2) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffIneg1) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffIneg2) =>
% 106.27/14.59 ((
% 106.27/14.59 (secondinupair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIR) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairiskpair) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairp) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowerset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1102])).
% 106.27/14.59 thf(zip_derived_cl1115, plain,
% 106.27/14.59 (~ (((binunionEcases) =>
% 106.27/14.59 (((binunionE) =>
% 106.27/14.59 (((binunionLsub) =>
% 106.27/14.59 (((binunionRsub) =>
% 106.27/14.59 (((binintersectI) =>
% 106.27/14.59 (((binintersectSubset5) =>
% 106.27/14.59 (((binintersectEL) =>
% 106.27/14.59 (((binintersectLsub) =>
% 106.27/14.59 (((binintersectSubset2) =>
% 106.27/14.59 (((binintersectSubset3) =>
% 106.27/14.59 (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 (((symdiffI1) =>
% 106.27/14.59 (((symdiffI2) =>
% 106.27/14.59 (((symdiffIneg1) =>
% 106.27/14.59 ((
% 106.27/14.59 (symdiffIneg2) =>
% 106.27/14.59 ((
% 106.27/14.59 (secondinupair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIR) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairiskpair) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairp) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowerset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1109])).
% 106.27/14.59 thf(zip_derived_cl1121, plain,
% 106.27/14.59 (~ (((binunionE) =>
% 106.27/14.59 (((binunionLsub) =>
% 106.27/14.59 (((binunionRsub) =>
% 106.27/14.59 (((binintersectI) =>
% 106.27/14.59 (((binintersectSubset5) =>
% 106.27/14.59 (((binintersectEL) =>
% 106.27/14.59 (((binintersectLsub) =>
% 106.27/14.59 (((binintersectSubset2) =>
% 106.27/14.59 (((binintersectSubset3) =>
% 106.27/14.59 (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 (((symdiffI1) =>
% 106.27/14.59 (((symdiffI2) =>
% 106.27/14.59 (((symdiffIneg1) =>
% 106.27/14.59 (((symdiffIneg2) =>
% 106.27/14.59 ((
% 106.27/14.59 (secondinupair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIR) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairiskpair) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairp) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowerset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1115])).
% 106.27/14.59 thf(zip_derived_cl1128, plain,
% 106.27/14.59 (~ (((binunionLsub) =>
% 106.27/14.59 (((binunionRsub) =>
% 106.27/14.59 (((binintersectI) =>
% 106.27/14.59 (((binintersectSubset5) =>
% 106.27/14.59 (((binintersectEL) =>
% 106.27/14.59 (((binintersectLsub) =>
% 106.27/14.59 (((binintersectSubset2) =>
% 106.27/14.59 (((binintersectSubset3) =>
% 106.27/14.59 (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 (((symdiffI1) =>
% 106.27/14.59 (((symdiffI2) =>
% 106.27/14.59 (((symdiffIneg1) =>
% 106.27/14.59 (((symdiffIneg2) =>
% 106.27/14.59 (((secondinupair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIR) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairiskpair) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairp) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowerset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1121])).
% 106.27/14.59 thf(zip_derived_cl1135, plain,
% 106.27/14.59 (~ (((binunionRsub) =>
% 106.27/14.59 (((binintersectI) =>
% 106.27/14.59 (((binintersectSubset5) =>
% 106.27/14.59 (((binintersectEL) =>
% 106.27/14.59 (((binintersectLsub) =>
% 106.27/14.59 (((binintersectSubset2) =>
% 106.27/14.59 (((binintersectSubset3) =>
% 106.27/14.59 (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 (((symdiffI1) =>
% 106.27/14.59 (((symdiffI2) =>
% 106.27/14.59 (((symdiffIneg1) =>
% 106.27/14.59 (((symdiffIneg2) =>
% 106.27/14.59 (((secondinupair) =>
% 106.27/14.59 (((setukpairIL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairIR) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairiskpair) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairp) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowerset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1128])).
% 106.27/14.59 thf(zip_derived_cl1142, plain,
% 106.27/14.59 (~ (((binintersectI) =>
% 106.27/14.59 (((binintersectSubset5) =>
% 106.27/14.59 (((binintersectEL) =>
% 106.27/14.59 (((binintersectLsub) =>
% 106.27/14.59 (((binintersectSubset2) =>
% 106.27/14.59 (((binintersectSubset3) =>
% 106.27/14.59 (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 (((symdiffI1) =>
% 106.27/14.59 (((symdiffI2) =>
% 106.27/14.59 (((symdiffIneg1) =>
% 106.27/14.59 (((symdiffIneg2) =>
% 106.27/14.59 (((secondinupair) =>
% 106.27/14.59 (((setukpairIL) =>
% 106.27/14.59 (((setukpairIR) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairiskpair) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairp) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowerset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1135])).
% 106.27/14.59 thf(zip_derived_cl1150, plain,
% 106.27/14.59 (~ (((binintersectSubset5) =>
% 106.27/14.59 (((binintersectEL) =>
% 106.27/14.59 (((binintersectLsub) =>
% 106.27/14.59 (((binintersectSubset2) =>
% 106.27/14.59 (((binintersectSubset3) =>
% 106.27/14.59 (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 (((symdiffI1) =>
% 106.27/14.59 (((symdiffI2) =>
% 106.27/14.59 (((symdiffIneg1) =>
% 106.27/14.59 (((symdiffIneg2) =>
% 106.27/14.59 (((secondinupair) =>
% 106.27/14.59 (((setukpairIL) =>
% 106.27/14.59 (((setukpairIR) =>
% 106.27/14.59 (((kpairiskpair) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairp) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowerset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1142])).
% 106.27/14.59 thf(zip_derived_cl1158, plain,
% 106.27/14.59 (~ (((binintersectEL) =>
% 106.27/14.59 (((binintersectLsub) =>
% 106.27/14.59 (((binintersectSubset2) =>
% 106.27/14.59 (((binintersectSubset3) =>
% 106.27/14.59 (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 (((symdiffI1) =>
% 106.27/14.59 (((symdiffI2) =>
% 106.27/14.59 (((symdiffIneg1) =>
% 106.27/14.59 (((symdiffIneg2) =>
% 106.27/14.59 (((secondinupair) =>
% 106.27/14.59 (((setukpairIL) =>
% 106.27/14.59 (((setukpairIR) =>
% 106.27/14.59 (((kpairiskpair) =>
% 106.27/14.59 (((kpairp) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowerset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1150])).
% 106.27/14.59 thf(zip_derived_cl1166, plain,
% 106.27/14.59 (~ (((binintersectLsub) =>
% 106.27/14.59 (((binintersectSubset2) =>
% 106.27/14.59 (((binintersectSubset3) =>
% 106.27/14.59 (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 (((symdiffI1) =>
% 106.27/14.59 (((symdiffI2) =>
% 106.27/14.59 (((symdiffIneg1) =>
% 106.27/14.59 (((symdiffIneg2) =>
% 106.27/14.59 (((secondinupair) =>
% 106.27/14.59 (((setukpairIL) =>
% 106.27/14.59 (((setukpairIR) =>
% 106.27/14.59 (((kpairiskpair) =>
% 106.27/14.59 (((kpairp) =>
% 106.27/14.59 (((singletonsubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowerset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1158])).
% 106.27/14.59 thf(zip_derived_cl1174, plain,
% 106.27/14.59 (~ (((binintersectSubset2) =>
% 106.27/14.59 (((binintersectSubset3) =>
% 106.27/14.59 (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 (((symdiffI1) =>
% 106.27/14.59 (((symdiffI2) =>
% 106.27/14.59 (((symdiffIneg1) =>
% 106.27/14.59 (((symdiffIneg2) =>
% 106.27/14.59 (((secondinupair) =>
% 106.27/14.59 (((setukpairIL) =>
% 106.27/14.59 (((setukpairIR) =>
% 106.27/14.59 (((kpairiskpair) =>
% 106.27/14.59 (((kpairp) =>
% 106.27/14.59 (((singletonsubset) =>
% 106.27/14.59 (((singletoninpowerset) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1166])).
% 106.27/14.59 thf(zip_derived_cl1183, plain,
% 106.27/14.59 (~ (((binintersectSubset3) =>
% 106.27/14.59 (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 (((symdiffI1) =>
% 106.27/14.59 (((symdiffI2) =>
% 106.27/14.59 (((symdiffIneg1) =>
% 106.27/14.59 (((symdiffIneg2) =>
% 106.27/14.59 (((secondinupair) =>
% 106.27/14.59 (((setukpairIL) =>
% 106.27/14.59 (((setukpairIR) =>
% 106.27/14.59 (((kpairiskpair) =>
% 106.27/14.59 (((kpairp) =>
% 106.27/14.59 (((singletonsubset) =>
% 106.27/14.59 (((singletoninpowerset) =>
% 106.27/14.59 (((singletoninpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTELcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectTERcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT1) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT2) =>
% 106.27/14.59 ((
% 106.27/14.59 (contrasubsetT3) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementI1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementE1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub1) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementSub2) =>
% 106.27/14.59 ((
% 106.27/14.59 (doubleComplementEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTnotintersectT) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementImpComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementSubsetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementInPowersetComplementIntersect) =>
% 106.27/14.59 ((
% 106.27/14.59 (contraSubsetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementTcontraSubset) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTILcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTIRcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInUnion2) =>
% 106.27/14.59 ((
% 106.27/14.59 (inIntersectImpInIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (intersectInPowersetIntersectUnions) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpNotIn1) =>
% 106.27/14.59 ((
% 106.27/14.59 (inComplementUnionImpInComplement1) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTE) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionTEcontra) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a1) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementUnionInPowersetComplement) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan1) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2a) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b2) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2b) =>
% 106.27/14.59 ((
% 106.27/14.59 (demorgan2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule0) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz13rule4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_1) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_2) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_3) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_4) =>
% 106.27/14.59 ((
% 106.27/14.59 (woz1_5) =>
% 106.27/14.59 ((
% 106.27/14.59 (breln1all2) =>
% 106.27/14.59 ((
% 106.27/14.59 (!!) @ (
% 106.27/14.59 (('#B') @ (
% 106.27/14.59 !!) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#S') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 '#S') @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 =>))) @
% 106.27/14.59 (
% 106.27/14.59 (
% 106.27/14.59 ('#B') @ (
% 106.27/14.59 (
% 106.27/14.59 ('#C') @ in)) @
% 106.27/14.59 breln1Set)))))) @
% 106.27/14.59 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])).
% 106.27/14.59 thf(zip_derived_cl1193, plain,
% 106.27/14.59 (~ (((binintersectER) =>
% 106.27/14.59 (((disjointsetsI1) =>
% 106.27/14.59 (((binintersectRsub) =>
% 106.27/14.59 (((binintersectSubset4) =>
% 106.27/14.59 (((binintersectSubset1) =>
% 106.27/14.59 (((bs114d) =>
% 106.27/14.59 (((setminusI) =>
% 106.27/14.59 (((setminusEL) =>
% 106.27/14.59 (((setminusER) =>
% 106.27/14.59 (((setminusSubset2) =>
% 106.27/14.59 (((setminusERneg) =>
% 106.27/14.59 (((setminusELneg) =>
% 106.27/14.59 (((setminusILneg) =>
% 106.27/14.59 (((setminusIRneg) =>
% 106.27/14.59 (((setminusLsub) =>
% 106.27/14.59 (((setminusSubset1) =>
% 106.27/14.59 (((symdiffE) =>
% 106.27/14.59 (((symdiffI1) =>
% 106.27/14.59 (((symdiffI2) =>
% 106.27/14.59 (((symdiffIneg1) =>
% 106.27/14.59 (((symdiffIneg2) =>
% 106.27/14.59 (((secondinupair) =>
% 106.27/14.59 (((setukpairIL) =>
% 106.27/14.59 (((setukpairIR) =>
% 106.27/14.59 (((kpairiskpair) =>
% 106.27/14.59 (((kpairp) =>
% 106.27/14.59 (((singletonsubset) =>
% 106.27/14.59 (((singletoninpowerset) =>
% 106.27/14.59 (((singletoninpowunion) =>
% 106.27/14.59 (((upairset2E) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairsubunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairinpowunion) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ubforcartprodlem3) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair1) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempair) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionE2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton1) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setunionsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1I2) =>
% 106.27/14.59 ((
% 106.27/14.59 (singletonsuniq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (theprop) =>
% 106.27/14.59 ((
% 106.27/14.59 (kfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstin) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjL) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR11) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR12) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR1) =>
% 106.27/14.59 ((
% 106.27/14.59 (upairequniteq) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR2) =>
% 106.27/14.59 ((
% 106.27/14.59 (setukpairinjR) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndsingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ksndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (kpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndin) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemEL) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairmemER) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodmempaircEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodfstpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodsndpairEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (cartprodpairsurjEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrI) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrSub) =>
% 106.27/14.59 ((
% 106.27/14.59 (setOfPairsIsBReln) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrERa) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL1) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrEL2) =>
% 106.27/14.59 ((
% 106.27/14.59 (dpsetconstrER) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcImageSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (apProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (app) =>
% 106.27/14.59 ((
% 106.27/14.59 (infuncsetfunc) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcinfuncset) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamProp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lamp) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2p) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall1) =>
% 106.27/14.59 ((
% 106.27/14.59 (brelnall2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ex1E2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp3) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcextLem) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcGraphProp4) =>
% 106.27/14.59 ((
% 106.27/14.59 (subbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (eqbreln) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext) =>
% 106.27/14.59 ((
% 106.27/14.59 (funcext2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq1) =>
% 106.27/14.59 ((
% 106.27/14.59 (ap2apEq2) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta1) =>
% 106.27/14.59 ((
% 106.27/14.59 (lam2lamEq) =>
% 106.27/14.59 ((
% 106.27/14.59 (beta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (eta2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalseProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp1) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueProp2) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifSingleton) =>
% 106.27/14.59 ((
% 106.27/14.59 (ifp) =>
% 106.27/14.59 ((
% 106.27/14.59 (theeq) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrue) =>
% 106.27/14.59 ((
% 106.27/14.59 (iffalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (iftrueorfalse) =>
% 106.27/14.59 ((
% 106.27/14.59 (binintersectT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (binunionT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setminusT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (complementT_lem) =>
% 106.27/14.59 ((
% 106.27/14.59 (setextT) =>
% 106.27/14.59 ((
% 106.27/14.59 (subsetTI) =>
% 106.27/14.59 ((
% 106.27/14.59 (powersetTI1) =>
% 106.27/14.59 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1183])).
% 106.27/14.60 thf(zip_derived_cl1206, plain,
% 106.27/14.60 (~ (((disjointsetsI1) =>
% 106.27/14.60 (((binintersectRsub) =>
% 106.27/14.60 (((binintersectSubset4) =>
% 106.27/14.60 (((binintersectSubset1) =>
% 106.27/14.60 (((bs114d) =>
% 106.27/14.60 (((setminusI) =>
% 106.27/14.60 (((setminusEL) =>
% 106.27/14.60 (((setminusER) =>
% 106.27/14.60 (((setminusSubset2) =>
% 106.27/14.60 (((setminusERneg) =>
% 106.27/14.60 (((setminusELneg) =>
% 106.27/14.60 (((setminusILneg) =>
% 106.27/14.60 (((setminusIRneg) =>
% 106.27/14.60 (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairinpowunion) =>
% 106.27/14.60 ((
% 106.27/14.60 (ubforcartprodlem1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ubforcartprodlem2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ubforcartprodlem3) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempair1) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempair) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionE2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton1) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1193])).
% 106.27/14.60 thf(zip_derived_cl1216, plain,
% 106.27/14.60 (~ (((binintersectRsub) =>
% 106.27/14.60 (((binintersectSubset4) =>
% 106.27/14.60 (((binintersectSubset1) =>
% 106.27/14.60 (((bs114d) =>
% 106.27/14.60 (((setminusI) =>
% 106.27/14.60 (((setminusEL) =>
% 106.27/14.60 (((setminusER) =>
% 106.27/14.60 (((setminusSubset2) =>
% 106.27/14.60 (((setminusERneg) =>
% 106.27/14.60 (((setminusELneg) =>
% 106.27/14.60 (((setminusILneg) =>
% 106.27/14.60 (((setminusIRneg) =>
% 106.27/14.60 (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 ((
% 106.27/14.60 (ubforcartprodlem1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ubforcartprodlem2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ubforcartprodlem3) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempair1) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempair) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionE2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton1) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1206])).
% 106.27/14.60 thf(zip_derived_cl1223, plain,
% 106.27/14.60 (~ (((binintersectSubset4) =>
% 106.27/14.60 (((binintersectSubset1) =>
% 106.27/14.60 (((bs114d) =>
% 106.27/14.60 (((setminusI) =>
% 106.27/14.60 (((setminusEL) =>
% 106.27/14.60 (((setminusER) =>
% 106.27/14.60 (((setminusSubset2) =>
% 106.27/14.60 (((setminusERneg) =>
% 106.27/14.60 (((setminusELneg) =>
% 106.27/14.60 (((setminusILneg) =>
% 106.27/14.60 (((setminusIRneg) =>
% 106.27/14.60 (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ubforcartprodlem2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ubforcartprodlem3) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempair1) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempair) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionE2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton1) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])).
% 106.27/14.60 thf(zip_derived_cl1231, plain,
% 106.27/14.60 (~ (((binintersectSubset1) =>
% 106.27/14.60 (((bs114d) =>
% 106.27/14.60 (((setminusI) =>
% 106.27/14.60 (((setminusEL) =>
% 106.27/14.60 (((setminusER) =>
% 106.27/14.60 (((setminusSubset2) =>
% 106.27/14.60 (((setminusERneg) =>
% 106.27/14.60 (((setminusELneg) =>
% 106.27/14.60 (((setminusILneg) =>
% 106.27/14.60 (((setminusIRneg) =>
% 106.27/14.60 (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 (((ubforcartprodlem2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ubforcartprodlem3) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempair1) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempair) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionE2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton1) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1223])).
% 106.27/14.60 thf(zip_derived_cl1239, plain,
% 106.27/14.60 (~ (((bs114d) =>
% 106.27/14.60 (((setminusI) =>
% 106.27/14.60 (((setminusEL) =>
% 106.27/14.60 (((setminusER) =>
% 106.27/14.60 (((setminusSubset2) =>
% 106.27/14.60 (((setminusERneg) =>
% 106.27/14.60 (((setminusELneg) =>
% 106.27/14.60 (((setminusILneg) =>
% 106.27/14.60 (((setminusIRneg) =>
% 106.27/14.60 (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 (((ubforcartprodlem2) =>
% 106.27/14.60 (((ubforcartprodlem3) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempair1) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempair) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionE2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton1) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1231])).
% 106.27/14.60 thf(zip_derived_cl1247, plain,
% 106.27/14.60 (~ (((setminusI) =>
% 106.27/14.60 (((setminusEL) =>
% 106.27/14.60 (((setminusER) =>
% 106.27/14.60 (((setminusSubset2) =>
% 106.27/14.60 (((setminusERneg) =>
% 106.27/14.60 (((setminusELneg) =>
% 106.27/14.60 (((setminusILneg) =>
% 106.27/14.60 (((setminusIRneg) =>
% 106.27/14.60 (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 (((ubforcartprodlem2) =>
% 106.27/14.60 (((ubforcartprodlem3) =>
% 106.27/14.60 (((cartprodpairin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempair1) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempair) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionE2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton1) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1239])).
% 106.27/14.60 thf(zip_derived_cl1255, plain,
% 106.27/14.60 (~ (((setminusEL) =>
% 106.27/14.60 (((setminusER) =>
% 106.27/14.60 (((setminusSubset2) =>
% 106.27/14.60 (((setminusERneg) =>
% 106.27/14.60 (((setminusELneg) =>
% 106.27/14.60 (((setminusILneg) =>
% 106.27/14.60 (((setminusIRneg) =>
% 106.27/14.60 (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 (((ubforcartprodlem2) =>
% 106.27/14.60 (((ubforcartprodlem3) =>
% 106.27/14.60 (((cartprodpairin) =>
% 106.27/14.60 (((cartprodmempair1) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempair) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionE2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton1) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1247])).
% 106.27/14.60 thf(zip_derived_cl1264, plain,
% 106.27/14.60 (~ (((setminusER) =>
% 106.27/14.60 (((setminusSubset2) =>
% 106.27/14.60 (((setminusERneg) =>
% 106.27/14.60 (((setminusELneg) =>
% 106.27/14.60 (((setminusILneg) =>
% 106.27/14.60 (((setminusIRneg) =>
% 106.27/14.60 (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 (((ubforcartprodlem2) =>
% 106.27/14.60 (((ubforcartprodlem3) =>
% 106.27/14.60 (((cartprodpairin) =>
% 106.27/14.60 (((cartprodmempair1) =>
% 106.27/14.60 (((cartprodmempair) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionE2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton1) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1255])).
% 106.27/14.60 thf(zip_derived_cl1272, plain,
% 106.27/14.60 (~ (((setminusSubset2) =>
% 106.27/14.60 (((setminusERneg) =>
% 106.27/14.60 (((setminusELneg) =>
% 106.27/14.60 (((setminusILneg) =>
% 106.27/14.60 (((setminusIRneg) =>
% 106.27/14.60 (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 (((ubforcartprodlem2) =>
% 106.27/14.60 (((ubforcartprodlem3) =>
% 106.27/14.60 (((cartprodpairin) =>
% 106.27/14.60 (((cartprodmempair1) =>
% 106.27/14.60 (((cartprodmempair) =>
% 106.27/14.60 (((setunionE2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton1) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1264])).
% 106.27/14.60 thf(zip_derived_cl1280, plain,
% 106.27/14.60 (~ (((setminusERneg) =>
% 106.27/14.60 (((setminusELneg) =>
% 106.27/14.60 (((setminusILneg) =>
% 106.27/14.60 (((setminusIRneg) =>
% 106.27/14.60 (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 (((ubforcartprodlem2) =>
% 106.27/14.60 (((ubforcartprodlem3) =>
% 106.27/14.60 (((cartprodpairin) =>
% 106.27/14.60 (((cartprodmempair1) =>
% 106.27/14.60 (((cartprodmempair) =>
% 106.27/14.60 (((setunionE2) =>
% 106.27/14.60 (((setunionsingleton1) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1272])).
% 106.27/14.60 thf(zip_derived_cl1288, plain,
% 106.27/14.60 (~ (((setminusELneg) =>
% 106.27/14.60 (((setminusILneg) =>
% 106.27/14.60 (((setminusIRneg) =>
% 106.27/14.60 (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 (((ubforcartprodlem2) =>
% 106.27/14.60 (((ubforcartprodlem3) =>
% 106.27/14.60 (((cartprodpairin) =>
% 106.27/14.60 (((cartprodmempair1) =>
% 106.27/14.60 (((cartprodmempair) =>
% 106.27/14.60 (((setunionE2) =>
% 106.27/14.60 (((setunionsingleton1) =>
% 106.27/14.60 (((setunionsingleton2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setunionsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1280])).
% 106.27/14.60 thf(zip_derived_cl1296, plain,
% 106.27/14.60 (~ (((setminusILneg) =>
% 106.27/14.60 (((setminusIRneg) =>
% 106.27/14.60 (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 (((ubforcartprodlem2) =>
% 106.27/14.60 (((ubforcartprodlem3) =>
% 106.27/14.60 (((cartprodpairin) =>
% 106.27/14.60 (((cartprodmempair1) =>
% 106.27/14.60 (((cartprodmempair) =>
% 106.27/14.60 (((setunionE2) =>
% 106.27/14.60 (((setunionsingleton1) =>
% 106.27/14.60 (((setunionsingleton2) =>
% 106.27/14.60 (((setunionsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])).
% 106.27/14.60 thf(zip_derived_cl1305, plain,
% 106.27/14.60 (~ (((setminusIRneg) =>
% 106.27/14.60 (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 (((ubforcartprodlem2) =>
% 106.27/14.60 (((ubforcartprodlem3) =>
% 106.27/14.60 (((cartprodpairin) =>
% 106.27/14.60 (((cartprodmempair1) =>
% 106.27/14.60 (((cartprodmempair) =>
% 106.27/14.60 (((setunionE2) =>
% 106.27/14.60 (((setunionsingleton1) =>
% 106.27/14.60 (((setunionsingleton2) =>
% 106.27/14.60 (((setunionsingleton) =>
% 106.27/14.60 (((singletonprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1296])).
% 106.27/14.60 thf(zip_derived_cl1313, plain,
% 106.27/14.60 (~ (((setminusLsub) =>
% 106.27/14.60 (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 (((ubforcartprodlem2) =>
% 106.27/14.60 (((ubforcartprodlem3) =>
% 106.27/14.60 (((cartprodpairin) =>
% 106.27/14.60 (((cartprodmempair1) =>
% 106.27/14.60 (((cartprodmempair) =>
% 106.27/14.60 (((setunionE2) =>
% 106.27/14.60 (((setunionsingleton1) =>
% 106.27/14.60 (((setunionsingleton2) =>
% 106.27/14.60 (((setunionsingleton) =>
% 106.27/14.60 (((singletonprop) =>
% 106.27/14.60 (((ex1E1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])).
% 106.27/14.60 thf(zip_derived_cl1321, plain,
% 106.27/14.60 (~ (((setminusSubset1) =>
% 106.27/14.60 (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 (((ubforcartprodlem2) =>
% 106.27/14.60 (((ubforcartprodlem3) =>
% 106.27/14.60 (((cartprodpairin) =>
% 106.27/14.60 (((cartprodmempair1) =>
% 106.27/14.60 (((cartprodmempair) =>
% 106.27/14.60 (((setunionE2) =>
% 106.27/14.60 (((setunionsingleton1) =>
% 106.27/14.60 (((setunionsingleton2) =>
% 106.27/14.60 (((setunionsingleton) =>
% 106.27/14.60 (((singletonprop) =>
% 106.27/14.60 (((ex1E1) =>
% 106.27/14.60 (((ex1I) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setminusT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementT_lem) =>
% 106.27/14.60 ((
% 106.27/14.60 (setextT) =>
% 106.27/14.60 ((
% 106.27/14.60 (subsetTI) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (powersetTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTELcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binintersectTERcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT1) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT2) =>
% 106.27/14.60 ((
% 106.27/14.60 (contrasubsetT3) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementI1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementE1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub1) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementSub2) =>
% 106.27/14.60 ((
% 106.27/14.60 (doubleComplementEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTnotintersectT) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementImpComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementSubsetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementInPowersetComplementIntersect) =>
% 106.27/14.60 ((
% 106.27/14.60 (contraSubsetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementTcontraSubset) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTILcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTIRcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInUnion2) =>
% 106.27/14.60 ((
% 106.27/14.60 (inIntersectImpInIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (intersectInPowersetIntersectUnions) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpNotIn1) =>
% 106.27/14.60 ((
% 106.27/14.60 (inComplementUnionImpInComplement1) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTE) =>
% 106.27/14.60 ((
% 106.27/14.60 (binunionTEcontra) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a1) =>
% 106.27/14.60 ((
% 106.27/14.60 (complementUnionInPowersetComplement) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan1) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2a) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b2) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2b) =>
% 106.27/14.60 ((
% 106.27/14.60 (demorgan2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule0) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz13rule4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_1) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_2) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_3) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_4) =>
% 106.27/14.60 ((
% 106.27/14.60 (woz1_5) =>
% 106.27/14.60 ((
% 106.27/14.60 (breln1all2) =>
% 106.27/14.60 ((
% 106.27/14.60 (!!) @ (
% 106.27/14.60 (('#B') @ (
% 106.27/14.60 !!) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#S') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 '#S') @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 =>))) @
% 106.27/14.60 (
% 106.27/14.60 (
% 106.27/14.60 ('#B') @ (
% 106.27/14.60 (
% 106.27/14.60 ('#C') @ in)) @
% 106.27/14.60 breln1Set)))))) @
% 106.27/14.60 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 106.27/14.60 thf(zip_derived_cl1329, plain,
% 106.27/14.60 (~ (((symdiffE) =>
% 106.27/14.60 (((symdiffI1) =>
% 106.27/14.60 (((symdiffI2) =>
% 106.27/14.60 (((symdiffIneg1) =>
% 106.27/14.60 (((symdiffIneg2) =>
% 106.27/14.60 (((secondinupair) =>
% 106.27/14.60 (((setukpairIL) =>
% 106.27/14.60 (((setukpairIR) =>
% 106.27/14.60 (((kpairiskpair) =>
% 106.27/14.60 (((kpairp) =>
% 106.27/14.60 (((singletonsubset) =>
% 106.27/14.60 (((singletoninpowerset) =>
% 106.27/14.60 (((singletoninpowunion) =>
% 106.27/14.60 (((upairset2E) =>
% 106.27/14.60 (((upairsubunion) =>
% 106.27/14.60 (((upairinpowunion) =>
% 106.27/14.60 (((ubforcartprodlem1) =>
% 106.27/14.60 (((ubforcartprodlem2) =>
% 106.27/14.60 (((ubforcartprodlem3) =>
% 106.27/14.60 (((cartprodpairin) =>
% 106.27/14.60 (((cartprodmempair1) =>
% 106.27/14.60 (((cartprodmempair) =>
% 106.27/14.60 (((setunionE2) =>
% 106.27/14.60 (((setunionsingleton1) =>
% 106.27/14.60 (((setunionsingleton2) =>
% 106.27/14.60 (((setunionsingleton) =>
% 106.27/14.60 (((singletonprop) =>
% 106.27/14.60 (((ex1E1) =>
% 106.27/14.60 (((ex1I) =>
% 106.27/14.60 (((ex1I2) =>
% 106.27/14.60 ((
% 106.27/14.60 (singletonsuniq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (theprop) =>
% 106.27/14.60 ((
% 106.27/14.60 (kfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstin) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjL) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR11) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR12) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR1) =>
% 106.27/14.60 ((
% 106.27/14.60 (upairequniteq) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR2) =>
% 106.27/14.60 ((
% 106.27/14.60 (setukpairinjR) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndsingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ksndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (kpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndin) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemEL) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairmemER) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodmempaircEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodfstpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodsndpairEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (cartprodpairsurjEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrI) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrSub) =>
% 106.27/14.60 ((
% 106.27/14.60 (setOfPairsIsBReln) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrERa) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL1) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrEL2) =>
% 106.27/14.60 ((
% 106.27/14.60 (dpsetconstrER) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcImageSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (apProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (app) =>
% 106.27/14.60 ((
% 106.27/14.60 (infuncsetfunc) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcinfuncset) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamProp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lamp) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2p) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall1) =>
% 106.27/14.60 ((
% 106.27/14.60 (brelnall2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ex1E2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp3) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcextLem) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcGraphProp4) =>
% 106.27/14.60 ((
% 106.27/14.60 (subbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (eqbreln) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext) =>
% 106.27/14.60 ((
% 106.27/14.60 (funcext2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq1) =>
% 106.27/14.60 ((
% 106.27/14.60 (ap2apEq2) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta1) =>
% 106.27/14.60 ((
% 106.27/14.60 (lam2lamEq) =>
% 106.27/14.60 ((
% 106.27/14.60 (beta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (eta2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalseProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp1) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueProp2) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifSingleton) =>
% 106.27/14.60 ((
% 106.27/14.60 (ifp) =>
% 106.27/14.60 ((
% 106.27/14.60 (theeq) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrue) =>
% 106.27/14.60 ((
% 106.27/14.60 (iffalse) =>
% 106.27/14.60 ((
% 106.27/14.60 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1321])).
% 106.27/14.61 thf(zip_derived_cl1338, plain,
% 106.27/14.61 (~ (((symdiffI1) =>
% 106.27/14.61 (((symdiffI2) =>
% 106.27/14.61 (((symdiffIneg1) =>
% 106.27/14.61 (((symdiffIneg2) =>
% 106.27/14.61 (((secondinupair) =>
% 106.27/14.61 (((setukpairIL) =>
% 106.27/14.61 (((setukpairIR) =>
% 106.27/14.61 (((kpairiskpair) =>
% 106.27/14.61 (((kpairp) =>
% 106.27/14.61 (((singletonsubset) =>
% 106.27/14.61 (((singletoninpowerset) =>
% 106.27/14.61 (((singletoninpowunion) =>
% 106.27/14.61 (((upairset2E) =>
% 106.27/14.61 (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (kfstsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (theprop) =>
% 106.27/14.61 ((
% 106.27/14.61 (kfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstin) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR11) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR12) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR1) =>
% 106.27/14.61 ((
% 106.27/14.61 (upairequniteq) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1329])).
% 106.27/14.61 thf(zip_derived_cl1347, plain,
% 106.27/14.61 (~ (((symdiffI2) =>
% 106.27/14.61 (((symdiffIneg1) =>
% 106.27/14.61 (((symdiffIneg2) =>
% 106.27/14.61 (((secondinupair) =>
% 106.27/14.61 (((setukpairIL) =>
% 106.27/14.61 (((setukpairIR) =>
% 106.27/14.61 (((kpairiskpair) =>
% 106.27/14.61 (((kpairp) =>
% 106.27/14.61 (((singletonsubset) =>
% 106.27/14.61 (((singletoninpowerset) =>
% 106.27/14.61 (((singletoninpowunion) =>
% 106.27/14.61 (((upairset2E) =>
% 106.27/14.61 (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (kfstsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (theprop) =>
% 106.27/14.61 ((
% 106.27/14.61 (kfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstin) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR11) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR12) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR1) =>
% 106.27/14.61 ((
% 106.27/14.61 (upairequniteq) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1338])).
% 106.27/14.61 thf(zip_derived_cl1354, plain,
% 106.27/14.61 (~ (((symdiffIneg1) =>
% 106.27/14.61 (((symdiffIneg2) =>
% 106.27/14.61 (((secondinupair) =>
% 106.27/14.61 (((setukpairIL) =>
% 106.27/14.61 (((setukpairIR) =>
% 106.27/14.61 (((kpairiskpair) =>
% 106.27/14.61 (((kpairp) =>
% 106.27/14.61 (((singletonsubset) =>
% 106.27/14.61 (((singletoninpowerset) =>
% 106.27/14.61 (((singletoninpowunion) =>
% 106.27/14.61 (((upairset2E) =>
% 106.27/14.61 (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (theprop) =>
% 106.27/14.61 ((
% 106.27/14.61 (kfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstin) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR11) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR12) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR1) =>
% 106.27/14.61 ((
% 106.27/14.61 (upairequniteq) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1347])).
% 106.27/14.61 thf(zip_derived_cl1361, plain,
% 106.27/14.61 (~ (((symdiffIneg2) =>
% 106.27/14.61 (((secondinupair) =>
% 106.27/14.61 (((setukpairIL) =>
% 106.27/14.61 (((setukpairIR) =>
% 106.27/14.61 (((kpairiskpair) =>
% 106.27/14.61 (((kpairp) =>
% 106.27/14.61 (((singletonsubset) =>
% 106.27/14.61 (((singletoninpowerset) =>
% 106.27/14.61 (((singletoninpowunion) =>
% 106.27/14.61 (((upairset2E) =>
% 106.27/14.61 (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 ((
% 106.27/14.61 (kfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstin) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR11) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR12) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR1) =>
% 106.27/14.61 ((
% 106.27/14.61 (upairequniteq) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1354])).
% 106.27/14.61 thf(zip_derived_cl1369, plain,
% 106.27/14.61 (~ (((secondinupair) =>
% 106.27/14.61 (((setukpairIL) =>
% 106.27/14.61 (((setukpairIR) =>
% 106.27/14.61 (((kpairiskpair) =>
% 106.27/14.61 (((kpairp) =>
% 106.27/14.61 (((singletonsubset) =>
% 106.27/14.61 (((singletoninpowerset) =>
% 106.27/14.61 (((singletoninpowunion) =>
% 106.27/14.61 (((upairset2E) =>
% 106.27/14.61 (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstin) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR11) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR12) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR1) =>
% 106.27/14.61 ((
% 106.27/14.61 (upairequniteq) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])).
% 106.27/14.61 thf(zip_derived_cl1377, plain,
% 106.27/14.61 (~ (((setukpairIL) =>
% 106.27/14.61 (((setukpairIR) =>
% 106.27/14.61 (((kpairiskpair) =>
% 106.27/14.61 (((kpairp) =>
% 106.27/14.61 (((singletonsubset) =>
% 106.27/14.61 (((singletoninpowerset) =>
% 106.27/14.61 (((singletoninpowunion) =>
% 106.27/14.61 (((upairset2E) =>
% 106.27/14.61 (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 (((cartprodfstin) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR11) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR12) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR1) =>
% 106.27/14.61 ((
% 106.27/14.61 (upairequniteq) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1369])).
% 106.27/14.61 thf(zip_derived_cl1386, plain,
% 106.27/14.61 (~ (((setukpairIR) =>
% 106.27/14.61 (((kpairiskpair) =>
% 106.27/14.61 (((kpairp) =>
% 106.27/14.61 (((singletonsubset) =>
% 106.27/14.61 (((singletoninpowerset) =>
% 106.27/14.61 (((singletoninpowunion) =>
% 106.27/14.61 (((upairset2E) =>
% 106.27/14.61 (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 (((cartprodfstin) =>
% 106.27/14.61 (((setukpairinjL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjL) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR11) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR12) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR1) =>
% 106.27/14.61 ((
% 106.27/14.61 (upairequniteq) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])).
% 106.27/14.61 thf(zip_derived_cl1396, plain,
% 106.27/14.61 (~ (((kpairiskpair) =>
% 106.27/14.61 (((kpairp) =>
% 106.27/14.61 (((singletonsubset) =>
% 106.27/14.61 (((singletoninpowerset) =>
% 106.27/14.61 (((singletoninpowunion) =>
% 106.27/14.61 (((upairset2E) =>
% 106.27/14.61 (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 (((cartprodfstin) =>
% 106.27/14.61 (((setukpairinjL2) =>
% 106.27/14.61 (((setukpairinjL) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR11) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR12) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR1) =>
% 106.27/14.61 ((
% 106.27/14.61 (upairequniteq) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1386])).
% 106.27/14.61 thf(zip_derived_cl1407, plain,
% 106.27/14.61 (~ (((kpairp) =>
% 106.27/14.61 (((singletonsubset) =>
% 106.27/14.61 (((singletoninpowerset) =>
% 106.27/14.61 (((singletoninpowunion) =>
% 106.27/14.61 (((upairset2E) =>
% 106.27/14.61 (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 (((cartprodfstin) =>
% 106.27/14.61 (((setukpairinjL2) =>
% 106.27/14.61 (((setukpairinjL) =>
% 106.27/14.61 (((setukpairinjR11) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR12) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR1) =>
% 106.27/14.61 ((
% 106.27/14.61 (upairequniteq) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
% 106.27/14.61 thf(zip_derived_cl1420, plain,
% 106.27/14.61 (~ (((singletonsubset) =>
% 106.27/14.61 (((singletoninpowerset) =>
% 106.27/14.61 (((singletoninpowunion) =>
% 106.27/14.61 (((upairset2E) =>
% 106.27/14.61 (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 (((cartprodfstin) =>
% 106.27/14.61 (((setukpairinjL2) =>
% 106.27/14.61 (((setukpairinjL) =>
% 106.27/14.61 (((setukpairinjR11) =>
% 106.27/14.61 (((setukpairinjR12) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR1) =>
% 106.27/14.61 ((
% 106.27/14.61 (upairequniteq) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1407])).
% 106.27/14.61 thf(zip_derived_cl1433, plain,
% 106.27/14.61 (~ (((singletoninpowerset) =>
% 106.27/14.61 (((singletoninpowunion) =>
% 106.27/14.61 (((upairset2E) =>
% 106.27/14.61 (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 (((cartprodfstin) =>
% 106.27/14.61 (((setukpairinjL2) =>
% 106.27/14.61 (((setukpairinjL) =>
% 106.27/14.61 (((setukpairinjR11) =>
% 106.27/14.61 (((setukpairinjR12) =>
% 106.27/14.61 (((setukpairinjR1) =>
% 106.27/14.61 ((
% 106.27/14.61 (upairequniteq) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1420])).
% 106.27/14.61 thf(zip_derived_cl1444, plain,
% 106.27/14.61 (~ (((singletoninpowunion) =>
% 106.27/14.61 (((upairset2E) =>
% 106.27/14.61 (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 (((cartprodfstin) =>
% 106.27/14.61 (((setukpairinjL2) =>
% 106.27/14.61 (((setukpairinjL) =>
% 106.27/14.61 (((setukpairinjR11) =>
% 106.27/14.61 (((setukpairinjR12) =>
% 106.27/14.61 (((setukpairinjR1) =>
% 106.27/14.61 (((upairequniteq) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1433])).
% 106.27/14.61 thf(zip_derived_cl1452, plain,
% 106.27/14.61 (~ (((upairset2E) =>
% 106.27/14.61 (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 (((cartprodfstin) =>
% 106.27/14.61 (((setukpairinjL2) =>
% 106.27/14.61 (((setukpairinjL) =>
% 106.27/14.61 (((setukpairinjR11) =>
% 106.27/14.61 (((setukpairinjR12) =>
% 106.27/14.61 (((setukpairinjR1) =>
% 106.27/14.61 (((upairequniteq) =>
% 106.27/14.61 (((setukpairinjR2) =>
% 106.27/14.61 ((
% 106.27/14.61 (setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1444])).
% 106.27/14.61 thf(zip_derived_cl1459, plain,
% 106.27/14.61 (~ (((upairsubunion) =>
% 106.27/14.61 (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 (((cartprodfstin) =>
% 106.27/14.61 (((setukpairinjL2) =>
% 106.27/14.61 (((setukpairinjL) =>
% 106.27/14.61 (((setukpairinjR11) =>
% 106.27/14.61 (((setukpairinjR12) =>
% 106.27/14.61 (((setukpairinjR1) =>
% 106.27/14.61 (((upairequniteq) =>
% 106.27/14.61 (((setukpairinjR2) =>
% 106.27/14.61 (((setukpairinjR) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1452])).
% 106.27/14.61 thf(zip_derived_cl1466, plain,
% 106.27/14.61 (~ (((upairinpowunion) =>
% 106.27/14.61 (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 (((cartprodfstin) =>
% 106.27/14.61 (((setukpairinjL2) =>
% 106.27/14.61 (((setukpairinjL) =>
% 106.27/14.61 (((setukpairinjR11) =>
% 106.27/14.61 (((setukpairinjR12) =>
% 106.27/14.61 (((setukpairinjR1) =>
% 106.27/14.61 (((upairequniteq) =>
% 106.27/14.61 (((setukpairinjR2) =>
% 106.27/14.61 (((setukpairinjR) =>
% 106.27/14.61 (((ksndsingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1459])).
% 106.27/14.61 thf(zip_derived_cl1473, plain,
% 106.27/14.61 (~ (((ubforcartprodlem1) =>
% 106.27/14.61 (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 (((cartprodfstin) =>
% 106.27/14.61 (((setukpairinjL2) =>
% 106.27/14.61 (((setukpairinjL) =>
% 106.27/14.61 (((setukpairinjR11) =>
% 106.27/14.61 (((setukpairinjR12) =>
% 106.27/14.61 (((setukpairinjR1) =>
% 106.27/14.61 (((upairequniteq) =>
% 106.27/14.61 (((setukpairinjR2) =>
% 106.27/14.61 (((setukpairinjR) =>
% 106.27/14.61 (((ksndsingleton) =>
% 106.27/14.61 (((ksndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1466])).
% 106.27/14.61 thf(zip_derived_cl1480, plain,
% 106.27/14.61 (~ (((ubforcartprodlem2) =>
% 106.27/14.61 (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 (((cartprodfstin) =>
% 106.27/14.61 (((setukpairinjL2) =>
% 106.27/14.61 (((setukpairinjL) =>
% 106.27/14.61 (((setukpairinjR11) =>
% 106.27/14.61 (((setukpairinjR12) =>
% 106.27/14.61 (((setukpairinjR1) =>
% 106.27/14.61 (((upairequniteq) =>
% 106.27/14.61 (((setukpairinjR2) =>
% 106.27/14.61 (((setukpairinjR) =>
% 106.27/14.61 (((ksndsingleton) =>
% 106.27/14.61 (((ksndpairEq) =>
% 106.27/14.61 (((kpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall1) =>
% 106.27/14.61 ((
% 106.27/14.61 (brelnall2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ex1E2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp3) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcextLem) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcGraphProp4) =>
% 106.27/14.61 ((
% 106.27/14.61 (subbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (eqbreln) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcext2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq1) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2apEq2) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta1) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2lamEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (beta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (eta2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalseProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp1) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueProp2) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (ifp) =>
% 106.27/14.61 ((
% 106.27/14.61 (theeq) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrue) =>
% 106.27/14.61 ((
% 106.27/14.61 (iffalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (iftrueorfalse) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setminusT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementT_lem) =>
% 106.27/14.61 ((
% 106.27/14.61 (setextT) =>
% 106.27/14.61 ((
% 106.27/14.61 (subsetTI) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (powersetTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTELcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binintersectTERcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT1) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT2) =>
% 106.27/14.61 ((
% 106.27/14.61 (contrasubsetT3) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementI1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementE1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub1) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementSub2) =>
% 106.27/14.61 ((
% 106.27/14.61 (doubleComplementEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTnotintersectT) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementImpComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementSubsetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementInPowersetComplementIntersect) =>
% 106.27/14.61 ((
% 106.27/14.61 (contraSubsetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementTcontraSubset) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTILcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTIRcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInUnion2) =>
% 106.27/14.61 ((
% 106.27/14.61 (inIntersectImpInIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (intersectInPowersetIntersectUnions) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpNotIn1) =>
% 106.27/14.61 ((
% 106.27/14.61 (inComplementUnionImpInComplement1) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTE) =>
% 106.27/14.61 ((
% 106.27/14.61 (binunionTEcontra) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a1) =>
% 106.27/14.61 ((
% 106.27/14.61 (complementUnionInPowersetComplement) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan1) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2a) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b2) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2b) =>
% 106.27/14.61 ((
% 106.27/14.61 (demorgan2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule0) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz13rule4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_1) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_2) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_3) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_4) =>
% 106.27/14.61 ((
% 106.27/14.61 (woz1_5) =>
% 106.27/14.61 ((
% 106.27/14.61 (breln1all2) =>
% 106.27/14.61 ((
% 106.27/14.61 (!!) @ (
% 106.27/14.61 (('#B') @ (
% 106.27/14.61 !!) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#S') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 '#S') @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 =>))) @
% 106.27/14.61 (
% 106.27/14.61 (
% 106.27/14.61 ('#B') @ (
% 106.27/14.61 (
% 106.27/14.61 ('#C') @ in)) @
% 106.27/14.61 breln1Set)))))) @
% 106.27/14.61 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1473])).
% 106.27/14.61 thf(zip_derived_cl1488, plain,
% 106.27/14.61 (~ (((ubforcartprodlem3) =>
% 106.27/14.61 (((cartprodpairin) =>
% 106.27/14.61 (((cartprodmempair1) =>
% 106.27/14.61 (((cartprodmempair) =>
% 106.27/14.61 (((setunionE2) =>
% 106.27/14.61 (((setunionsingleton1) =>
% 106.27/14.61 (((setunionsingleton2) =>
% 106.27/14.61 (((setunionsingleton) =>
% 106.27/14.61 (((singletonprop) =>
% 106.27/14.61 (((ex1E1) =>
% 106.27/14.61 (((ex1I) =>
% 106.27/14.61 (((ex1I2) =>
% 106.27/14.61 (((singletonsuniq) =>
% 106.27/14.61 (((setukpairinjL1) =>
% 106.27/14.61 (((kfstsingleton) =>
% 106.27/14.61 (((theprop) =>
% 106.27/14.61 (((kfstpairEq) =>
% 106.27/14.61 (((cartprodfstin) =>
% 106.27/14.61 (((setukpairinjL2) =>
% 106.27/14.61 (((setukpairinjL) =>
% 106.27/14.61 (((setukpairinjR11) =>
% 106.27/14.61 (((setukpairinjR12) =>
% 106.27/14.61 (((setukpairinjR1) =>
% 106.27/14.61 (((upairequniteq) =>
% 106.27/14.61 (((setukpairinjR2) =>
% 106.27/14.61 (((setukpairinjR) =>
% 106.27/14.61 (((ksndsingleton) =>
% 106.27/14.61 (((ksndpairEq) =>
% 106.27/14.61 (((kpairsurjEq) =>
% 106.27/14.61 (((cartprodsndin) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemEL) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairmemER) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodmempaircEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodfstpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodsndpairEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (cartprodpairsurjEq) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrI) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrSub) =>
% 106.27/14.61 ((
% 106.27/14.61 (setOfPairsIsBReln) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrERa) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL1) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrEL2) =>
% 106.27/14.61 ((
% 106.27/14.61 (dpsetconstrER) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcImageSingleton) =>
% 106.27/14.61 ((
% 106.27/14.61 (apProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (app) =>
% 106.27/14.61 ((
% 106.27/14.61 (infuncsetfunc) =>
% 106.27/14.61 ((
% 106.27/14.61 (ap2p) =>
% 106.27/14.61 ((
% 106.27/14.61 (funcinfuncset) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamProp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lamp) =>
% 106.27/14.61 ((
% 106.27/14.61 (lam2p) =>
% 106.27/14.61 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1480])).
% 106.27/14.62 thf(zip_derived_cl1496, plain,
% 106.27/14.62 (~ (((cartprodpairin) =>
% 106.27/14.62 (((cartprodmempair1) =>
% 106.27/14.62 (((cartprodmempair) =>
% 106.27/14.62 (((setunionE2) =>
% 106.27/14.62 (((setunionsingleton1) =>
% 106.27/14.62 (((setunionsingleton2) =>
% 106.27/14.62 (((setunionsingleton) =>
% 106.27/14.62 (((singletonprop) =>
% 106.27/14.62 (((ex1E1) =>
% 106.27/14.62 (((ex1I) =>
% 106.27/14.62 (((ex1I2) =>
% 106.27/14.62 (((singletonsuniq) =>
% 106.27/14.62 (((setukpairinjL1) =>
% 106.27/14.62 (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodpairmemER) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodmempaircEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodfstpairEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodsndpairEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodpairsurjEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrI) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrSub) =>
% 106.27/14.62 ((
% 106.27/14.62 (setOfPairsIsBReln) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrERa) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL1) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL2) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrER) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1488])).
% 106.27/14.62 thf(zip_derived_cl1505, plain,
% 106.27/14.62 (~ (((cartprodmempair1) =>
% 106.27/14.62 (((cartprodmempair) =>
% 106.27/14.62 (((setunionE2) =>
% 106.27/14.62 (((setunionsingleton1) =>
% 106.27/14.62 (((setunionsingleton2) =>
% 106.27/14.62 (((setunionsingleton) =>
% 106.27/14.62 (((singletonprop) =>
% 106.27/14.62 (((ex1E1) =>
% 106.27/14.62 (((ex1I) =>
% 106.27/14.62 (((ex1I2) =>
% 106.27/14.62 (((singletonsuniq) =>
% 106.27/14.62 (((setukpairinjL1) =>
% 106.27/14.62 (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodmempaircEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodfstpairEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodsndpairEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodpairsurjEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrI) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrSub) =>
% 106.27/14.62 ((
% 106.27/14.62 (setOfPairsIsBReln) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrERa) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL1) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL2) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrER) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1496])).
% 106.27/14.62 thf(zip_derived_cl1515, plain,
% 106.27/14.62 (~ (((cartprodmempair) =>
% 106.27/14.62 (((setunionE2) =>
% 106.27/14.62 (((setunionsingleton1) =>
% 106.27/14.62 (((setunionsingleton2) =>
% 106.27/14.62 (((setunionsingleton) =>
% 106.27/14.62 (((singletonprop) =>
% 106.27/14.62 (((ex1E1) =>
% 106.27/14.62 (((ex1I) =>
% 106.27/14.62 (((ex1I2) =>
% 106.27/14.62 (((singletonsuniq) =>
% 106.27/14.62 (((setukpairinjL1) =>
% 106.27/14.62 (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodfstpairEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodsndpairEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodpairsurjEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrI) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrSub) =>
% 106.27/14.62 ((
% 106.27/14.62 (setOfPairsIsBReln) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrERa) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL1) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL2) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrER) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1505])).
% 106.27/14.62 thf(zip_derived_cl1525, plain,
% 106.27/14.62 (~ (((setunionE2) =>
% 106.27/14.62 (((setunionsingleton1) =>
% 106.27/14.62 (((setunionsingleton2) =>
% 106.27/14.62 (((setunionsingleton) =>
% 106.27/14.62 (((singletonprop) =>
% 106.27/14.62 (((ex1E1) =>
% 106.27/14.62 (((ex1I) =>
% 106.27/14.62 (((ex1I2) =>
% 106.27/14.62 (((singletonsuniq) =>
% 106.27/14.62 (((setukpairinjL1) =>
% 106.27/14.62 (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodsndpairEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodpairsurjEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrI) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrSub) =>
% 106.27/14.62 ((
% 106.27/14.62 (setOfPairsIsBReln) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrERa) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL1) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL2) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrER) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1515])).
% 106.27/14.62 thf(zip_derived_cl1535, plain,
% 106.27/14.62 (~ (((setunionsingleton1) =>
% 106.27/14.62 (((setunionsingleton2) =>
% 106.27/14.62 (((setunionsingleton) =>
% 106.27/14.62 (((singletonprop) =>
% 106.27/14.62 (((ex1E1) =>
% 106.27/14.62 (((ex1I) =>
% 106.27/14.62 (((ex1I2) =>
% 106.27/14.62 (((singletonsuniq) =>
% 106.27/14.62 (((setukpairinjL1) =>
% 106.27/14.62 (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (cartprodpairsurjEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrI) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrSub) =>
% 106.27/14.62 ((
% 106.27/14.62 (setOfPairsIsBReln) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrERa) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL1) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL2) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrER) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1525])).
% 106.27/14.62 thf(zip_derived_cl1545, plain,
% 106.27/14.62 (~ (((setunionsingleton2) =>
% 106.27/14.62 (((setunionsingleton) =>
% 106.27/14.62 (((singletonprop) =>
% 106.27/14.62 (((ex1E1) =>
% 106.27/14.62 (((ex1I) =>
% 106.27/14.62 (((ex1I2) =>
% 106.27/14.62 (((singletonsuniq) =>
% 106.27/14.62 (((setukpairinjL1) =>
% 106.27/14.62 (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrI) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrSub) =>
% 106.27/14.62 ((
% 106.27/14.62 (setOfPairsIsBReln) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrERa) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL1) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL2) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrER) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1535])).
% 106.27/14.62 thf(zip_derived_cl1555, plain,
% 106.27/14.62 (~ (((setunionsingleton) =>
% 106.27/14.62 (((singletonprop) =>
% 106.27/14.62 (((ex1E1) =>
% 106.27/14.62 (((ex1I) =>
% 106.27/14.62 (((ex1I2) =>
% 106.27/14.62 (((singletonsuniq) =>
% 106.27/14.62 (((setukpairinjL1) =>
% 106.27/14.62 (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrSub) =>
% 106.27/14.62 ((
% 106.27/14.62 (setOfPairsIsBReln) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrERa) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL1) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL2) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrER) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1545])).
% 106.27/14.62 thf(zip_derived_cl1565, plain,
% 106.27/14.62 (~ (((singletonprop) =>
% 106.27/14.62 (((ex1E1) =>
% 106.27/14.62 (((ex1I) =>
% 106.27/14.62 (((ex1I2) =>
% 106.27/14.62 (((singletonsuniq) =>
% 106.27/14.62 (((setukpairinjL1) =>
% 106.27/14.62 (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 (((dpsetconstrSub) =>
% 106.27/14.62 ((
% 106.27/14.62 (setOfPairsIsBReln) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrERa) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL1) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL2) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrER) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1555])).
% 106.27/14.62 thf(zip_derived_cl1574, plain,
% 106.27/14.62 (~ (((ex1E1) =>
% 106.27/14.62 (((ex1I) =>
% 106.27/14.62 (((ex1I2) =>
% 106.27/14.62 (((singletonsuniq) =>
% 106.27/14.62 (((setukpairinjL1) =>
% 106.27/14.62 (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 (((dpsetconstrSub) =>
% 106.27/14.62 (((setOfPairsIsBReln) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrERa) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL1) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL2) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrER) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1565])).
% 106.27/14.62 thf(zip_derived_cl1582, plain,
% 106.27/14.62 (~ (((ex1I) =>
% 106.27/14.62 (((ex1I2) =>
% 106.27/14.62 (((singletonsuniq) =>
% 106.27/14.62 (((setukpairinjL1) =>
% 106.27/14.62 (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 (((dpsetconstrSub) =>
% 106.27/14.62 (((setOfPairsIsBReln) =>
% 106.27/14.62 (((dpsetconstrERa) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL1) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL2) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrER) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1574])).
% 106.27/14.62 thf(zip_derived_cl1591, plain,
% 106.27/14.62 (~ (((ex1I2) =>
% 106.27/14.62 (((singletonsuniq) =>
% 106.27/14.62 (((setukpairinjL1) =>
% 106.27/14.62 (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 (((dpsetconstrSub) =>
% 106.27/14.62 (((setOfPairsIsBReln) =>
% 106.27/14.62 (((dpsetconstrERa) =>
% 106.27/14.62 (((dpsetconstrEL1) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrEL2) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrER) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1582])).
% 106.27/14.62 thf(zip_derived_cl1599, plain,
% 106.27/14.62 (~ (((singletonsuniq) =>
% 106.27/14.62 (((setukpairinjL1) =>
% 106.27/14.62 (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 (((dpsetconstrSub) =>
% 106.27/14.62 (((setOfPairsIsBReln) =>
% 106.27/14.62 (((dpsetconstrERa) =>
% 106.27/14.62 (((dpsetconstrEL1) =>
% 106.27/14.62 (((dpsetconstrEL2) =>
% 106.27/14.62 ((
% 106.27/14.62 (dpsetconstrER) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1591])).
% 106.27/14.62 thf(zip_derived_cl1607, plain,
% 106.27/14.62 (~ (((setukpairinjL1) =>
% 106.27/14.62 (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 (((dpsetconstrSub) =>
% 106.27/14.62 (((setOfPairsIsBReln) =>
% 106.27/14.62 (((dpsetconstrERa) =>
% 106.27/14.62 (((dpsetconstrEL1) =>
% 106.27/14.62 (((dpsetconstrEL2) =>
% 106.27/14.62 (((dpsetconstrER) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1599])).
% 106.27/14.62 thf(zip_derived_cl1616, plain,
% 106.27/14.62 (~ (((kfstsingleton) =>
% 106.27/14.62 (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 (((dpsetconstrSub) =>
% 106.27/14.62 (((setOfPairsIsBReln) =>
% 106.27/14.62 (((dpsetconstrERa) =>
% 106.27/14.62 (((dpsetconstrEL1) =>
% 106.27/14.62 (((dpsetconstrEL2) =>
% 106.27/14.62 (((dpsetconstrER) =>
% 106.27/14.62 (((funcImageSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1607])).
% 106.27/14.62 thf(zip_derived_cl1627, plain,
% 106.27/14.62 (~ (((theprop) =>
% 106.27/14.62 (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 (((dpsetconstrSub) =>
% 106.27/14.62 (((setOfPairsIsBReln) =>
% 106.27/14.62 (((dpsetconstrERa) =>
% 106.27/14.62 (((dpsetconstrEL1) =>
% 106.27/14.62 (((dpsetconstrEL2) =>
% 106.27/14.62 (((dpsetconstrER) =>
% 106.27/14.62 (((funcImageSingleton) =>
% 106.27/14.62 (((apProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1616])).
% 106.27/14.62 thf(zip_derived_cl1640, plain,
% 106.27/14.62 (~ (((kfstpairEq) =>
% 106.27/14.62 (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 (((dpsetconstrSub) =>
% 106.27/14.62 (((setOfPairsIsBReln) =>
% 106.27/14.62 (((dpsetconstrERa) =>
% 106.27/14.62 (((dpsetconstrEL1) =>
% 106.27/14.62 (((dpsetconstrEL2) =>
% 106.27/14.62 (((dpsetconstrER) =>
% 106.27/14.62 (((funcImageSingleton) =>
% 106.27/14.62 (((apProp) =>
% 106.27/14.62 (((app) =>
% 106.27/14.62 ((
% 106.27/14.62 (infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1627])).
% 106.27/14.62 thf(zip_derived_cl1652, plain,
% 106.27/14.62 (~ (((cartprodfstin) =>
% 106.27/14.62 (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 (((dpsetconstrSub) =>
% 106.27/14.62 (((setOfPairsIsBReln) =>
% 106.27/14.62 (((dpsetconstrERa) =>
% 106.27/14.62 (((dpsetconstrEL1) =>
% 106.27/14.62 (((dpsetconstrEL2) =>
% 106.27/14.62 (((dpsetconstrER) =>
% 106.27/14.62 (((funcImageSingleton) =>
% 106.27/14.62 (((apProp) =>
% 106.27/14.62 (((app) =>
% 106.27/14.62 (((infuncsetfunc) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1640])).
% 106.27/14.62 thf(zip_derived_cl1667, plain,
% 106.27/14.62 (~ (((setukpairinjL2) =>
% 106.27/14.62 (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 (((dpsetconstrSub) =>
% 106.27/14.62 (((setOfPairsIsBReln) =>
% 106.27/14.62 (((dpsetconstrERa) =>
% 106.27/14.62 (((dpsetconstrEL1) =>
% 106.27/14.62 (((dpsetconstrEL2) =>
% 106.27/14.62 (((dpsetconstrER) =>
% 106.27/14.62 (((funcImageSingleton) =>
% 106.27/14.62 (((apProp) =>
% 106.27/14.62 (((app) =>
% 106.27/14.62 (((infuncsetfunc) =>
% 106.27/14.62 (((ap2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1652])).
% 106.27/14.62 thf(zip_derived_cl1681, plain,
% 106.27/14.62 (~ (((setukpairinjL) =>
% 106.27/14.62 (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 (((dpsetconstrSub) =>
% 106.27/14.62 (((setOfPairsIsBReln) =>
% 106.27/14.62 (((dpsetconstrERa) =>
% 106.27/14.62 (((dpsetconstrEL1) =>
% 106.27/14.62 (((dpsetconstrEL2) =>
% 106.27/14.62 (((dpsetconstrER) =>
% 106.27/14.62 (((funcImageSingleton) =>
% 106.27/14.62 (((apProp) =>
% 106.27/14.62 (((app) =>
% 106.27/14.62 (((infuncsetfunc) =>
% 106.27/14.62 (((ap2p) =>
% 106.27/14.62 (((funcinfuncset) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTE) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTEcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementUnionInPowersetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan1) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2a) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b2) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2b) =>
% 106.27/14.62 ((
% 106.27/14.62 (demorgan2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule0) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz13rule4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_1) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_2) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_3) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_4) =>
% 106.27/14.62 ((
% 106.27/14.62 (woz1_5) =>
% 106.27/14.62 ((
% 106.27/14.62 (breln1all2) =>
% 106.27/14.62 ((
% 106.27/14.62 (!!) @ (
% 106.27/14.62 (('#B') @ (
% 106.27/14.62 !!) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#S') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 '#S') @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 =>))) @
% 106.27/14.62 (
% 106.27/14.62 (
% 106.27/14.62 ('#B') @ (
% 106.27/14.62 (
% 106.27/14.62 ('#C') @ in)) @
% 106.27/14.62 breln1Set)))))) @
% 106.27/14.62 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1667])).
% 106.27/14.62 thf(zip_derived_cl1698, plain,
% 106.27/14.62 (~ (((setukpairinjR11) =>
% 106.27/14.62 (((setukpairinjR12) =>
% 106.27/14.62 (((setukpairinjR1) =>
% 106.27/14.62 (((upairequniteq) =>
% 106.27/14.62 (((setukpairinjR2) =>
% 106.27/14.62 (((setukpairinjR) =>
% 106.27/14.62 (((ksndsingleton) =>
% 106.27/14.62 (((ksndpairEq) =>
% 106.27/14.62 (((kpairsurjEq) =>
% 106.27/14.62 (((cartprodsndin) =>
% 106.27/14.62 (((cartprodpairmemEL) =>
% 106.27/14.62 (((cartprodpairmemER) =>
% 106.27/14.62 (((cartprodmempaircEq) =>
% 106.27/14.62 (((cartprodfstpairEq) =>
% 106.27/14.62 (((cartprodsndpairEq) =>
% 106.27/14.62 (((cartprodpairsurjEq) =>
% 106.27/14.62 (((dpsetconstrI) =>
% 106.27/14.62 (((dpsetconstrSub) =>
% 106.27/14.62 (((setOfPairsIsBReln) =>
% 106.27/14.62 (((dpsetconstrERa) =>
% 106.27/14.62 (((dpsetconstrEL1) =>
% 106.27/14.62 (((dpsetconstrEL2) =>
% 106.27/14.62 (((dpsetconstrER) =>
% 106.27/14.62 (((funcImageSingleton) =>
% 106.27/14.62 (((apProp) =>
% 106.27/14.62 (((app) =>
% 106.27/14.62 (((infuncsetfunc) =>
% 106.27/14.62 (((ap2p) =>
% 106.27/14.62 (((funcinfuncset) =>
% 106.27/14.62 (((lamProp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lamp) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2p) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall1) =>
% 106.27/14.62 ((
% 106.27/14.62 (brelnall2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ex1E2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp3) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcextLem) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcGraphProp4) =>
% 106.27/14.62 ((
% 106.27/14.62 (subbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (eqbreln) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext) =>
% 106.27/14.62 ((
% 106.27/14.62 (funcext2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq1) =>
% 106.27/14.62 ((
% 106.27/14.62 (ap2apEq2) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta1) =>
% 106.27/14.62 ((
% 106.27/14.62 (lam2lamEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (beta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (eta2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalseProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp1) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueProp2) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifSingleton) =>
% 106.27/14.62 ((
% 106.27/14.62 (ifp) =>
% 106.27/14.62 ((
% 106.27/14.62 (theeq) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrue) =>
% 106.27/14.62 ((
% 106.27/14.62 (iffalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (iftrueorfalse) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setminusT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementT_lem) =>
% 106.27/14.62 ((
% 106.27/14.62 (setextT) =>
% 106.27/14.62 ((
% 106.27/14.62 (subsetTI) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (powersetTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTELcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binintersectTERcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT1) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT2) =>
% 106.27/14.62 ((
% 106.27/14.62 (contrasubsetT3) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementI1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementE1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub1) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementSub2) =>
% 106.27/14.62 ((
% 106.27/14.62 (doubleComplementEq) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTnotintersectT) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementImpComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementSubsetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementInPowersetComplementIntersect) =>
% 106.27/14.62 ((
% 106.27/14.62 (contraSubsetComplement) =>
% 106.27/14.62 ((
% 106.27/14.62 (complementTcontraSubset) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTILcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (binunionTIRcontra) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInUnion2) =>
% 106.27/14.62 ((
% 106.27/14.62 (inIntersectImpInIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (intersectInPowersetIntersectUnions) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpNotIn1) =>
% 106.27/14.62 ((
% 106.27/14.62 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1681])).
% 106.27/14.63 thf(zip_derived_cl1714, plain,
% 106.27/14.63 (~ (((setukpairinjR12) =>
% 106.27/14.63 (((setukpairinjR1) =>
% 106.27/14.63 (((upairequniteq) =>
% 106.27/14.63 (((setukpairinjR2) =>
% 106.27/14.63 (((setukpairinjR) =>
% 106.27/14.63 (((ksndsingleton) =>
% 106.27/14.63 (((ksndpairEq) =>
% 106.27/14.63 (((kpairsurjEq) =>
% 106.27/14.63 (((cartprodsndin) =>
% 106.27/14.63 (((cartprodpairmemEL) =>
% 106.27/14.63 (((cartprodpairmemER) =>
% 106.27/14.63 (((cartprodmempaircEq) =>
% 106.27/14.63 (((cartprodfstpairEq) =>
% 106.27/14.63 (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2p) =>
% 106.27/14.63 ((
% 106.27/14.63 (brelnall1) =>
% 106.27/14.63 ((
% 106.27/14.63 (brelnall2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ex1E2) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp3) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcextLem) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp4) =>
% 106.27/14.63 ((
% 106.27/14.63 (subbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (eqbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1698])).
% 106.27/14.63 thf(zip_derived_cl1728, plain,
% 106.27/14.63 (~ (((setukpairinjR1) =>
% 106.27/14.63 (((upairequniteq) =>
% 106.27/14.63 (((setukpairinjR2) =>
% 106.27/14.63 (((setukpairinjR) =>
% 106.27/14.63 (((ksndsingleton) =>
% 106.27/14.63 (((ksndpairEq) =>
% 106.27/14.63 (((kpairsurjEq) =>
% 106.27/14.63 (((cartprodsndin) =>
% 106.27/14.63 (((cartprodpairmemEL) =>
% 106.27/14.63 (((cartprodpairmemER) =>
% 106.27/14.63 (((cartprodmempaircEq) =>
% 106.27/14.63 (((cartprodfstpairEq) =>
% 106.27/14.63 (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 ((
% 106.27/14.63 (brelnall1) =>
% 106.27/14.63 ((
% 106.27/14.63 (brelnall2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ex1E2) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp3) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcextLem) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp4) =>
% 106.27/14.63 ((
% 106.27/14.63 (subbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (eqbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1714])).
% 106.27/14.63 thf(zip_derived_cl1741, plain,
% 106.27/14.63 (~ (((upairequniteq) =>
% 106.27/14.63 (((setukpairinjR2) =>
% 106.27/14.63 (((setukpairinjR) =>
% 106.27/14.63 (((ksndsingleton) =>
% 106.27/14.63 (((ksndpairEq) =>
% 106.27/14.63 (((kpairsurjEq) =>
% 106.27/14.63 (((cartprodsndin) =>
% 106.27/14.63 (((cartprodpairmemEL) =>
% 106.27/14.63 (((cartprodpairmemER) =>
% 106.27/14.63 (((cartprodmempaircEq) =>
% 106.27/14.63 (((cartprodfstpairEq) =>
% 106.27/14.63 (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 ((
% 106.27/14.63 (brelnall2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ex1E2) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp3) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcextLem) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp4) =>
% 106.27/14.63 ((
% 106.27/14.63 (subbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (eqbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1728])).
% 106.27/14.63 thf(zip_derived_cl1752, plain,
% 106.27/14.63 (~ (((setukpairinjR2) =>
% 106.27/14.63 (((setukpairinjR) =>
% 106.27/14.63 (((ksndsingleton) =>
% 106.27/14.63 (((ksndpairEq) =>
% 106.27/14.63 (((kpairsurjEq) =>
% 106.27/14.63 (((cartprodsndin) =>
% 106.27/14.63 (((cartprodpairmemEL) =>
% 106.27/14.63 (((cartprodpairmemER) =>
% 106.27/14.63 (((cartprodmempaircEq) =>
% 106.27/14.63 (((cartprodfstpairEq) =>
% 106.27/14.63 (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ex1E2) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp3) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcextLem) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp4) =>
% 106.27/14.63 ((
% 106.27/14.63 (subbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (eqbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1741])).
% 106.27/14.63 thf(zip_derived_cl1763, plain,
% 106.27/14.63 (~ (((setukpairinjR) =>
% 106.27/14.63 (((ksndsingleton) =>
% 106.27/14.63 (((ksndpairEq) =>
% 106.27/14.63 (((kpairsurjEq) =>
% 106.27/14.63 (((cartprodsndin) =>
% 106.27/14.63 (((cartprodpairmemEL) =>
% 106.27/14.63 (((cartprodpairmemER) =>
% 106.27/14.63 (((cartprodmempaircEq) =>
% 106.27/14.63 (((cartprodfstpairEq) =>
% 106.27/14.63 (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp3) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcextLem) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp4) =>
% 106.27/14.63 ((
% 106.27/14.63 (subbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (eqbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1752])).
% 106.27/14.63 thf(zip_derived_cl1773, plain,
% 106.27/14.63 (~ (((ksndsingleton) =>
% 106.27/14.63 (((ksndpairEq) =>
% 106.27/14.63 (((kpairsurjEq) =>
% 106.27/14.63 (((cartprodsndin) =>
% 106.27/14.63 (((cartprodpairmemEL) =>
% 106.27/14.63 (((cartprodpairmemER) =>
% 106.27/14.63 (((cartprodmempaircEq) =>
% 106.27/14.63 (((cartprodfstpairEq) =>
% 106.27/14.63 (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp3) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcextLem) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp4) =>
% 106.27/14.63 ((
% 106.27/14.63 (subbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (eqbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1763])).
% 106.27/14.63 thf(zip_derived_cl1782, plain,
% 106.27/14.63 (~ (((ksndpairEq) =>
% 106.27/14.63 (((kpairsurjEq) =>
% 106.27/14.63 (((cartprodsndin) =>
% 106.27/14.63 (((cartprodpairmemEL) =>
% 106.27/14.63 (((cartprodpairmemER) =>
% 106.27/14.63 (((cartprodmempaircEq) =>
% 106.27/14.63 (((cartprodfstpairEq) =>
% 106.27/14.63 (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcextLem) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp4) =>
% 106.27/14.63 ((
% 106.27/14.63 (subbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (eqbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1773])).
% 106.27/14.63 thf(zip_derived_cl1790, plain,
% 106.27/14.63 (~ (((kpairsurjEq) =>
% 106.27/14.63 (((cartprodsndin) =>
% 106.27/14.63 (((cartprodpairmemEL) =>
% 106.27/14.63 (((cartprodpairmemER) =>
% 106.27/14.63 (((cartprodmempaircEq) =>
% 106.27/14.63 (((cartprodfstpairEq) =>
% 106.27/14.63 (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcextLem) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp4) =>
% 106.27/14.63 ((
% 106.27/14.63 (subbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (eqbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1782])).
% 106.27/14.63 thf(zip_derived_cl1799, plain,
% 106.27/14.63 (~ (((cartprodsndin) =>
% 106.27/14.63 (((cartprodpairmemEL) =>
% 106.27/14.63 (((cartprodpairmemER) =>
% 106.27/14.63 (((cartprodmempaircEq) =>
% 106.27/14.63 (((cartprodfstpairEq) =>
% 106.27/14.63 (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcGraphProp4) =>
% 106.27/14.63 ((
% 106.27/14.63 (subbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (eqbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1790])).
% 106.27/14.63 thf(zip_derived_cl1810, plain,
% 106.27/14.63 (~ (((cartprodpairmemEL) =>
% 106.27/14.63 (((cartprodpairmemER) =>
% 106.27/14.63 (((cartprodmempaircEq) =>
% 106.27/14.63 (((cartprodfstpairEq) =>
% 106.27/14.63 (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 ((
% 106.27/14.63 (subbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (eqbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1799])).
% 106.27/14.63 thf(zip_derived_cl1819, plain,
% 106.27/14.63 (~ (((cartprodpairmemER) =>
% 106.27/14.63 (((cartprodmempaircEq) =>
% 106.27/14.63 (((cartprodfstpairEq) =>
% 106.27/14.63 (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (eqbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1810])).
% 106.27/14.63 thf(zip_derived_cl1828, plain,
% 106.27/14.63 (~ (((cartprodmempaircEq) =>
% 106.27/14.63 (((cartprodfstpairEq) =>
% 106.27/14.63 (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1819])).
% 106.27/14.63 thf(zip_derived_cl1836, plain,
% 106.27/14.63 (~ (((cartprodfstpairEq) =>
% 106.27/14.63 (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 (((funcext) =>
% 106.27/14.63 ((
% 106.27/14.63 (funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1828])).
% 106.27/14.63 thf(zip_derived_cl1843, plain,
% 106.27/14.63 (~ (((cartprodsndpairEq) =>
% 106.27/14.63 (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 (((funcext) =>
% 106.27/14.63 (((funcext2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1836])).
% 106.27/14.63 thf(zip_derived_cl1851, plain,
% 106.27/14.63 (~ (((cartprodpairsurjEq) =>
% 106.27/14.63 (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 (((funcext) =>
% 106.27/14.63 (((funcext2) =>
% 106.27/14.63 (((ap2apEq1) =>
% 106.27/14.63 ((
% 106.27/14.63 (ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1843])).
% 106.27/14.63 thf(zip_derived_cl1859, plain,
% 106.27/14.63 (~ (((dpsetconstrI) =>
% 106.27/14.63 (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 (((funcext) =>
% 106.27/14.63 (((funcext2) =>
% 106.27/14.63 (((ap2apEq1) =>
% 106.27/14.63 (((ap2apEq2) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1851])).
% 106.27/14.63 thf(zip_derived_cl1868, plain,
% 106.27/14.63 (~ (((dpsetconstrSub) =>
% 106.27/14.63 (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 (((funcext) =>
% 106.27/14.63 (((funcext2) =>
% 106.27/14.63 (((ap2apEq1) =>
% 106.27/14.63 (((ap2apEq2) =>
% 106.27/14.63 (((beta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1859])).
% 106.27/14.63 thf(zip_derived_cl1877, plain,
% 106.27/14.63 (~ (((setOfPairsIsBReln) =>
% 106.27/14.63 (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 (((funcext) =>
% 106.27/14.63 (((funcext2) =>
% 106.27/14.63 (((ap2apEq1) =>
% 106.27/14.63 (((ap2apEq2) =>
% 106.27/14.63 (((beta1) =>
% 106.27/14.63 (((eta1) =>
% 106.27/14.63 ((
% 106.27/14.63 (lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1868])).
% 106.27/14.63 thf(zip_derived_cl1886, plain,
% 106.27/14.63 (~ (((dpsetconstrERa) =>
% 106.27/14.63 (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 (((funcext) =>
% 106.27/14.63 (((funcext2) =>
% 106.27/14.63 (((ap2apEq1) =>
% 106.27/14.63 (((ap2apEq2) =>
% 106.27/14.63 (((beta1) =>
% 106.27/14.63 (((eta1) =>
% 106.27/14.63 (((lam2lamEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1877])).
% 106.27/14.63 thf(zip_derived_cl1896, plain,
% 106.27/14.63 (~ (((dpsetconstrEL1) =>
% 106.27/14.63 (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 (((funcext) =>
% 106.27/14.63 (((funcext2) =>
% 106.27/14.63 (((ap2apEq1) =>
% 106.27/14.63 (((ap2apEq2) =>
% 106.27/14.63 (((beta1) =>
% 106.27/14.63 (((eta1) =>
% 106.27/14.63 (((lam2lamEq) =>
% 106.27/14.63 (((beta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1886])).
% 106.27/14.63 thf(zip_derived_cl1906, plain,
% 106.27/14.63 (~ (((dpsetconstrEL2) =>
% 106.27/14.63 (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 (((funcext) =>
% 106.27/14.63 (((funcext2) =>
% 106.27/14.63 (((ap2apEq1) =>
% 106.27/14.63 (((ap2apEq2) =>
% 106.27/14.63 (((beta1) =>
% 106.27/14.63 (((eta1) =>
% 106.27/14.63 (((lam2lamEq) =>
% 106.27/14.63 (((beta2) =>
% 106.27/14.63 (((eta2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1896])).
% 106.27/14.63 thf(zip_derived_cl1917, plain,
% 106.27/14.63 (~ (((dpsetconstrER) =>
% 106.27/14.63 (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 (((funcext) =>
% 106.27/14.63 (((funcext2) =>
% 106.27/14.63 (((ap2apEq1) =>
% 106.27/14.63 (((ap2apEq2) =>
% 106.27/14.63 (((beta1) =>
% 106.27/14.63 (((eta1) =>
% 106.27/14.63 (((lam2lamEq) =>
% 106.27/14.63 (((beta2) =>
% 106.27/14.63 (((eta2) =>
% 106.27/14.63 (((iffalseProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1906])).
% 106.27/14.63 thf(zip_derived_cl1926, plain,
% 106.27/14.63 (~ (((funcImageSingleton) =>
% 106.27/14.63 (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 (((funcext) =>
% 106.27/14.63 (((funcext2) =>
% 106.27/14.63 (((ap2apEq1) =>
% 106.27/14.63 (((ap2apEq2) =>
% 106.27/14.63 (((beta1) =>
% 106.27/14.63 (((eta1) =>
% 106.27/14.63 (((lam2lamEq) =>
% 106.27/14.63 (((beta2) =>
% 106.27/14.63 (((eta2) =>
% 106.27/14.63 (((iffalseProp1) =>
% 106.27/14.63 (((iffalseProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1917])).
% 106.27/14.63 thf(zip_derived_cl1935, plain,
% 106.27/14.63 (~ (((apProp) =>
% 106.27/14.63 (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 (((funcext) =>
% 106.27/14.63 (((funcext2) =>
% 106.27/14.63 (((ap2apEq1) =>
% 106.27/14.63 (((ap2apEq2) =>
% 106.27/14.63 (((beta1) =>
% 106.27/14.63 (((eta1) =>
% 106.27/14.63 (((lam2lamEq) =>
% 106.27/14.63 (((beta2) =>
% 106.27/14.63 (((eta2) =>
% 106.27/14.63 (((iffalseProp1) =>
% 106.27/14.63 (((iffalseProp2) =>
% 106.27/14.63 (((iftrueProp1) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule0) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz13rule4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_1) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_2) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_3) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_4) =>
% 106.27/14.63 ((
% 106.27/14.63 (woz1_5) =>
% 106.27/14.63 ((
% 106.27/14.63 (breln1all2) =>
% 106.27/14.63 ((
% 106.27/14.63 (!!) @ (
% 106.27/14.63 (('#B') @ (
% 106.27/14.63 !!) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#S') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 '#S') @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 =>))) @
% 106.27/14.63 (
% 106.27/14.63 (
% 106.27/14.63 ('#B') @ (
% 106.27/14.63 (
% 106.27/14.63 ('#C') @ in)) @
% 106.27/14.63 breln1Set)))))) @
% 106.27/14.63 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1926])).
% 106.27/14.63 thf(zip_derived_cl1944, plain,
% 106.27/14.63 (~ (((app) =>
% 106.27/14.63 (((infuncsetfunc) =>
% 106.27/14.63 (((ap2p) =>
% 106.27/14.63 (((funcinfuncset) =>
% 106.27/14.63 (((lamProp) =>
% 106.27/14.63 (((lamp) =>
% 106.27/14.63 (((lam2p) =>
% 106.27/14.63 (((brelnall1) =>
% 106.27/14.63 (((brelnall2) =>
% 106.27/14.63 (((ex1E2) =>
% 106.27/14.63 (((funcGraphProp1) =>
% 106.27/14.63 (((funcGraphProp3) =>
% 106.27/14.63 (((funcGraphProp2) =>
% 106.27/14.63 (((funcextLem) =>
% 106.27/14.63 (((funcGraphProp4) =>
% 106.27/14.63 (((subbreln) =>
% 106.27/14.63 (((eqbreln) =>
% 106.27/14.63 (((funcext) =>
% 106.27/14.63 (((funcext2) =>
% 106.27/14.63 (((ap2apEq1) =>
% 106.27/14.63 (((ap2apEq2) =>
% 106.27/14.63 (((beta1) =>
% 106.27/14.63 (((eta1) =>
% 106.27/14.63 (((lam2lamEq) =>
% 106.27/14.63 (((beta2) =>
% 106.27/14.63 (((eta2) =>
% 106.27/14.63 (((iffalseProp1) =>
% 106.27/14.63 (((iffalseProp2) =>
% 106.27/14.63 (((iftrueProp1) =>
% 106.27/14.63 (((iftrueProp2) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifSingleton) =>
% 106.27/14.63 ((
% 106.27/14.63 (ifp) =>
% 106.27/14.63 ((
% 106.27/14.63 (theeq) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrue) =>
% 106.27/14.63 ((
% 106.27/14.63 (iffalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (iftrueorfalse) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setminusT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementT_lem) =>
% 106.27/14.63 ((
% 106.27/14.63 (setextT) =>
% 106.27/14.63 ((
% 106.27/14.63 (subsetTI) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (powersetTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTELcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binintersectTERcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT1) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT2) =>
% 106.27/14.63 ((
% 106.27/14.63 (contrasubsetT3) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementI1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementE1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub1) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementSub2) =>
% 106.27/14.63 ((
% 106.27/14.63 (doubleComplementEq) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTnotintersectT) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementImpComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementSubsetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementInPowersetComplementIntersect) =>
% 106.27/14.63 ((
% 106.27/14.63 (contraSubsetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementTcontraSubset) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTILcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTIRcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInUnion2) =>
% 106.27/14.63 ((
% 106.27/14.63 (inIntersectImpInIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (intersectInPowersetIntersectUnions) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpNotIn1) =>
% 106.27/14.63 ((
% 106.27/14.63 (inComplementUnionImpInComplement1) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTE) =>
% 106.27/14.63 ((
% 106.27/14.63 (binunionTEcontra) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a1) =>
% 106.27/14.63 ((
% 106.27/14.63 (complementUnionInPowersetComplement) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan2a2) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1a) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1b) =>
% 106.27/14.63 ((
% 106.27/14.63 (demorgan1) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule0) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_5) =>
% 106.27/14.64 ((
% 106.27/14.64 (breln1all2) =>
% 106.27/14.64 ((
% 106.27/14.64 (!!) @ (
% 106.27/14.64 (('#B') @ (
% 106.27/14.64 !!) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#S') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 '#S') @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 =>))) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#C') @ in)) @
% 106.27/14.64 breln1Set)))))) @
% 106.27/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1935])).
% 106.27/14.64 thf(zip_derived_cl1954, plain,
% 106.27/14.64 (~ (((infuncsetfunc) =>
% 106.27/14.64 (((ap2p) =>
% 106.27/14.64 (((funcinfuncset) =>
% 106.27/14.64 (((lamProp) =>
% 106.27/14.64 (((lamp) =>
% 106.27/14.64 (((lam2p) =>
% 106.27/14.64 (((brelnall1) =>
% 106.27/14.64 (((brelnall2) =>
% 106.27/14.64 (((ex1E2) =>
% 106.27/14.64 (((funcGraphProp1) =>
% 106.27/14.64 (((funcGraphProp3) =>
% 106.27/14.64 (((funcGraphProp2) =>
% 106.27/14.64 (((funcextLem) =>
% 106.27/14.64 (((funcGraphProp4) =>
% 106.27/14.64 (((subbreln) =>
% 106.27/14.64 (((eqbreln) =>
% 106.27/14.64 (((funcext) =>
% 106.27/14.64 (((funcext2) =>
% 106.27/14.64 (((ap2apEq1) =>
% 106.27/14.64 (((ap2apEq2) =>
% 106.27/14.64 (((beta1) =>
% 106.27/14.64 (((eta1) =>
% 106.27/14.64 (((lam2lamEq) =>
% 106.27/14.64 (((beta2) =>
% 106.27/14.64 (((eta2) =>
% 106.27/14.64 (((iffalseProp1) =>
% 106.27/14.64 (((iffalseProp2) =>
% 106.27/14.64 (((iftrueProp1) =>
% 106.27/14.64 (((iftrueProp2) =>
% 106.27/14.64 (((ifSingleton) =>
% 106.27/14.64 ((
% 106.27/14.64 (ifp) =>
% 106.27/14.64 ((
% 106.27/14.64 (theeq) =>
% 106.27/14.64 ((
% 106.27/14.64 (iftrue) =>
% 106.27/14.64 ((
% 106.27/14.64 (iffalse) =>
% 106.27/14.64 ((
% 106.27/14.64 (iftrueorfalse) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setminusT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setextT) =>
% 106.27/14.64 ((
% 106.27/14.64 (subsetTI) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTELcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTERcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT1) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT2) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT3) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub2) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementEq) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTnotintersectT) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementImpComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementSubsetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementInPowersetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (contraSubsetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTcontraSubset) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTILcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTIRcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion2) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (intersectInPowersetIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpNotIn1) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpInComplement1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTE) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTEcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementUnionInPowersetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule0) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_5) =>
% 106.27/14.64 ((
% 106.27/14.64 (breln1all2) =>
% 106.27/14.64 ((
% 106.27/14.64 (!!) @ (
% 106.27/14.64 (('#B') @ (
% 106.27/14.64 !!) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#S') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 '#S') @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 =>))) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#C') @ in)) @
% 106.27/14.64 breln1Set)))))) @
% 106.27/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1944])).
% 106.27/14.64 thf(zip_derived_cl1964, plain,
% 106.27/14.64 (~ (((ap2p) =>
% 106.27/14.64 (((funcinfuncset) =>
% 106.27/14.64 (((lamProp) =>
% 106.27/14.64 (((lamp) =>
% 106.27/14.64 (((lam2p) =>
% 106.27/14.64 (((brelnall1) =>
% 106.27/14.64 (((brelnall2) =>
% 106.27/14.64 (((ex1E2) =>
% 106.27/14.64 (((funcGraphProp1) =>
% 106.27/14.64 (((funcGraphProp3) =>
% 106.27/14.64 (((funcGraphProp2) =>
% 106.27/14.64 (((funcextLem) =>
% 106.27/14.64 (((funcGraphProp4) =>
% 106.27/14.64 (((subbreln) =>
% 106.27/14.64 (((eqbreln) =>
% 106.27/14.64 (((funcext) =>
% 106.27/14.64 (((funcext2) =>
% 106.27/14.64 (((ap2apEq1) =>
% 106.27/14.64 (((ap2apEq2) =>
% 106.27/14.64 (((beta1) =>
% 106.27/14.64 (((eta1) =>
% 106.27/14.64 (((lam2lamEq) =>
% 106.27/14.64 (((beta2) =>
% 106.27/14.64 (((eta2) =>
% 106.27/14.64 (((iffalseProp1) =>
% 106.27/14.64 (((iffalseProp2) =>
% 106.27/14.64 (((iftrueProp1) =>
% 106.27/14.64 (((iftrueProp2) =>
% 106.27/14.64 (((ifSingleton) =>
% 106.27/14.64 (((ifp) =>
% 106.27/14.64 ((
% 106.27/14.64 (theeq) =>
% 106.27/14.64 ((
% 106.27/14.64 (iftrue) =>
% 106.27/14.64 ((
% 106.27/14.64 (iffalse) =>
% 106.27/14.64 ((
% 106.27/14.64 (iftrueorfalse) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setminusT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setextT) =>
% 106.27/14.64 ((
% 106.27/14.64 (subsetTI) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTELcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTERcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT1) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT2) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT3) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub2) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementEq) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTnotintersectT) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementImpComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementSubsetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementInPowersetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (contraSubsetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTcontraSubset) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTILcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTIRcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion2) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (intersectInPowersetIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpNotIn1) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpInComplement1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTE) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTEcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementUnionInPowersetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule0) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_5) =>
% 106.27/14.64 ((
% 106.27/14.64 (breln1all2) =>
% 106.27/14.64 ((
% 106.27/14.64 (!!) @ (
% 106.27/14.64 (('#B') @ (
% 106.27/14.64 !!) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#S') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 '#S') @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 =>))) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#C') @ in)) @
% 106.27/14.64 breln1Set)))))) @
% 106.27/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1954])).
% 106.27/14.64 thf(zip_derived_cl1975, plain,
% 106.27/14.64 (~ (((funcinfuncset) =>
% 106.27/14.64 (((lamProp) =>
% 106.27/14.64 (((lamp) =>
% 106.27/14.64 (((lam2p) =>
% 106.27/14.64 (((brelnall1) =>
% 106.27/14.64 (((brelnall2) =>
% 106.27/14.64 (((ex1E2) =>
% 106.27/14.64 (((funcGraphProp1) =>
% 106.27/14.64 (((funcGraphProp3) =>
% 106.27/14.64 (((funcGraphProp2) =>
% 106.27/14.64 (((funcextLem) =>
% 106.27/14.64 (((funcGraphProp4) =>
% 106.27/14.64 (((subbreln) =>
% 106.27/14.64 (((eqbreln) =>
% 106.27/14.64 (((funcext) =>
% 106.27/14.64 (((funcext2) =>
% 106.27/14.64 (((ap2apEq1) =>
% 106.27/14.64 (((ap2apEq2) =>
% 106.27/14.64 (((beta1) =>
% 106.27/14.64 (((eta1) =>
% 106.27/14.64 (((lam2lamEq) =>
% 106.27/14.64 (((beta2) =>
% 106.27/14.64 (((eta2) =>
% 106.27/14.64 (((iffalseProp1) =>
% 106.27/14.64 (((iffalseProp2) =>
% 106.27/14.64 (((iftrueProp1) =>
% 106.27/14.64 (((iftrueProp2) =>
% 106.27/14.64 (((ifSingleton) =>
% 106.27/14.64 (((ifp) =>
% 106.27/14.64 (((theeq) =>
% 106.27/14.64 ((
% 106.27/14.64 (iftrue) =>
% 106.27/14.64 ((
% 106.27/14.64 (iffalse) =>
% 106.27/14.64 ((
% 106.27/14.64 (iftrueorfalse) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setminusT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setextT) =>
% 106.27/14.64 ((
% 106.27/14.64 (subsetTI) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTELcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTERcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT1) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT2) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT3) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub2) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementEq) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTnotintersectT) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementImpComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementSubsetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementInPowersetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (contraSubsetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTcontraSubset) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTILcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTIRcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion2) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (intersectInPowersetIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpNotIn1) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpInComplement1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTE) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTEcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementUnionInPowersetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule0) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_5) =>
% 106.27/14.64 ((
% 106.27/14.64 (breln1all2) =>
% 106.27/14.64 ((
% 106.27/14.64 (!!) @ (
% 106.27/14.64 (('#B') @ (
% 106.27/14.64 !!) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#S') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 '#S') @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 =>))) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#C') @ in)) @
% 106.27/14.64 breln1Set)))))) @
% 106.27/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1964])).
% 106.27/14.64 thf(zip_derived_cl1986, plain,
% 106.27/14.64 (~ (((lamProp) =>
% 106.27/14.64 (((lamp) =>
% 106.27/14.64 (((lam2p) =>
% 106.27/14.64 (((brelnall1) =>
% 106.27/14.64 (((brelnall2) =>
% 106.27/14.64 (((ex1E2) =>
% 106.27/14.64 (((funcGraphProp1) =>
% 106.27/14.64 (((funcGraphProp3) =>
% 106.27/14.64 (((funcGraphProp2) =>
% 106.27/14.64 (((funcextLem) =>
% 106.27/14.64 (((funcGraphProp4) =>
% 106.27/14.64 (((subbreln) =>
% 106.27/14.64 (((eqbreln) =>
% 106.27/14.64 (((funcext) =>
% 106.27/14.64 (((funcext2) =>
% 106.27/14.64 (((ap2apEq1) =>
% 106.27/14.64 (((ap2apEq2) =>
% 106.27/14.64 (((beta1) =>
% 106.27/14.64 (((eta1) =>
% 106.27/14.64 (((lam2lamEq) =>
% 106.27/14.64 (((beta2) =>
% 106.27/14.64 (((eta2) =>
% 106.27/14.64 (((iffalseProp1) =>
% 106.27/14.64 (((iffalseProp2) =>
% 106.27/14.64 (((iftrueProp1) =>
% 106.27/14.64 (((iftrueProp2) =>
% 106.27/14.64 (((ifSingleton) =>
% 106.27/14.64 (((ifp) =>
% 106.27/14.64 (((theeq) =>
% 106.27/14.64 (((iftrue) =>
% 106.27/14.64 ((
% 106.27/14.64 (iffalse) =>
% 106.27/14.64 ((
% 106.27/14.64 (iftrueorfalse) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setminusT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setextT) =>
% 106.27/14.64 ((
% 106.27/14.64 (subsetTI) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTELcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTERcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT1) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT2) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT3) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub2) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementEq) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTnotintersectT) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementImpComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementSubsetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementInPowersetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (contraSubsetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTcontraSubset) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTILcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTIRcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion2) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (intersectInPowersetIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpNotIn1) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpInComplement1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTE) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTEcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementUnionInPowersetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule0) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_5) =>
% 106.27/14.64 ((
% 106.27/14.64 (breln1all2) =>
% 106.27/14.64 ((
% 106.27/14.64 (!!) @ (
% 106.27/14.64 (('#B') @ (
% 106.27/14.64 !!) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#S') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 '#S') @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 =>))) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#C') @ in)) @
% 106.27/14.64 breln1Set)))))) @
% 106.27/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1975])).
% 106.27/14.64 thf(zip_derived_cl1996, plain,
% 106.27/14.64 (~ (((lamp) =>
% 106.27/14.64 (((lam2p) =>
% 106.27/14.64 (((brelnall1) =>
% 106.27/14.64 (((brelnall2) =>
% 106.27/14.64 (((ex1E2) =>
% 106.27/14.64 (((funcGraphProp1) =>
% 106.27/14.64 (((funcGraphProp3) =>
% 106.27/14.64 (((funcGraphProp2) =>
% 106.27/14.64 (((funcextLem) =>
% 106.27/14.64 (((funcGraphProp4) =>
% 106.27/14.64 (((subbreln) =>
% 106.27/14.64 (((eqbreln) =>
% 106.27/14.64 (((funcext) =>
% 106.27/14.64 (((funcext2) =>
% 106.27/14.64 (((ap2apEq1) =>
% 106.27/14.64 (((ap2apEq2) =>
% 106.27/14.64 (((beta1) =>
% 106.27/14.64 (((eta1) =>
% 106.27/14.64 (((lam2lamEq) =>
% 106.27/14.64 (((beta2) =>
% 106.27/14.64 (((eta2) =>
% 106.27/14.64 (((iffalseProp1) =>
% 106.27/14.64 (((iffalseProp2) =>
% 106.27/14.64 (((iftrueProp1) =>
% 106.27/14.64 (((iftrueProp2) =>
% 106.27/14.64 (((ifSingleton) =>
% 106.27/14.64 (((ifp) =>
% 106.27/14.64 (((theeq) =>
% 106.27/14.64 (((iftrue) =>
% 106.27/14.64 (((iffalse) =>
% 106.27/14.64 ((
% 106.27/14.64 (iftrueorfalse) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setminusT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setextT) =>
% 106.27/14.64 ((
% 106.27/14.64 (subsetTI) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTELcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTERcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT1) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT2) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT3) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub2) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementEq) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTnotintersectT) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementImpComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementSubsetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementInPowersetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (contraSubsetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTcontraSubset) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTILcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTIRcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion2) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (intersectInPowersetIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpNotIn1) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpInComplement1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTE) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTEcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementUnionInPowersetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule0) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_5) =>
% 106.27/14.64 ((
% 106.27/14.64 (breln1all2) =>
% 106.27/14.64 ((
% 106.27/14.64 (!!) @ (
% 106.27/14.64 (('#B') @ (
% 106.27/14.64 !!) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#S') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 '#S') @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 =>))) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#C') @ in)) @
% 106.27/14.64 breln1Set)))))) @
% 106.27/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1986])).
% 106.27/14.64 thf(zip_derived_cl2006, plain,
% 106.27/14.64 (~ (((lam2p) =>
% 106.27/14.64 (((brelnall1) =>
% 106.27/14.64 (((brelnall2) =>
% 106.27/14.64 (((ex1E2) =>
% 106.27/14.64 (((funcGraphProp1) =>
% 106.27/14.64 (((funcGraphProp3) =>
% 106.27/14.64 (((funcGraphProp2) =>
% 106.27/14.64 (((funcextLem) =>
% 106.27/14.64 (((funcGraphProp4) =>
% 106.27/14.64 (((subbreln) =>
% 106.27/14.64 (((eqbreln) =>
% 106.27/14.64 (((funcext) =>
% 106.27/14.64 (((funcext2) =>
% 106.27/14.64 (((ap2apEq1) =>
% 106.27/14.64 (((ap2apEq2) =>
% 106.27/14.64 (((beta1) =>
% 106.27/14.64 (((eta1) =>
% 106.27/14.64 (((lam2lamEq) =>
% 106.27/14.64 (((beta2) =>
% 106.27/14.64 (((eta2) =>
% 106.27/14.64 (((iffalseProp1) =>
% 106.27/14.64 (((iffalseProp2) =>
% 106.27/14.64 (((iftrueProp1) =>
% 106.27/14.64 (((iftrueProp2) =>
% 106.27/14.64 (((ifSingleton) =>
% 106.27/14.64 (((ifp) =>
% 106.27/14.64 (((theeq) =>
% 106.27/14.64 (((iftrue) =>
% 106.27/14.64 (((iffalse) =>
% 106.27/14.64 (((iftrueorfalse) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setminusT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setextT) =>
% 106.27/14.64 ((
% 106.27/14.64 (subsetTI) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTELcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTERcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT1) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT2) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT3) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub2) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementEq) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTnotintersectT) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementImpComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementSubsetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementInPowersetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (contraSubsetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTcontraSubset) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTILcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTIRcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion2) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (intersectInPowersetIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpNotIn1) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpInComplement1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTE) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTEcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementUnionInPowersetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule0) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_5) =>
% 106.27/14.64 ((
% 106.27/14.64 (breln1all2) =>
% 106.27/14.64 ((
% 106.27/14.64 (!!) @ (
% 106.27/14.64 (('#B') @ (
% 106.27/14.64 !!) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#S') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 '#S') @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 =>))) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#C') @ in)) @
% 106.27/14.64 breln1Set)))))) @
% 106.27/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1996])).
% 106.27/14.64 thf(zip_derived_cl2016, plain,
% 106.27/14.64 (~ (((brelnall1) =>
% 106.27/14.64 (((brelnall2) =>
% 106.27/14.64 (((ex1E2) =>
% 106.27/14.64 (((funcGraphProp1) =>
% 106.27/14.64 (((funcGraphProp3) =>
% 106.27/14.64 (((funcGraphProp2) =>
% 106.27/14.64 (((funcextLem) =>
% 106.27/14.64 (((funcGraphProp4) =>
% 106.27/14.64 (((subbreln) =>
% 106.27/14.64 (((eqbreln) =>
% 106.27/14.64 (((funcext) =>
% 106.27/14.64 (((funcext2) =>
% 106.27/14.64 (((ap2apEq1) =>
% 106.27/14.64 (((ap2apEq2) =>
% 106.27/14.64 (((beta1) =>
% 106.27/14.64 (((eta1) =>
% 106.27/14.64 (((lam2lamEq) =>
% 106.27/14.64 (((beta2) =>
% 106.27/14.64 (((eta2) =>
% 106.27/14.64 (((iffalseProp1) =>
% 106.27/14.64 (((iffalseProp2) =>
% 106.27/14.64 (((iftrueProp1) =>
% 106.27/14.64 (((iftrueProp2) =>
% 106.27/14.64 (((ifSingleton) =>
% 106.27/14.64 (((ifp) =>
% 106.27/14.64 (((theeq) =>
% 106.27/14.64 (((iftrue) =>
% 106.27/14.64 (((iffalse) =>
% 106.27/14.64 (((iftrueorfalse) =>
% 106.27/14.64 (((binintersectT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setminusT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setextT) =>
% 106.27/14.64 ((
% 106.27/14.64 (subsetTI) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTELcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binintersectTERcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT1) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT2) =>
% 106.27/14.64 ((
% 106.27/14.64 (contrasubsetT3) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementI1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementE1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub1) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementSub2) =>
% 106.27/14.64 ((
% 106.27/14.64 (doubleComplementEq) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTnotintersectT) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementImpComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementSubsetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementInPowersetComplementIntersect) =>
% 106.27/14.64 ((
% 106.27/14.64 (contraSubsetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementTcontraSubset) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTILcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTIRcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInUnion2) =>
% 106.27/14.64 ((
% 106.27/14.64 (inIntersectImpInIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (intersectInPowersetIntersectUnions) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpNotIn1) =>
% 106.27/14.64 ((
% 106.27/14.64 (inComplementUnionImpInComplement1) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTE) =>
% 106.27/14.64 ((
% 106.27/14.64 (binunionTEcontra) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a1) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementUnionInPowersetComplement) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan1) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2a) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b2) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2b) =>
% 106.27/14.64 ((
% 106.27/14.64 (demorgan2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule0) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz13rule4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_1) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_2) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_3) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_4) =>
% 106.27/14.64 ((
% 106.27/14.64 (woz1_5) =>
% 106.27/14.64 ((
% 106.27/14.64 (breln1all2) =>
% 106.27/14.64 ((
% 106.27/14.64 (!!) @ (
% 106.27/14.64 (('#B') @ (
% 106.27/14.64 !!) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#S') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 '#S') @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 =>))) @
% 106.27/14.64 (
% 106.27/14.64 (
% 106.27/14.64 ('#B') @ (
% 106.27/14.64 (
% 106.27/14.64 ('#C') @ in)) @
% 106.27/14.64 breln1Set)))))) @
% 106.27/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.27/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2006])).
% 106.27/14.64 thf(zip_derived_cl2025, plain,
% 106.27/14.64 (~ (((brelnall2) =>
% 106.27/14.64 (((ex1E2) =>
% 106.27/14.64 (((funcGraphProp1) =>
% 106.27/14.64 (((funcGraphProp3) =>
% 106.27/14.64 (((funcGraphProp2) =>
% 106.27/14.64 (((funcextLem) =>
% 106.27/14.64 (((funcGraphProp4) =>
% 106.27/14.64 (((subbreln) =>
% 106.27/14.64 (((eqbreln) =>
% 106.27/14.64 (((funcext) =>
% 106.27/14.64 (((funcext2) =>
% 106.27/14.64 (((ap2apEq1) =>
% 106.27/14.64 (((ap2apEq2) =>
% 106.27/14.64 (((beta1) =>
% 106.27/14.64 (((eta1) =>
% 106.27/14.64 (((lam2lamEq) =>
% 106.27/14.64 (((beta2) =>
% 106.27/14.64 (((eta2) =>
% 106.27/14.64 (((iffalseProp1) =>
% 106.27/14.64 (((iffalseProp2) =>
% 106.27/14.64 (((iftrueProp1) =>
% 106.27/14.64 (((iftrueProp2) =>
% 106.27/14.64 (((ifSingleton) =>
% 106.27/14.64 (((ifp) =>
% 106.27/14.64 (((theeq) =>
% 106.27/14.64 (((iftrue) =>
% 106.27/14.64 (((iffalse) =>
% 106.27/14.64 (((iftrueorfalse) =>
% 106.27/14.64 (((binintersectT_lem) =>
% 106.27/14.64 (((binunionT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (powersetT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (setminusT_lem) =>
% 106.27/14.64 ((
% 106.27/14.64 (complementT_lem) =>
% 106.27/14.64 ((
% 106.85/14.64 (setextT) =>
% 106.85/14.64 ((
% 106.85/14.64 (subsetTI) =>
% 106.85/14.64 ((
% 106.85/14.64 (powersetTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (powersetTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTELcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTERcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2016])).
% 106.85/14.64 thf(zip_derived_cl2034, plain,
% 106.85/14.64 (~ (((ex1E2) =>
% 106.85/14.64 (((funcGraphProp1) =>
% 106.85/14.64 (((funcGraphProp3) =>
% 106.85/14.64 (((funcGraphProp2) =>
% 106.85/14.64 (((funcextLem) =>
% 106.85/14.64 (((funcGraphProp4) =>
% 106.85/14.64 (((subbreln) =>
% 106.85/14.64 (((eqbreln) =>
% 106.85/14.64 (((funcext) =>
% 106.85/14.64 (((funcext2) =>
% 106.85/14.64 (((ap2apEq1) =>
% 106.85/14.64 (((ap2apEq2) =>
% 106.85/14.64 (((beta1) =>
% 106.85/14.64 (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 ((
% 106.85/14.64 (setminusT_lem) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementT_lem) =>
% 106.85/14.64 ((
% 106.85/14.64 (setextT) =>
% 106.85/14.64 ((
% 106.85/14.64 (subsetTI) =>
% 106.85/14.64 ((
% 106.85/14.64 (powersetTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (powersetTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTELcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTERcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2025])).
% 106.85/14.64 thf(zip_derived_cl2043, plain,
% 106.85/14.64 (~ (((funcGraphProp1) =>
% 106.85/14.64 (((funcGraphProp3) =>
% 106.85/14.64 (((funcGraphProp2) =>
% 106.85/14.64 (((funcextLem) =>
% 106.85/14.64 (((funcGraphProp4) =>
% 106.85/14.64 (((subbreln) =>
% 106.85/14.64 (((eqbreln) =>
% 106.85/14.64 (((funcext) =>
% 106.85/14.64 (((funcext2) =>
% 106.85/14.64 (((ap2apEq1) =>
% 106.85/14.64 (((ap2apEq2) =>
% 106.85/14.64 (((beta1) =>
% 106.85/14.64 (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementT_lem) =>
% 106.85/14.64 ((
% 106.85/14.64 (setextT) =>
% 106.85/14.64 ((
% 106.85/14.64 (subsetTI) =>
% 106.85/14.64 ((
% 106.85/14.64 (powersetTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (powersetTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTELcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTERcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2034])).
% 106.85/14.64 thf(zip_derived_cl2052, plain,
% 106.85/14.64 (~ (((funcGraphProp3) =>
% 106.85/14.64 (((funcGraphProp2) =>
% 106.85/14.64 (((funcextLem) =>
% 106.85/14.64 (((funcGraphProp4) =>
% 106.85/14.64 (((subbreln) =>
% 106.85/14.64 (((eqbreln) =>
% 106.85/14.64 (((funcext) =>
% 106.85/14.64 (((funcext2) =>
% 106.85/14.64 (((ap2apEq1) =>
% 106.85/14.64 (((ap2apEq2) =>
% 106.85/14.64 (((beta1) =>
% 106.85/14.64 (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 ((
% 106.85/14.64 (setextT) =>
% 106.85/14.64 ((
% 106.85/14.64 (subsetTI) =>
% 106.85/14.64 ((
% 106.85/14.64 (powersetTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (powersetTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTELcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTERcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2043])).
% 106.85/14.64 thf(zip_derived_cl2063, plain,
% 106.85/14.64 (~ (((funcGraphProp2) =>
% 106.85/14.64 (((funcextLem) =>
% 106.85/14.64 (((funcGraphProp4) =>
% 106.85/14.64 (((subbreln) =>
% 106.85/14.64 (((eqbreln) =>
% 106.85/14.64 (((funcext) =>
% 106.85/14.64 (((funcext2) =>
% 106.85/14.64 (((ap2apEq1) =>
% 106.85/14.64 (((ap2apEq2) =>
% 106.85/14.64 (((beta1) =>
% 106.85/14.64 (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 ((
% 106.85/14.64 (subsetTI) =>
% 106.85/14.64 ((
% 106.85/14.64 (powersetTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (powersetTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTELcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTERcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2052])).
% 106.85/14.64 thf(zip_derived_cl2075, plain,
% 106.85/14.64 (~ (((funcextLem) =>
% 106.85/14.64 (((funcGraphProp4) =>
% 106.85/14.64 (((subbreln) =>
% 106.85/14.64 (((eqbreln) =>
% 106.85/14.64 (((funcext) =>
% 106.85/14.64 (((funcext2) =>
% 106.85/14.64 (((ap2apEq1) =>
% 106.85/14.64 (((ap2apEq2) =>
% 106.85/14.64 (((beta1) =>
% 106.85/14.64 (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 ((
% 106.85/14.64 (powersetTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (powersetTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTELcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTERcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2063])).
% 106.85/14.64 thf(zip_derived_cl2088, plain,
% 106.85/14.64 (~ (((funcGraphProp4) =>
% 106.85/14.64 (((subbreln) =>
% 106.85/14.64 (((eqbreln) =>
% 106.85/14.64 (((funcext) =>
% 106.85/14.64 (((funcext2) =>
% 106.85/14.64 (((ap2apEq1) =>
% 106.85/14.64 (((ap2apEq2) =>
% 106.85/14.64 (((beta1) =>
% 106.85/14.64 (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (powersetTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTELcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTERcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2075])).
% 106.85/14.64 thf(zip_derived_cl2098, plain,
% 106.85/14.64 (~ (((subbreln) =>
% 106.85/14.64 (((eqbreln) =>
% 106.85/14.64 (((funcext) =>
% 106.85/14.64 (((funcext2) =>
% 106.85/14.64 (((ap2apEq1) =>
% 106.85/14.64 (((ap2apEq2) =>
% 106.85/14.64 (((beta1) =>
% 106.85/14.64 (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTELcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTERcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2088])).
% 106.85/14.64 thf(zip_derived_cl2109, plain,
% 106.85/14.64 (~ (((eqbreln) =>
% 106.85/14.64 (((funcext) =>
% 106.85/14.64 (((funcext2) =>
% 106.85/14.64 (((ap2apEq1) =>
% 106.85/14.64 (((ap2apEq2) =>
% 106.85/14.64 (((beta1) =>
% 106.85/14.64 (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTELcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTERcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2098])).
% 106.85/14.64 thf(zip_derived_cl2122, plain,
% 106.85/14.64 (~ (((funcext) =>
% 106.85/14.64 (((funcext2) =>
% 106.85/14.64 (((ap2apEq1) =>
% 106.85/14.64 (((ap2apEq2) =>
% 106.85/14.64 (((beta1) =>
% 106.85/14.64 (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTELcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTERcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2109])).
% 106.85/14.64 thf(zip_derived_cl2137, plain,
% 106.85/14.64 (~ (((funcext2) =>
% 106.85/14.64 (((ap2apEq1) =>
% 106.85/14.64 (((ap2apEq2) =>
% 106.85/14.64 (((beta1) =>
% 106.85/14.64 (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binintersectTERcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2122])).
% 106.85/14.64 thf(zip_derived_cl2153, plain,
% 106.85/14.64 (~ (((ap2apEq1) =>
% 106.85/14.64 (((ap2apEq2) =>
% 106.85/14.64 (((beta1) =>
% 106.85/14.64 (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2137])).
% 106.85/14.64 thf(zip_derived_cl2170, plain,
% 106.85/14.64 (~ (((ap2apEq2) =>
% 106.85/14.64 (((beta1) =>
% 106.85/14.64 (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2153])).
% 106.85/14.64 thf(zip_derived_cl2189, plain,
% 106.85/14.64 (~ (((beta1) =>
% 106.85/14.64 (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2170])).
% 106.85/14.64 thf(zip_derived_cl2207, plain,
% 106.85/14.64 (~ (((eta1) =>
% 106.85/14.64 (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 (((contrasubsetT2) =>
% 106.85/14.64 ((
% 106.85/14.64 (contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2189])).
% 106.85/14.64 thf(zip_derived_cl2223, plain,
% 106.85/14.64 (~ (((lam2lamEq) =>
% 106.85/14.64 (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 (((contrasubsetT2) =>
% 106.85/14.64 (((contrasubsetT3) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2207])).
% 106.85/14.64 thf(zip_derived_cl2239, plain,
% 106.85/14.64 (~ (((beta2) =>
% 106.85/14.64 (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 (((contrasubsetT2) =>
% 106.85/14.64 (((contrasubsetT3) =>
% 106.85/14.64 (((doubleComplementI1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2223])).
% 106.85/14.64 thf(zip_derived_cl2255, plain,
% 106.85/14.64 (~ (((eta2) =>
% 106.85/14.64 (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 (((contrasubsetT2) =>
% 106.85/14.64 (((contrasubsetT3) =>
% 106.85/14.64 (((doubleComplementI1) =>
% 106.85/14.64 (((doubleComplementE1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2239])).
% 106.85/14.64 thf(zip_derived_cl2272, plain,
% 106.85/14.64 (~ (((iffalseProp1) =>
% 106.85/14.64 (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 (((contrasubsetT2) =>
% 106.85/14.64 (((contrasubsetT3) =>
% 106.85/14.64 (((doubleComplementI1) =>
% 106.85/14.64 (((doubleComplementE1) =>
% 106.85/14.64 (((doubleComplementSub1) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2255])).
% 106.85/14.64 thf(zip_derived_cl2290, plain,
% 106.85/14.64 (~ (((iffalseProp2) =>
% 106.85/14.64 (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 (((contrasubsetT2) =>
% 106.85/14.64 (((contrasubsetT3) =>
% 106.85/14.64 (((doubleComplementI1) =>
% 106.85/14.64 (((doubleComplementE1) =>
% 106.85/14.64 (((doubleComplementSub1) =>
% 106.85/14.64 (((doubleComplementSub2) =>
% 106.85/14.64 ((
% 106.85/14.64 (doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2272])).
% 106.85/14.64 thf(zip_derived_cl2310, plain,
% 106.85/14.64 (~ (((iftrueProp1) =>
% 106.85/14.64 (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 (((contrasubsetT2) =>
% 106.85/14.64 (((contrasubsetT3) =>
% 106.85/14.64 (((doubleComplementI1) =>
% 106.85/14.64 (((doubleComplementE1) =>
% 106.85/14.64 (((doubleComplementSub1) =>
% 106.85/14.64 (((doubleComplementSub2) =>
% 106.85/14.64 (((doubleComplementEq) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2290])).
% 106.85/14.64 thf(zip_derived_cl2332, plain,
% 106.85/14.64 (~ (((iftrueProp2) =>
% 106.85/14.64 (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 (((contrasubsetT2) =>
% 106.85/14.64 (((contrasubsetT3) =>
% 106.85/14.64 (((doubleComplementI1) =>
% 106.85/14.64 (((doubleComplementE1) =>
% 106.85/14.64 (((doubleComplementSub1) =>
% 106.85/14.64 (((doubleComplementSub2) =>
% 106.85/14.64 (((doubleComplementEq) =>
% 106.85/14.64 (((complementTnotintersectT) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2310])).
% 106.85/14.64 thf(zip_derived_cl2348, plain,
% 106.85/14.64 (~ (((ifSingleton) =>
% 106.85/14.64 (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 (((contrasubsetT2) =>
% 106.85/14.64 (((contrasubsetT3) =>
% 106.85/14.64 (((doubleComplementI1) =>
% 106.85/14.64 (((doubleComplementE1) =>
% 106.85/14.64 (((doubleComplementSub1) =>
% 106.85/14.64 (((doubleComplementSub2) =>
% 106.85/14.64 (((doubleComplementEq) =>
% 106.85/14.64 (((complementTnotintersectT) =>
% 106.85/14.64 (((complementImpComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2332])).
% 106.85/14.64 thf(zip_derived_cl2364, plain,
% 106.85/14.64 (~ (((ifp) =>
% 106.85/14.64 (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 (((contrasubsetT2) =>
% 106.85/14.64 (((contrasubsetT3) =>
% 106.85/14.64 (((doubleComplementI1) =>
% 106.85/14.64 (((doubleComplementE1) =>
% 106.85/14.64 (((doubleComplementSub1) =>
% 106.85/14.64 (((doubleComplementSub2) =>
% 106.85/14.64 (((doubleComplementEq) =>
% 106.85/14.64 (((complementTnotintersectT) =>
% 106.85/14.64 (((complementImpComplementIntersect) =>
% 106.85/14.64 (((complementSubsetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2348])).
% 106.85/14.64 thf(zip_derived_cl2385, plain,
% 106.85/14.64 (~ (((theeq) =>
% 106.85/14.64 (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 (((contrasubsetT2) =>
% 106.85/14.64 (((contrasubsetT3) =>
% 106.85/14.64 (((doubleComplementI1) =>
% 106.85/14.64 (((doubleComplementE1) =>
% 106.85/14.64 (((doubleComplementSub1) =>
% 106.85/14.64 (((doubleComplementSub2) =>
% 106.85/14.64 (((doubleComplementEq) =>
% 106.85/14.64 (((complementTnotintersectT) =>
% 106.85/14.64 (((complementImpComplementIntersect) =>
% 106.85/14.64 (((complementSubsetComplementIntersect) =>
% 106.85/14.64 (((complementInPowersetComplementIntersect) =>
% 106.85/14.64 ((
% 106.85/14.64 (contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2364])).
% 106.85/14.64 thf(zip_derived_cl2403, plain,
% 106.85/14.64 (~ (((iftrue) =>
% 106.85/14.64 (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 (((contrasubsetT2) =>
% 106.85/14.64 (((contrasubsetT3) =>
% 106.85/14.64 (((doubleComplementI1) =>
% 106.85/14.64 (((doubleComplementE1) =>
% 106.85/14.64 (((doubleComplementSub1) =>
% 106.85/14.64 (((doubleComplementSub2) =>
% 106.85/14.64 (((doubleComplementEq) =>
% 106.85/14.64 (((complementTnotintersectT) =>
% 106.85/14.64 (((complementImpComplementIntersect) =>
% 106.85/14.64 (((complementSubsetComplementIntersect) =>
% 106.85/14.64 (((complementInPowersetComplementIntersect) =>
% 106.85/14.64 (((contraSubsetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule0) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz13rule4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_1) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_2) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_3) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_4) =>
% 106.85/14.64 ((
% 106.85/14.64 (woz1_5) =>
% 106.85/14.64 ((
% 106.85/14.64 (breln1all2) =>
% 106.85/14.64 ((
% 106.85/14.64 (!!) @ (
% 106.85/14.64 (('#B') @ (
% 106.85/14.64 !!) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#S') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 '#S') @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 =>))) @
% 106.85/14.64 (
% 106.85/14.64 (
% 106.85/14.64 ('#B') @ (
% 106.85/14.64 (
% 106.85/14.64 ('#C') @ in)) @
% 106.85/14.64 breln1Set)))))) @
% 106.85/14.64 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2385])).
% 106.85/14.64 thf(zip_derived_cl2419, plain,
% 106.85/14.64 (~ (((iffalse) =>
% 106.85/14.64 (((iftrueorfalse) =>
% 106.85/14.64 (((binintersectT_lem) =>
% 106.85/14.64 (((binunionT_lem) =>
% 106.85/14.64 (((powersetT_lem) =>
% 106.85/14.64 (((setminusT_lem) =>
% 106.85/14.64 (((complementT_lem) =>
% 106.85/14.64 (((setextT) =>
% 106.85/14.64 (((subsetTI) =>
% 106.85/14.64 (((powersetTI1) =>
% 106.85/14.64 (((powersetTE1) =>
% 106.85/14.64 (((complementTI1) =>
% 106.85/14.64 (((complementTE1) =>
% 106.85/14.64 (((binintersectTELcontra) =>
% 106.85/14.64 (((binintersectTERcontra) =>
% 106.85/14.64 (((contrasubsetT) =>
% 106.85/14.64 (((contrasubsetT1) =>
% 106.85/14.64 (((contrasubsetT2) =>
% 106.85/14.64 (((contrasubsetT3) =>
% 106.85/14.64 (((doubleComplementI1) =>
% 106.85/14.64 (((doubleComplementE1) =>
% 106.85/14.64 (((doubleComplementSub1) =>
% 106.85/14.64 (((doubleComplementSub2) =>
% 106.85/14.64 (((doubleComplementEq) =>
% 106.85/14.64 (((complementTnotintersectT) =>
% 106.85/14.64 (((complementImpComplementIntersect) =>
% 106.85/14.64 (((complementSubsetComplementIntersect) =>
% 106.85/14.64 (((complementInPowersetComplementIntersect) =>
% 106.85/14.64 (((contraSubsetComplement) =>
% 106.85/14.64 (((complementTcontraSubset) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTILcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTIRcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInUnion2) =>
% 106.85/14.64 ((
% 106.85/14.64 (inIntersectImpInIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (intersectInPowersetIntersectUnions) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpNotIn1) =>
% 106.85/14.64 ((
% 106.85/14.64 (inComplementUnionImpInComplement1) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTE) =>
% 106.85/14.64 ((
% 106.85/14.64 (binunionTEcontra) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a1) =>
% 106.85/14.64 ((
% 106.85/14.64 (complementUnionInPowersetComplement) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan2a2) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1a) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1b) =>
% 106.85/14.64 ((
% 106.85/14.64 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2403])).
% 106.85/14.65 thf(zip_derived_cl2438, plain,
% 106.85/14.65 (~ (((iftrueorfalse) =>
% 106.85/14.65 (((binintersectT_lem) =>
% 106.85/14.65 (((binunionT_lem) =>
% 106.85/14.65 (((powersetT_lem) =>
% 106.85/14.65 (((setminusT_lem) =>
% 106.85/14.65 (((complementT_lem) =>
% 106.85/14.65 (((setextT) =>
% 106.85/14.65 (((subsetTI) =>
% 106.85/14.65 (((powersetTI1) =>
% 106.85/14.65 (((powersetTE1) =>
% 106.85/14.65 (((complementTI1) =>
% 106.85/14.65 (((complementTE1) =>
% 106.85/14.65 (((binintersectTELcontra) =>
% 106.85/14.65 (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTIRcontra) =>
% 106.85/14.65 ((
% 106.85/14.65 (inIntersectImpInUnion) =>
% 106.85/14.65 ((
% 106.85/14.65 (inIntersectImpInUnion2) =>
% 106.85/14.65 ((
% 106.85/14.65 (inIntersectImpInIntersectUnions) =>
% 106.85/14.65 ((
% 106.85/14.65 (intersectInPowersetIntersectUnions) =>
% 106.85/14.65 ((
% 106.85/14.65 (inComplementUnionImpNotIn1) =>
% 106.85/14.65 ((
% 106.85/14.65 (inComplementUnionImpInComplement1) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTE) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTEcontra) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a1) =>
% 106.85/14.65 ((
% 106.85/14.65 (complementUnionInPowersetComplement) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2419])).
% 106.85/14.65 thf(zip_derived_cl2453, plain,
% 106.85/14.65 (~ (((binintersectT_lem) =>
% 106.85/14.65 (((binunionT_lem) =>
% 106.85/14.65 (((powersetT_lem) =>
% 106.85/14.65 (((setminusT_lem) =>
% 106.85/14.65 (((complementT_lem) =>
% 106.85/14.65 (((setextT) =>
% 106.85/14.65 (((subsetTI) =>
% 106.85/14.65 (((powersetTI1) =>
% 106.85/14.65 (((powersetTE1) =>
% 106.85/14.65 (((complementTI1) =>
% 106.85/14.65 (((complementTE1) =>
% 106.85/14.65 (((binintersectTELcontra) =>
% 106.85/14.65 (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 ((
% 106.85/14.65 (inIntersectImpInUnion) =>
% 106.85/14.65 ((
% 106.85/14.65 (inIntersectImpInUnion2) =>
% 106.85/14.65 ((
% 106.85/14.65 (inIntersectImpInIntersectUnions) =>
% 106.85/14.65 ((
% 106.85/14.65 (intersectInPowersetIntersectUnions) =>
% 106.85/14.65 ((
% 106.85/14.65 (inComplementUnionImpNotIn1) =>
% 106.85/14.65 ((
% 106.85/14.65 (inComplementUnionImpInComplement1) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTE) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTEcontra) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a1) =>
% 106.85/14.65 ((
% 106.85/14.65 (complementUnionInPowersetComplement) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2438])).
% 106.85/14.65 thf(zip_derived_cl2465, plain,
% 106.85/14.65 (~ (((binunionT_lem) =>
% 106.85/14.65 (((powersetT_lem) =>
% 106.85/14.65 (((setminusT_lem) =>
% 106.85/14.65 (((complementT_lem) =>
% 106.85/14.65 (((setextT) =>
% 106.85/14.65 (((subsetTI) =>
% 106.85/14.65 (((powersetTI1) =>
% 106.85/14.65 (((powersetTE1) =>
% 106.85/14.65 (((complementTI1) =>
% 106.85/14.65 (((complementTE1) =>
% 106.85/14.65 (((binintersectTELcontra) =>
% 106.85/14.65 (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 ((
% 106.85/14.65 (inIntersectImpInUnion2) =>
% 106.85/14.65 ((
% 106.85/14.65 (inIntersectImpInIntersectUnions) =>
% 106.85/14.65 ((
% 106.85/14.65 (intersectInPowersetIntersectUnions) =>
% 106.85/14.65 ((
% 106.85/14.65 (inComplementUnionImpNotIn1) =>
% 106.85/14.65 ((
% 106.85/14.65 (inComplementUnionImpInComplement1) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTE) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTEcontra) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a1) =>
% 106.85/14.65 ((
% 106.85/14.65 (complementUnionInPowersetComplement) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2453])).
% 106.85/14.65 thf(zip_derived_cl2476, plain,
% 106.85/14.65 (~ (((powersetT_lem) =>
% 106.85/14.65 (((setminusT_lem) =>
% 106.85/14.65 (((complementT_lem) =>
% 106.85/14.65 (((setextT) =>
% 106.85/14.65 (((subsetTI) =>
% 106.85/14.65 (((powersetTI1) =>
% 106.85/14.65 (((powersetTE1) =>
% 106.85/14.65 (((complementTI1) =>
% 106.85/14.65 (((complementTE1) =>
% 106.85/14.65 (((binintersectTELcontra) =>
% 106.85/14.65 (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 ((
% 106.85/14.65 (inIntersectImpInIntersectUnions) =>
% 106.85/14.65 ((
% 106.85/14.65 (intersectInPowersetIntersectUnions) =>
% 106.85/14.65 ((
% 106.85/14.65 (inComplementUnionImpNotIn1) =>
% 106.85/14.65 ((
% 106.85/14.65 (inComplementUnionImpInComplement1) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTE) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTEcontra) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a1) =>
% 106.85/14.65 ((
% 106.85/14.65 (complementUnionInPowersetComplement) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2465])).
% 106.85/14.65 thf(zip_derived_cl2487, plain,
% 106.85/14.65 (~ (((setminusT_lem) =>
% 106.85/14.65 (((complementT_lem) =>
% 106.85/14.65 (((setextT) =>
% 106.85/14.65 (((subsetTI) =>
% 106.85/14.65 (((powersetTI1) =>
% 106.85/14.65 (((powersetTE1) =>
% 106.85/14.65 (((complementTI1) =>
% 106.85/14.65 (((complementTE1) =>
% 106.85/14.65 (((binintersectTELcontra) =>
% 106.85/14.65 (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 ((
% 106.85/14.65 (intersectInPowersetIntersectUnions) =>
% 106.85/14.65 ((
% 106.85/14.65 (inComplementUnionImpNotIn1) =>
% 106.85/14.65 ((
% 106.85/14.65 (inComplementUnionImpInComplement1) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTE) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTEcontra) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a1) =>
% 106.85/14.65 ((
% 106.85/14.65 (complementUnionInPowersetComplement) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2476])).
% 106.85/14.65 thf(zip_derived_cl2496, plain,
% 106.85/14.65 (~ (((complementT_lem) =>
% 106.85/14.65 (((setextT) =>
% 106.85/14.65 (((subsetTI) =>
% 106.85/14.65 (((powersetTI1) =>
% 106.85/14.65 (((powersetTE1) =>
% 106.85/14.65 (((complementTI1) =>
% 106.85/14.65 (((complementTE1) =>
% 106.85/14.65 (((binintersectTELcontra) =>
% 106.85/14.65 (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 ((
% 106.85/14.65 (inComplementUnionImpNotIn1) =>
% 106.85/14.65 ((
% 106.85/14.65 (inComplementUnionImpInComplement1) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTE) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTEcontra) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a1) =>
% 106.85/14.65 ((
% 106.85/14.65 (complementUnionInPowersetComplement) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2487])).
% 106.85/14.65 thf(zip_derived_cl2506, plain,
% 106.85/14.65 (~ (((setextT) =>
% 106.85/14.65 (((subsetTI) =>
% 106.85/14.65 (((powersetTI1) =>
% 106.85/14.65 (((powersetTE1) =>
% 106.85/14.65 (((complementTI1) =>
% 106.85/14.65 (((complementTE1) =>
% 106.85/14.65 (((binintersectTELcontra) =>
% 106.85/14.65 (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 ((
% 106.85/14.65 (inComplementUnionImpInComplement1) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTE) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTEcontra) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a1) =>
% 106.85/14.65 ((
% 106.85/14.65 (complementUnionInPowersetComplement) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2496])).
% 106.85/14.65 thf(zip_derived_cl2517, plain,
% 106.85/14.65 (~ (((subsetTI) =>
% 106.85/14.65 (((powersetTI1) =>
% 106.85/14.65 (((powersetTE1) =>
% 106.85/14.65 (((complementTI1) =>
% 106.85/14.65 (((complementTE1) =>
% 106.85/14.65 (((binintersectTELcontra) =>
% 106.85/14.65 (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTE) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTEcontra) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a1) =>
% 106.85/14.65 ((
% 106.85/14.65 (complementUnionInPowersetComplement) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2506])).
% 106.85/14.65 thf(zip_derived_cl2529, plain,
% 106.85/14.65 (~ (((powersetTI1) =>
% 106.85/14.65 (((powersetTE1) =>
% 106.85/14.65 (((complementTI1) =>
% 106.85/14.65 (((complementTE1) =>
% 106.85/14.65 (((binintersectTELcontra) =>
% 106.85/14.65 (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 ((
% 106.85/14.65 (binunionTEcontra) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a1) =>
% 106.85/14.65 ((
% 106.85/14.65 (complementUnionInPowersetComplement) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2517])).
% 106.85/14.65 thf(zip_derived_cl2538, plain,
% 106.85/14.65 (~ (((powersetTE1) =>
% 106.85/14.65 (((complementTI1) =>
% 106.85/14.65 (((complementTE1) =>
% 106.85/14.65 (((binintersectTELcontra) =>
% 106.85/14.65 (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a1) =>
% 106.85/14.65 ((
% 106.85/14.65 (complementUnionInPowersetComplement) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2529])).
% 106.85/14.65 thf(zip_derived_cl2546, plain,
% 106.85/14.65 (~ (((complementTI1) =>
% 106.85/14.65 (((complementTE1) =>
% 106.85/14.65 (((binintersectTELcontra) =>
% 106.85/14.65 (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 ((
% 106.85/14.65 (complementUnionInPowersetComplement) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2538])).
% 106.85/14.65 thf(zip_derived_cl2554, plain,
% 106.85/14.65 (~ (((complementTE1) =>
% 106.85/14.65 (((binintersectTELcontra) =>
% 106.85/14.65 (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2546])).
% 106.85/14.65 thf(zip_derived_cl2562, plain,
% 106.85/14.65 (~ (((binintersectTELcontra) =>
% 106.85/14.65 (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2554])).
% 106.85/14.65 thf(zip_derived_cl2571, plain,
% 106.85/14.65 (~ (((binintersectTERcontra) =>
% 106.85/14.65 (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2562])).
% 106.85/14.65 thf(zip_derived_cl2581, plain,
% 106.85/14.65 (~ (((contrasubsetT) =>
% 106.85/14.65 (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2571])).
% 106.85/14.65 thf(zip_derived_cl2592, plain,
% 106.85/14.65 (~ (((contrasubsetT1) =>
% 106.85/14.65 (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2581])).
% 106.85/14.65 thf(zip_derived_cl2605, plain,
% 106.85/14.65 (~ (((contrasubsetT2) =>
% 106.85/14.65 (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2592])).
% 106.85/14.65 thf(zip_derived_cl2621, plain,
% 106.85/14.65 (~ (((contrasubsetT3) =>
% 106.85/14.65 (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2605])).
% 106.85/14.65 thf(zip_derived_cl2640, plain,
% 106.85/14.65 (~ (((doubleComplementI1) =>
% 106.85/14.65 (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 ((
% 106.85/14.65 (demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2621])).
% 106.85/14.65 thf(zip_derived_cl2659, plain,
% 106.85/14.65 (~ (((doubleComplementE1) =>
% 106.85/14.65 (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2640])).
% 106.85/14.65 thf(zip_derived_cl2676, plain,
% 106.85/14.65 (~ (((doubleComplementSub1) =>
% 106.85/14.65 (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2659])).
% 106.85/14.65 thf(zip_derived_cl2691, plain,
% 106.85/14.65 (~ (((doubleComplementSub2) =>
% 106.85/14.65 (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2676])).
% 106.85/14.65 thf(zip_derived_cl2703, plain,
% 106.85/14.65 (~ (((doubleComplementEq) =>
% 106.85/14.65 (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2691])).
% 106.85/14.65 thf(zip_derived_cl2715, plain,
% 106.85/14.65 (~ (((complementTnotintersectT) =>
% 106.85/14.65 (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2703])).
% 106.85/14.65 thf(zip_derived_cl2727, plain,
% 106.85/14.65 (~ (((complementImpComplementIntersect) =>
% 106.85/14.65 (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2715])).
% 106.85/14.65 thf(zip_derived_cl2739, plain,
% 106.85/14.65 (~ (((complementSubsetComplementIntersect) =>
% 106.85/14.65 (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2727])).
% 106.85/14.65 thf(zip_derived_cl2749, plain,
% 106.85/14.65 (~ (((complementInPowersetComplementIntersect) =>
% 106.85/14.65 (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2739])).
% 106.85/14.65 thf(zip_derived_cl2757, plain,
% 106.85/14.65 (~ (((contraSubsetComplement) =>
% 106.85/14.65 (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2749])).
% 106.85/14.65 thf(zip_derived_cl2765, plain,
% 106.85/14.65 (~ (((complementTcontraSubset) =>
% 106.85/14.65 (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 ((
% 106.85/14.65 (woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2757])).
% 106.85/14.65 thf(zip_derived_cl2773, plain,
% 106.85/14.65 (~ (((binunionTILcontra) =>
% 106.85/14.65 (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 ((
% 106.85/14.65 (breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2765])).
% 106.85/14.65 thf(zip_derived_cl2782, plain,
% 106.85/14.65 (~ (((binunionTIRcontra) =>
% 106.85/14.65 (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 ((
% 106.85/14.65 (!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2773])).
% 106.85/14.65 thf(zip_derived_cl2792, plain,
% 106.85/14.65 (~ (((inIntersectImpInUnion) =>
% 106.85/14.65 (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2782])).
% 106.85/14.65 thf(zip_derived_cl2803, plain,
% 106.85/14.65 (~ (((inIntersectImpInUnion2) =>
% 106.85/14.65 (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 ((('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2792])).
% 106.85/14.65 thf(zip_derived_cl2814, plain,
% 106.85/14.65 (~ (((inIntersectImpInIntersectUnions) =>
% 106.85/14.65 (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 ((('#S') @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 ((
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2803])).
% 106.85/14.65 thf(zip_derived_cl2824, plain,
% 106.85/14.65 (~ (((intersectInPowersetIntersectUnions) =>
% 106.85/14.65 (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 ((('#S') @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 ((
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2814])).
% 106.85/14.65 thf(zip_derived_cl2834, plain,
% 106.85/14.65 (~ (((inComplementUnionImpNotIn1) =>
% 106.85/14.65 (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2824])).
% 106.85/14.65 thf(zip_derived_cl2845, plain,
% 106.85/14.65 (~ (((inComplementUnionImpInComplement1) =>
% 106.85/14.65 (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 ((('#S') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2834])).
% 106.85/14.65 thf(zip_derived_cl2856, plain,
% 106.85/14.65 (~ (((binunionTE) =>
% 106.85/14.65 (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 ((('#S') @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 ((
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2845])).
% 106.85/14.65 thf(zip_derived_cl2868, plain,
% 106.85/14.65 (~ (((binunionTEcontra) =>
% 106.85/14.65 (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 ((('#S') @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 ((
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2856])).
% 106.85/14.65 thf(zip_derived_cl2880, plain,
% 106.85/14.65 (~ (((demorgan2a1) =>
% 106.85/14.65 (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (
% 106.85/14.65 !!) @
% 106.85/14.65 ((('#S') @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2868])).
% 106.85/14.65 thf(zip_derived_cl2892, plain,
% 106.85/14.65 (~ (((complementUnionInPowersetComplement) =>
% 106.85/14.65 (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2880])).
% 106.85/14.65 thf(zip_derived_cl2904, plain,
% 106.85/14.65 (~ (((demorgan2a2) =>
% 106.85/14.65 (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2892])).
% 106.85/14.65 thf(zip_derived_cl2917, plain,
% 106.85/14.65 (~ (((demorgan1a) =>
% 106.85/14.65 (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 ((
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 (
% 106.85/14.65 (
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2904])).
% 106.85/14.65 thf(zip_derived_cl2931, plain,
% 106.85/14.65 (~ (((demorgan1b) =>
% 106.85/14.65 (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 ((
% 106.85/14.65 ('#B') @ (
% 106.85/14.65 (
% 106.85/14.65 ('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2917])).
% 106.85/14.65 thf(zip_derived_cl2944, plain,
% 106.85/14.65 (~ (((demorgan1) =>
% 106.85/14.65 (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2931])).
% 106.85/14.65 thf(zip_derived_cl2957, plain,
% 106.85/14.65 (~ (((demorgan2a) =>
% 106.85/14.65 (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2944])).
% 106.85/14.65 thf(zip_derived_cl2969, plain,
% 106.85/14.65 (~ (((demorgan2b2) =>
% 106.85/14.65 (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ (
% 106.85/14.65 '#S') @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2957])).
% 106.85/14.65 thf(zip_derived_cl2981, plain,
% 106.85/14.65 (~ (((demorgan2b) =>
% 106.85/14.65 (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2969])).
% 106.85/14.65 thf(zip_derived_cl2993, plain,
% 106.85/14.65 (~ (((demorgan2) =>
% 106.85/14.65 (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 ((('#B') @ (
% 106.85/14.65 (('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2981])).
% 106.85/14.65 thf(zip_derived_cl3006, plain,
% 106.85/14.65 (~ (((woz13rule0) =>
% 106.85/14.65 (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (
% 106.85/14.65 =>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2993])).
% 106.85/14.65 thf(zip_derived_cl3019, plain,
% 106.85/14.65 (~ (((woz13rule1) =>
% 106.85/14.65 (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3006])).
% 106.85/14.65 thf(zip_derived_cl3033, plain,
% 106.85/14.65 (~ (((woz13rule2) =>
% 106.85/14.65 (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3019])).
% 106.85/14.65 thf(zip_derived_cl3049, plain,
% 106.85/14.65 (~ (((woz13rule3) =>
% 106.85/14.65 (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3033])).
% 106.85/14.65 thf(zip_derived_cl3062, plain,
% 106.85/14.65 (~ (((woz13rule4) =>
% 106.85/14.65 (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3049])).
% 106.85/14.65 thf(zip_derived_cl3073, plain,
% 106.85/14.65 (~ (((woz1_1) =>
% 106.85/14.65 (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3062])).
% 106.85/14.65 thf(zip_derived_cl3085, plain,
% 106.85/14.65 (~ (((woz1_2) =>
% 106.85/14.65 (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3073])).
% 106.85/14.65 thf(zip_derived_cl3097, plain,
% 106.85/14.65 (~ (((woz1_3) =>
% 106.85/14.65 (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @
% 106.85/14.65 breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3085])).
% 106.85/14.65 thf(zip_derived_cl3109, plain,
% 106.85/14.65 (~ (((woz1_4) =>
% 106.85/14.65 (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @ breln1Set)))))) @
% 106.85/14.65 breln1))))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3097])).
% 106.85/14.65 thf(zip_derived_cl3120, plain,
% 106.85/14.65 (~ (((woz1_5) =>
% 106.85/14.65 (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @ breln1Set)))))) @
% 106.85/14.65 breln1))))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3109])).
% 106.85/14.65 thf(zip_derived_cl3131, plain,
% 106.85/14.65 (~ (((breln1all2) =>
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @ breln1Set)))))) @
% 106.85/14.65 breln1))))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3120])).
% 106.85/14.65 thf(zip_derived_cl3143, plain,
% 106.85/14.65 (~ (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @ breln1Set)))))) @
% 106.85/14.65 breln1))))))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3131])).
% 106.85/14.65 thf(zip_derived_cl3154, plain,
% 106.85/14.65 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 106.85/14.65 ((('#C') @ in @ (breln1Set @ '#sk42'))))) @
% 106.85/14.65 (breln1 @ '#sk42')))))),
% 106.85/14.65 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3143])).
% 106.85/14.65 thf(breln1Set, axiom,(( breln1Set @ (X0)) =
% 106.85/14.65 ((dsetconstr @ (powerset @ (cartprod @ X0 @ X0)) @
% 106.85/14.65 (^[Y0 : $i]: (breln1 @ X0 @ Y0)))))).
% 106.85/14.65 thf('4', plain,
% 106.85/14.65 (![X0:$i]:
% 106.85/14.65 ( ( breln1Set @ X0 ) =
% 106.85/14.65 ( dsetconstr @
% 106.85/14.65 ( powerset @ ( cartprod @ X0 @ X0 ) ) @
% 106.85/14.65 ( ^[V_1:$i]: ( breln1 @ X0 @ V_1 ) ) ) )),
% 106.85/14.65 define([status(thm)])).
% 106.85/14.65 thf(zip_derived_cl3163, plain,
% 106.85/14.65 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 106.85/14.65 ((('#C') @ in @
% 106.85/14.65 (dsetconstr @
% 106.85/14.65 (powerset @ (cartprod @ '#sk42' @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')))))) @
% 106.85/14.65 (breln1 @ '#sk42')))))),
% 106.85/14.65 inference('rw', [status(thm)], [zip_derived_cl3154, '4'])).
% 106.85/14.65 thf(zip_derived_cl3164, plain,
% 106.85/14.65 (~ (((in @
% 106.85/14.65 ('#sk21' @
% 106.85/14.65 (dsetconstr @ (powerset @ (cartprod @ '#sk42' @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')) @
% 106.85/14.65 (dsetconstr @ (powerset @ (cartprod @ '#sk42' @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42'))) =>
% 106.85/14.65 (breln1 @ '#sk42' @
% 106.85/14.65 ('#sk21' @
% 106.85/14.65 (dsetconstr @ (powerset @ (cartprod @ '#sk42' @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')))))),
% 106.85/14.65 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3163])).
% 106.85/14.65 thf(breln, axiom,(( breln @ (X1)@ (X2)@ (X0)) =
% 106.85/14.65 ((subset @ X0 @ (cartprod @ X1 @ X2))))).
% 106.85/14.65 thf('5', plain,
% 106.85/14.65 (![X2:$i,X1:$i,X0:$i]:
% 106.85/14.65 ( ( breln @ X1 @ X2 @ X0 ) = ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) )),
% 106.85/14.65 define([status(thm)])).
% 106.85/14.65 thf(breln1, axiom,(( breln1 @ (X0)@ (X1)) = ((breln @ X0 @ X0 @ X1)))).
% 106.85/14.65 thf('6', plain,
% 106.85/14.65 (![X1:$i,X0:$i]: ( ( breln1 @ X0 @ X1 ) = ( breln @ X0 @ X0 @ X1 ) )),
% 106.85/14.65 define([status(thm)])).
% 106.85/14.65 thf(zip_derived_cl3172, plain,
% 106.85/14.65 (~ (((in @
% 106.85/14.65 ('#sk21' @
% 106.85/14.65 (dsetconstr @ (powerset @ (cartprod @ '#sk42' @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')) @
% 106.85/14.65 (dsetconstr @ (powerset @ (cartprod @ '#sk42' @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42'))) =>
% 106.85/14.65 (subset @
% 106.85/14.65 ('#sk21' @
% 106.85/14.65 (dsetconstr @ (powerset @ (cartprod @ '#sk42' @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')) @
% 106.85/14.65 (cartprod @ '#sk42' @ '#sk42'))))),
% 106.85/14.65 inference('rw', [status(thm)], [zip_derived_cl3164, '5', '6'])).
% 106.85/14.65 thf(zip_derived_cl3174, plain,
% 106.85/14.65 (~ (subset @
% 106.85/14.65 ('#sk21' @
% 106.85/14.65 (dsetconstr @ (powerset @ (cartprod @ '#sk42' @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')) @
% 106.85/14.65 (cartprod @ '#sk42' @ '#sk42'))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3172])).
% 106.85/14.65 thf(zip_derived_cl3173, plain,
% 106.85/14.65 ( (in @
% 106.85/14.65 ('#sk21' @
% 106.85/14.65 (dsetconstr @ (powerset @ (cartprod @ '#sk42' @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')) @
% 106.85/14.65 (dsetconstr @ (powerset @ (cartprod @ '#sk42' @ '#sk42')) @
% 106.85/14.65 (breln1 @ '#sk42')))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3172])).
% 106.85/14.65 thf(zip_derived_cl1066, plain, ( (powersetE1)),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1055])).
% 106.85/14.65 thf(powersetE1, axiom, (powersetE1) =>
% 106.85/14.65 ((((!!) @ (^[Y0 : $i]:
% 106.85/14.65 (((!!) @ (^[Y1 : $i]:
% 106.85/14.65 (((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @
% 106.85/14.65 Y0)))))))))
% 106.85/14.65 = ($true))).
% 106.85/14.65 thf('7', plain,
% 106.85/14.65 (( powersetE1 ) <=>
% 106.85/14.65 ( ![X5:$i,X7:$i]:
% 106.85/14.65 ( ( in @ X7 @ ( powerset @ X5 ) ) => ( subset @ X7 @ X5 ) ) )),
% 106.85/14.65 inference('rw.lit', [status(esa)], [powersetE1])).
% 106.85/14.65 thf(zip_derived_cl1072, plain,
% 106.85/14.65 ( (((!!) @ (^[Y0 : $i]:
% 106.85/14.65 (((!!) @ (^[Y1 : $i]:
% 106.85/14.65 (((in @ Y1 @ (powerset @ Y0)) => (subset @
% 106.85/14.65 Y1 @ Y0)))))))))),
% 106.85/14.65 inference('rw_clause', [status(thm)], [zip_derived_cl1066, '7'])).
% 106.85/14.65 thf(zip_derived_cl1078, plain,
% 106.85/14.65 ( (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @ powerset)))))) @
% 106.85/14.65 ((('#C') @ subset))))))))),
% 106.85/14.65 inference('comb-normalize', [status(thm)], [zip_derived_cl1072])).
% 106.85/14.65 thf(zip_derived_cl1079, plain,
% 106.85/14.65 (![X2 : $i]:
% 106.85/14.65 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 106.85/14.65 ((('#C') @ in @ (powerset @ X2))))) @
% 106.85/14.65 ((('#C') @ subset @ X2))))))),
% 106.85/14.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1078])).
% 106.85/14.65 thf(zip_derived_cl1085, plain,
% 106.85/14.65 (![X2 : $i, X4 : $i]:
% 106.85/14.65 (((in @ X4 @ (powerset @ X2)) => (subset @ X4 @ X2)))),
% 106.85/14.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1079])).
% 106.85/14.65 thf(zip_derived_cl1091, plain,
% 106.85/14.65 (![X2 : $i, X4 : $i]:
% 106.85/14.65 (~ (in @ X4 @ (powerset @ X2)) | (subset @ X4 @ X2))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1085])).
% 106.85/14.65 thf(zip_derived_cl88, plain, ( (dsetconstrEL)),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 106.85/14.65 thf(dsetconstrEL, axiom, (dsetconstrEL) =>
% 106.85/14.65 ((((!!) @ (^[Y0 : $i]:
% 106.85/14.65 (((!!) @ (^[Y1 : $i > $o]:
% 106.85/14.65 (((!!) @ (^[Y2 : $i]:
% 106.85/14.65 (((in @ Y2 @
% 106.85/14.65 (dsetconstr @ Y0 @
% 106.85/14.65 (^[Y3 : $i]: (Y1 @ Y3)))) =>
% 106.85/14.65 (in @ Y2 @ Y0))))))))))))
% 106.85/14.65 = ($true))).
% 106.85/14.65 thf('8', plain,
% 106.85/14.65 (( dsetconstrEL ) <=>
% 106.85/14.65 ( ![X5:$i,X7:( $i > $o ),X9:$i]:
% 106.85/14.65 ( ( in @ X9 @ ( dsetconstr @ X5 @ ( ^[V_1:$i]: ( X7 @ V_1 ) ) ) ) =>
% 106.85/14.65 ( in @ X9 @ X5 ) ) )),
% 106.85/14.65 inference('rw.lit', [status(esa)], [dsetconstrEL])).
% 106.85/14.65 thf(zip_derived_cl103, plain,
% 106.85/14.65 ( (((!!) @ (^[Y0 : $i]:
% 106.85/14.65 (((!!) @ (^[Y1 : $i > $o]:
% 106.85/14.65 (((!!) @ (^[Y2 : $i]:
% 106.85/14.65 (((in @ Y2 @
% 106.85/14.65 (dsetconstr @ Y0 @
% 106.85/14.65 (^[Y3 : $i]: (Y1 @ Y3)))) =>
% 106.85/14.65 (in @ Y2 @ Y0))))))))))))),
% 106.85/14.65 inference('rw_clause', [status(thm)], [zip_derived_cl88, '8'])).
% 106.85/14.65 thf(zip_derived_cl119, plain,
% 106.85/14.65 ( (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#B') @ ((('#B') @ (!!))) @
% 106.85/14.65 ((('#S') @ ((('#B') @ ('#C') @
% 106.85/14.65 ((('#B') @ ((('#B') @ ('#S'))) @
% 106.85/14.65 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @
% 106.85/14.65 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 106.85/14.65 dsetconstr)))))))) @
% 106.85/14.65 ((('#C') @ in))))))))))),
% 106.85/14.65 inference('comb-normalize', [status(thm)], [zip_derived_cl103])).
% 106.85/14.65 thf(zip_derived_cl120, plain,
% 106.85/14.65 (![X2 : $i]:
% 106.85/14.65 (((!!) @ ((('#B') @ (!!) @
% 106.85/14.65 ((('#C') @ ((('#B') @ ('#S') @
% 106.85/14.65 ((('#B') @ ((('#B') @ (=>))) @
% 106.85/14.65 ((('#B') @ ((('#C') @ in)) @
% 106.85/14.65 (dsetconstr @ X2))))))) @
% 106.85/14.65 ((('#C') @ in @ X2))))))))),
% 106.85/14.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl119])).
% 106.85/14.65 thf(zip_derived_cl137, plain,
% 106.85/14.65 (![X2 : $i, X4 : $i > $o]:
% 106.85/14.65 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 106.85/14.65 ((('#C') @ in @ (dsetconstr @ X2 @ X4))))) @
% 106.85/14.65 ((('#C') @ in @ X2))))))),
% 106.85/14.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl120])).
% 106.85/14.65 thf(zip_derived_cl152, plain,
% 106.85/14.65 (![X2 : $i, X4 : $i > $o, X6 : $i]:
% 106.85/14.65 (((in @ X6 @ (dsetconstr @ X2 @ X4)) => (in @ X6 @ X2)))),
% 106.85/14.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl137])).
% 106.85/14.65 thf(zip_derived_cl167, plain,
% 106.85/14.65 (![X2 : $i, X4 : $i > $o, X6 : $i]:
% 106.85/14.65 (~ (in @ X6 @ (dsetconstr @ X2 @ X4)) | (in @ X6 @ X2))),
% 106.85/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl152])).
% 106.85/14.65 thf(zip_derived_cl3274, plain, ($false),
% 106.85/14.65 inference('eprover', [status(thm)],
% 106.85/14.65 [zip_derived_cl3174, zip_derived_cl3173, zip_derived_cl1091,
% 106.85/14.65 zip_derived_cl167])).
% 106.85/14.65
% 106.85/14.65 % SZS output end Refutation
% 106.85/14.65
% 106.85/14.65
% 106.85/14.65 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 106.85/14.65 % Terminating...
% 107.18/14.78 % Runner terminated.
% 107.18/14.80 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------